2 %%Title: C:\texinput\facility\stocproc.dvi
3 %%Creator: DVIPSONE (32) 2.0.5 1997 Mar 9 21:07:44 SN 603
4 %%CreationDate: 1998 Jun 12 01:04:55
5 %%BoundingBox: 72 81 540 720
8 %%DocumentSuppliedResources: font cmr17 cmmi12 cmr12 cmsy8 cmbx10 cmr10
9 %%+ font cmmi10 cmti10 cmmi7 cmr7 cmsy6 cmr8 cmtt8 cmsy10 cmex10 cmsy7
10 %%+ font cmsy5 cmmi5 cmr5
11 %%+ procset dvipream 2 0
12 %%Copyright: (C) 1990--1997, Y&Y, Inc. All rights reserved. (508) 371-3286
15 % C:\yandy\dvipsone\DVIPSONE -v -d=facility.ps C:\texinput\facility\stocproc.dvi
16 % TeX output 1998.05.13:0014
19 %%BeginResource: procset dvipream 2 0
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237 /textext[/Gamma/Delta/Theta/Lambda/Xi/Pi/Sigma/Upsilon
238 /Phi/Psi/Omega/ff/fi/fl/ffi/ffl
239 /dotlessi/dotlessj/grave/acute/caron/breve/macron/ring
240 /cedilla/germandbls/ae/oe/oslash/AE/OE/Oslash
241 /suppress/exclam/quotedblright/numbersign/dollar/percent/ampersand/quoteright
242 /parenleft/parenright/asterisk/plus/comma/hyphen/period/slash
243 /zero/one/two/three/four/five/six/seven
244 /eight/nine/colon/semicolon/exclamdown/equal/questiondown/question
248 /X/Y/Z/bracketleft/quotedblleft/bracketright/circumflex/dotaccent
249 /quoteleft/a/b/c/d/e/f/g
252 /x/y/z/endash/emdash/hungarumlaut/tilde/dieresis
257 /TEXNANSI[ n n n n/fraction/dotaccent/hungarumlaut/ogonek
258 /fl/fraction n/ff/fi/fl/ffi/ffl
259 /dotlessi/dotlessj/grave/acute/caron/breve/macron/ring
260 /cedilla/germandbls/ae/oe/oslash/AE/OE/Oslash
261 /space/exclam/quotedbl/numbersign/dollar/percent/ampersand/quoteright
262 /parenleft/parenright/asterisk/plus/comma/hyphen/period/slash
263 /zero/one/two/three/four/five/six/seven
264 /eight/nine/colon/semicolon/less/equal/greater/question
268 /X/Y/Z/bracketleft/backslash/bracketright/circumflex/underscore
269 /quoteleft/a/b/c/d/e/f/g
272 /x/y/z/braceleft/bar/braceright/tilde/dieresis
273 /Lslash/quotesingle/quotesinglbase/florin/quotedblbase/ellipsis/dagger/daggerdbl
274 /circumflex/perthousand/Scaron/guilsinglleft/OE/Zcaron/asciicircum/minus
275 /lslash/quoteleft/quoteright/quotedblleft/quotedblright/bullet/endash/emdash
276 /tilde/trademark/scaron/guilsinglright/oe/zcaron/asciitilde/Ydieresis
277 /space/exclamdown/cent/sterling/currency/yen/brokenbar/section
278 /dieresis/copyright/ordfeminine/guillemotleft/logicalnot/hyphen/registered/macron
279 /degree/plusminus/twosuperior/threesuperior/acute/mu/paragraph/periodcentered
280 /cedilla/onesuperior/ordmasculine/guillemotright/onequarter/onehalf/threequarters/questiondown
281 /Agrave/Aacute/Acircumflex/Atilde/Adieresis/Aring/AE/Ccedilla
282 /Egrave/Eacute/Ecircumflex/Edieresis/Igrave/Iacute/Icircumflex/Idieresis
283 /Eth/Ntilde/Ograve/Oacute/Ocircumflex/Otilde/Odieresis/multiply
284 /Oslash/Ugrave/Uacute/Ucircumflex/Udieresis/Yacute/Thorn/germandbls
285 /agrave/aacute/acircumflex/atilde/adieresis/aring/ae/ccedilla
286 /egrave/eacute/ecircumflex/edieresis/igrave/iacute/icircumflex/idieresis
287 /eth/ntilde/ograve/oacute/ocircumflex/otilde/odieresis/divide
288 /oslash/ugrave/uacute/ucircumflex/udieresis/yacute/thorn/ydieresis]def
293 %%BeginResource: font cmr17
294 %!PS-AdobeFont-1.1: CMR17 1.00B
295 %%CreationDate: 1992 Feb 19 19:54:59
296 % Copyright (C) 1988 Blue Sky Research. All rights reserved.
298 /FontInfo 8 dict dup begin
299 /version (1.00B) readonly def
300 /Notice (Computer Modern fonts were designed by Donald E. Knuth) readonly def
301 /FullName (CMR17) readonly def
302 /FamilyName (Computer Modern) readonly def
303 /Weight (Medium) readonly def
305 /isFixedPitch false def
306 /BaseFontName (CMR17) def
311 /FontMatrix [0.001 0 0 0.001 0 0] readonly def
312 /Encoding textext def
313 /FontBBox{-232 -250 945 963}readonly def
314 /UniqueID 5000795 def
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436 %%BeginResource: font cmmi12
437 %!PS-AdobeFont-1.1: CMMI12 1.00A
438 %%CreationDate: 1992 Jul 02 10:48:01
439 % Copyright (C) 1988 Blue Sky Research. All rights reserved.
441 /FontInfo 8 dict dup begin
442 /version (1.00A) readonly def
443 /Notice (Computer Modern fonts were designed by Donald E. Knuth) readonly def
444 /FullName (CMMI12) readonly def
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451 /FontName /cmmi12 def
454 /FontMatrix [0.001 0 0 0.001 0 0] readonly def
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504 %%BeginResource: font cmr12
505 %!PS-AdobeFont-1.1: CMR12 1.00B
506 %%CreationDate: 1992 Jun 07 22:11:29
507 % Copyright (C) 1988 Blue Sky Research. All rights reserved.
509 /FontInfo 8 dict dup begin
510 /version (1.00B) readonly def
511 /Notice (Computer Modern fonts were designed by Donald E. Knuth) readonly def
512 /FullName (CMR12) readonly def
513 /FamilyName (Computer Modern) readonly def
514 /Weight (Medium) readonly def
516 /isFixedPitch false def
517 /BaseFontName (CMR12) def
522 /FontMatrix [0.001 0 0 0.001 0 0] readonly def
523 /Encoding textext def
524 /FontBBox{-246 -251 988 968}readonly def
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680 %%BeginResource: font cmsy8
681 %!PS-AdobeFont-1.1: CMSY8 1.00
682 %%CreationDate: 1992 Jul 23 21:24:13
683 % Copyright (C) 1988 Blue Sky Research. All rights reserved.
685 /FontInfo 8 dict dup begin
686 /version (1.00) readonly def
687 /Notice (Computer Modern fonts were designed by Donald E. Knuth) readonly def
688 /FullName (CMSY8) readonly def
689 /FamilyName (Computer Modern) readonly def
690 /Weight (Medium) readonly def
691 /ItalicAngle -14.035 def
692 /isFixedPitch false def
693 /BaseFontName (CMSY8) def
698 /FontMatrix [0.001 0 0 0.001 0 0] readonly def
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705 /FontBBox{-30 -955 1185 779}readonly def
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766 %%BeginResource: font cmbx10
767 %!PS-AdobeFont-1.1: CMBX10 1.00B
768 %%CreationDate: 1992 Jun 07 22:10:37
769 % Copyright (C) 1988 Blue Sky Research. All rights reserved.
771 /FontInfo 8 dict dup begin
772 /version (1.00B) readonly def
773 /Notice (Computer Modern fonts were designed by Donald E. Knuth) readonly def
774 /FullName (CMBX10) readonly def
775 /FamilyName (Computer Modern) readonly def
776 /Weight (Bold) readonly def
778 /isFixedPitch false def
779 /BaseFontName (CMBX10) def
781 /FontName /cmbx10 def
784 /FontMatrix [0.001 0 0 0.001 0 0] readonly def
785 /Encoding textext def
786 /FontBBox{-301 -250 1164 946}readonly def
787 /UniqueID 5000768 def
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1053 %%BeginResource: font cmr10
1054 %!PS-AdobeFont-1.1: CMR10 1.00B
1055 %%CreationDate: 1992 Aug 11 21:18:25
1056 % Copyright (C) 1988 Blue Sky Research. All rights reserved.
1058 /FontInfo 8 dict dup begin
1059 /version (1.00B) readonly def
1060 /Notice (Computer Modern fonts were designed by Donald E. Knuth) readonly def
1061 /FullName (CMR10) readonly def
1062 /FamilyName (Computer Modern) readonly def
1063 /Weight (Medium) readonly def
1065 /isFixedPitch false def
1066 /BaseFontName (CMR10) def
1068 /FontName /cmr10 def
1071 /FontMatrix [0.001 0 0 0.001 0 0] readonly def
1072 /Encoding textext def
1073 /FontBBox{-40 -250 1009 969}readonly def
1074 /UniqueID 5000793 def
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1489 %%BeginResource: font cmmi10
1490 %!PS-AdobeFont-1.1: CMMI10 1.00A
1491 %%CreationDate: 1992 Jul 02 10:47:58
1492 % Copyright (C) 1988 Blue Sky Research. All rights reserved.
1494 /FontInfo 8 dict dup begin
1495 /version (1.00A) readonly def
1496 /Notice (Computer Modern fonts were designed by Donald E. Knuth) readonly def
1497 /FullName (CMMI10) readonly def
1498 /FamilyName (Computer Modern) readonly def
1499 /Weight (Medium) readonly def
1500 /ItalicAngle -14.04 def
1501 /isFixedPitch false def
1502 /BaseFontName (CMMI10) def
1504 /FontName /cmmi10 def
1507 /FontMatrix [0.001 0 0 0.001 0 0] readonly def
1509 0 1 255 {1 index exch /.notdef put} for
1510 dup 15 /epsilon1 put
1548 /FontBBox{-32 -250 1048 750}readonly def
1549 /UniqueID 5000785 def
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1766 %%BeginResource: font cmti10
1767 %!PS-AdobeFont-1.1: CMTI10 1.00B
1768 %%CreationDate: 1992 Feb 19 19:56:16
1769 % Copyright (C) 1988 Blue Sky Research. All rights reserved.
1771 /FontInfo 8 dict dup begin
1772 /version (1.00B) readonly def
1773 /Notice (Computer Modern fonts were designed by Donald E. Knuth) readonly def
1774 /FullName (CMTI10) readonly def
1775 /FamilyName (Computer Modern) readonly def
1776 /Weight (Medium) readonly def
1777 /ItalicAngle -14.04 def
1778 /isFixedPitch false def
1779 /BaseFontName (CMTI10) def
1781 /FontName /cmti10 def
1784 /FontMatrix [0.001 0 0 0.001 0 0] readonly def
1785 /Encoding textext def
1786 /FontBBox{-163 -250 1146 969}readonly def
1787 /UniqueID 5000828 def
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2091 %%BeginResource: font cmmi7
2092 %!PS-AdobeFont-1.1: CMMI7 1.00A
2093 %%CreationDate: 1992 Jul 02 10:48:10
2094 % Copyright (C) 1988 Blue Sky Research. All rights reserved.
2096 /FontInfo 8 dict dup begin
2097 /version (1.00A) readonly def
2098 /Notice (Computer Modern fonts were designed by Donald E. Knuth) readonly def
2099 /FullName (CMMI7) readonly def
2100 /FamilyName (Computer Modern) readonly def
2101 /Weight (Medium) readonly def
2102 /ItalicAngle -14.04 def
2103 /isFixedPitch false def
2104 /BaseFontName (CMMI7) def
2106 /FontName /cmmi7 def
2109 /FontMatrix [0.001 0 0 0.001 0 0] readonly def
2111 0 1 255 {1 index exch /.notdef put} for
2112 dup 15 /epsilon1 put
2132 /FontBBox{0 -250 1171 750}readonly def
2133 /UniqueID 5000782 def
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2265 %%BeginResource: font cmr7
2266 %!PS-AdobeFont-1.1: CMR7 1.00B
2267 %%CreationDate: 1992 Feb 19 19:55:08
2268 % Copyright (C) 1988 Blue Sky Research. All rights reserved.
2270 /FontInfo 8 dict dup begin
2271 /version (1.00B) readonly def
2272 /Notice (Computer Modern fonts were designed by Donald E. Knuth) readonly def
2273 /FullName (CMR7) readonly def
2274 /FamilyName (Computer Modern) readonly def
2275 /Weight (Medium) readonly def
2277 /isFixedPitch false def
2278 /BaseFontName (CMR7) def
2283 /FontMatrix [0.001 0 0 0.001 0 0] readonly def
2284 /Encoding textext def
2285 /FontBBox{-286 -250 1122 967}readonly def
2286 /UniqueID 5000790 def
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2373 %%BeginResource: font cmsy6
2374 %!PS-AdobeFont-1.1: CMSY6 1.00
2375 %%CreationDate: 1992 Jul 23 21:24:08
2376 % Copyright (C) 1988 Blue Sky Research. All rights reserved.
2378 /FontInfo 8 dict dup begin
2379 /version (1.00) readonly def
2380 /Notice (Computer Modern fonts were designed by Donald E. Knuth) readonly def
2381 /FullName (CMSY6) readonly def
2382 /FamilyName (Computer Modern) readonly def
2383 /Weight (Medium) readonly def
2384 /ItalicAngle -14.035 def
2385 /isFixedPitch false def
2386 /BaseFontName (CMSY6) def
2388 /FontName /cmsy6 def
2391 /FontMatrix [0.001 0 0 0.001 0 0] readonly def
2393 0 1 255 {1 index exch /.notdef put} for
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2398 /FontBBox{-4 -948 1329 786}readonly def
2399 /UniqueID 5000816 def
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2459 %%BeginResource: font cmr8
2460 %!PS-AdobeFont-1.1: CMR8 1.00B
2461 %%CreationDate: 1992 Feb 19 19:55:11
2462 % Copyright (C) 1988 Blue Sky Research. All rights reserved.
2464 /FontInfo 8 dict dup begin
2465 /version (1.00B) readonly def
2466 /Notice (Computer Modern fonts were designed by Donald E. Knuth) readonly def
2467 /FullName (CMR8) readonly def
2468 /FamilyName (Computer Modern) readonly def
2469 /Weight (Medium) readonly def
2471 /isFixedPitch false def
2472 /BaseFontName (CMR8) def
2477 /FontMatrix [0.001 0 0 0.001 0 0] readonly def
2478 /Encoding textext def
2479 /FontBBox{-267 -250 1070 968}readonly def
2480 /UniqueID 5000791 def
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2697 %%BeginResource: font cmtt8
2698 %!PS-AdobeFont-1.1: CMTT8 1.00B
2699 %%CreationDate: 1992 Feb 19 19:56:39
2700 % Copyright (C) 1988 Blue Sky Research. All rights reserved.
2702 /FontInfo 8 dict dup begin
2703 /version (1.00B) readonly def
2704 /Notice (Computer Modern fonts were designed by Donald E. Knuth) readonly def
2705 /FullName (CMTT8) readonly def
2706 /FamilyName (Computer Modern) readonly def
2707 /Weight (Medium) readonly def
2709 /isFixedPitch true def
2710 /BaseFontName (CMTT8) def
2712 /FontName /cmtt8 def
2715 /FontMatrix [0.001 0 0 0.001 0 0] readonly def
2716 /Encoding textext def
2717 /FontBBox{-5 -236 739 802}readonly def
2718 /UniqueID 5000830 def
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2810 %%BeginResource: font cmsy10
2811 %!PS-AdobeFont-1.1: CMSY10 1.00
2812 %%CreationDate: 1992 Jul 23 21:24:04
2813 % Copyright (C) 1988 Blue Sky Research. All rights reserved.
2815 /FontInfo 8 dict dup begin
2816 /version (1.00) readonly def
2817 /Notice (Computer Modern fonts were designed by Donald E. Knuth) readonly def
2818 /FullName (CMSY10) readonly def
2819 /FamilyName (Computer Modern) readonly def
2820 /Weight (Medium) readonly def
2821 /ItalicAngle -14.035 def
2822 /isFixedPitch false def
2823 /BaseFontName (CMSY10) def
2825 /FontName /cmsy10 def
2828 /FontMatrix [0.001 0 0 0.001 0 0] readonly def
2830 0 1 255 {1 index exch /.notdef put} for
2832 dup 1 /periodcentered put
2835 dup 20 /lessequal put
2836 dup 21 /greaterequal put
2838 dup 54 /negationslash put
2839 dup 60 /Rfractur put
2841 dup 102 /braceleft put
2842 dup 103 /braceright put
2844 dup 112 /radical put
2846 /FontBBox{-29 -960 1116 775}readonly def
2847 /UniqueID 5000820 def
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2941 %%BeginResource: font cmex10
2942 %!PS-AdobeFont-1.1: CMEX10 1.00
2943 %%CreationDate: 1992 Jul 23 21:22:48
2944 % Copyright (C) 1988 Blue Sky Research. All rights reserved.
2946 /FontInfo 8 dict dup begin
2947 /version (1.00) readonly def
2948 /Notice (Computer Modern fonts were designed by Donald E. Knuth) readonly def
2949 /FullName (CMEX10) readonly def
2950 /FamilyName (Computer Modern) readonly def
2951 /Weight (Medium) readonly def
2953 /isFixedPitch false def
2954 /BaseFontName (CMEX10) def
2956 /FontName /cmex10 def
2959 /FontMatrix [0.001 0 0 0.001 0 0] readonly def
2961 0 1 255 {1 index exch /.notdef put} for
2962 dup 0 /parenleftbig put
2963 dup 1 /parenrightbig put
2964 dup 80 /summationtext put
2965 dup 88 /summationdisplay put
2967 /FontBBox{-24 -2960 1454 772}readonly def
2968 /UniqueID 5000774 def
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3025 %%BeginResource: font cmsy7
3026 %!PS-AdobeFont-1.1: CMSY7 1.00
3027 %%CreationDate: 1992 Jul 23 21:24:11
3028 % Copyright (C) 1988 Blue Sky Research. All rights reserved.
3030 /FontInfo 8 dict dup begin
3031 /version (1.00) readonly def
3032 /Notice (Computer Modern fonts were designed by Donald E. Knuth) readonly def
3033 /FullName (CMSY7) readonly def
3034 /FamilyName (Computer Modern) readonly def
3035 /Weight (Medium) readonly def
3036 /ItalicAngle -14.035 def
3037 /isFixedPitch false def
3038 /BaseFontName (CMSY7) def
3040 /FontName /cmsy7 def
3043 /FontMatrix [0.001 0 0 0.001 0 0] readonly def
3045 0 1 255 {1 index exch /.notdef put} for
3047 dup 20 /lessequal put
3051 /FontBBox{-15 -951 1252 782}readonly def
3052 /UniqueID 5000817 def
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3057 37ADD94AC8FBD2022E3EC8F115D4B4BB7B7F15388F22CC6198EFE768BD9FCEB3446EE4A8DC27D6
3058 CD152485384EF5F59381FFDA43F2D20C8FB08AA27AB2015B774DB10DACFDCD33E60F178C461553
3059 146AB427BDD7DA12534BA078AD3D780414930C9525A8175CC2351CEB7962CBE3665ADFAA54B270
3060 F4CA3D79F11EA12CBA09F21EC9EE5521F2160F1880CD90A557A5F9EDC27A9DBEFEECDE4FABEFB9
3061 9FDEEA7E7467951EF942A2E7E95333AD9706597293E1B1661E5B3F58E394A3602719D6E6E09815
3062 BDD00757FD3803CE757C61280682F4D9351AED2780893C4E689DFC012F6BD7499CFA9CCA65EE83
3063 B102023E44FC207FD70F82EF3FA556FD75B3ED46A8476E38D022EDB328524A50EAC7481F3EAD76
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3103 %%BeginResource: font cmsy5
3104 %!PS-AdobeFont-1.1: CMSY5 1.00
3105 %%CreationDate: 1992 Jul 23 21:24:06
3106 % Copyright (C) 1988 Blue Sky Research. All rights reserved.
3108 /FontInfo 8 dict dup begin
3109 /version (1.00) readonly def
3110 /Notice (Computer Modern fonts were designed by Donald E. Knuth) readonly def
3111 /FullName (CMSY5) readonly def
3112 /FamilyName (Computer Modern) readonly def
3113 /Weight (Medium) readonly def
3114 /ItalicAngle -14.035 def
3115 /isFixedPitch false def
3116 /BaseFontName (CMSY5) def
3118 /FontName /cmsy5 def
3121 /FontMatrix [0.001 0 0 0.001 0 0] readonly def
3123 0 1 255 {1 index exch /.notdef put} for
3127 /FontBBox{21 -944 1448 791}readonly def
3128 /UniqueID 5000815 def
3131 80347982AB3942D930E069A70D0D48311D725E830D1C76FBA12E12486E989C9874C2B527F09257
3132 22787027F44470D484262C360CDFDDDF3657533A57BB16F73048BFBBFCB73A650484015441FDC8
3133 37ADD94AC8FBD2022E3EC8F115D4B4BB7B7F15388F22CC6198EFE768BD9FCEB3446EE4A8DC27D6
3134 CD152485384EF5F59381FFDA43F2D20C8FB08AA27AB2015B774DB10DACFDCD33E60F178C461553
3135 146AB427BDD7DA12534BA078AD3D780414930BC7FCF13EDB998263833438A0DA10BA2F2A1BB2BF
3136 41FE15C05E2672C5826BF72D96E066B497665A8EC8073792F450309F8C81FA135F1D7C905C4F73
3137 E3B8322C14233253DCD74FC8F4E02D91A69751B1D8327C5A5FC0FDB6BEA2895E1D2460BE2FEB87
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3139 CDD83465780471F910F880F11D9FE12D370F8CF50E70CD8B894D0DD3107696A3D024048E58CF86
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3172 %%BeginResource: font cmmi5
3173 %!PS-AdobeFont-1.1: CMMI5 1.00A
3174 %%CreationDate: 1992 Jul 02 10:48:04
3175 % Copyright (C) 1988 Blue Sky Research. All rights reserved.
3177 /FontInfo 8 dict dup begin
3178 /version (1.00A) readonly def
3179 /Notice (Computer Modern fonts were designed by Donald E. Knuth) readonly def
3180 /FullName (CMMI5) readonly def
3181 /FamilyName (Computer Modern) readonly def
3182 /Weight (Medium) readonly def
3183 /ItalicAngle -14.04 def
3184 /isFixedPitch false def
3185 /BaseFontName (CMMI5) def
3187 /FontName /cmmi5 def
3190 /FontMatrix [0.001 0 0 0.001 0 0] readonly def
3191 /Encoding textext def
3192 /FontBBox{37 -250 1349 750}readonly def
3193 /UniqueID 5000780 def
3196 80347982AB3942D930E069A70D0D48311D725E830D1C76FBA12E12486E989C9874C2B527F09257
3197 22787027F44470D484262C360CDFDDDF3657533A57BB16F73048BFBBFCB73A650484015441FDC8
3198 37ADD94AC8FBD2022E3EC8F115D4B4BB7B7F15388F22CC6198EFE768BD9FCEB3446EE4A8DC27D6
3199 CD152485384EF5F59381FFDA43F2D20C8FB08AA27AB2015B774DB10DACFDCD33E60F178C461553
3200 146AB427BDD7DA12534BA078AD3D780414930DA4F8D58ABEFD45DB119B10EB409DD897923C6E70
3201 5479464A4B33AE3D31BFE98EFE259F07F7950237BBAEE4F7B64FFEA83A757FA717D014A28BBCD1
3202 FBFEBA1EF8B9C61C576D0458E934D58839BF3BD7A46F73DF700682D3E8DE22199BE9CCA53A82B1
3203 190D757E5166AF8598D76FDE65BACB1F16455DEF48A0FCED6F7483D776726DCD7AFE91AD4E6E24
3204 1E35E96E5E6BC42158E01BB6C185108B1E6EA0D8CE1854D995A72D9AC27506EF395154F32060B3
3205 FA14E26DEF4C7004E039F9F33DF56691DE19FA6E4FDC18FB3CBD9BC4AFEA6E26D157944BE49D82
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3207 4FEF99C39CB4D38602CB94325A962D8B2EC1E519DD570FE0AD34320650DB8A16356A7ABE3792A6
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3220 B739D9B964259F1B7C674396943279627ED676D4C04A9729A4AA954BB50FF1ED8A56F70F9D41B2
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3227 432309BC953F81068B1F01FDB72F9F50CC2B53B087E926A1117E58DAB6E46188DA4C670285714E
3228 CFB2925BB826CC805A73EE283F60E5A7FE1F21CA0C4400F3F0C5275CDDCFD1DB11ACCFD5276A36
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3240 0000000000000000000000000000000000000000000000000000000000000000
3244 %%BeginResource: font cmr5
3245 %!PS-AdobeFont-1.1: CMR5 1.00B
3246 %%CreationDate: 1992 Feb 19 19:55:02
3247 % Copyright (C) 1988 Blue Sky Research. All rights reserved.
3249 /FontInfo 8 dict dup begin
3250 /version (1.00B) readonly def
3251 /Notice (Computer Modern fonts were designed by Donald E. Knuth) readonly def
3252 /FullName (CMR5) readonly def
3253 /FamilyName (Computer Modern) readonly def
3254 /Weight (Medium) readonly def
3256 /isFixedPitch false def
3257 /BaseFontName (CMR5) def
3262 /FontMatrix [0.001 0 0 0.001 0 0] readonly def
3263 /Encoding textext def
3264 /FontBBox{-341 -250 1304 965}readonly def
3265 /UniqueID 5000788 def
3268 80347982AB3942D930E069A70D0D48311D7190FA2D133A583138F76695558E7AE9348D37CAC665
3269 1806D08527C1BB4A062A4835AC37784CC39AD8841404E438B4D52D3901E47A1DE4F7924E0FB3DA
3270 F442499175BAB1226EDF692A4956739F8828E80592F450C5D5C22AC88BCFBE9748F61D18243A16
3271 F4A4467F084E8E2BE46EF47FC51C3A8199E3CDA62FF9C4FB73956DAB8B6683D2156377808CB350
3272 26073E80523F59A30D195FCF9B9FCE4FFAFC6F33457E3200F33E9A53D3B289D794EA7C8EA770CA
3273 5E9F22B46F1B98C218DE1BCBBB7C566EA09D85D7856B7378CDACFBCC06C5C63AA0627D66BD2C48
3274 47C2D9ADA8F1AB19D3B555DA1CC9647BF7C0ECB159CF1A53256A33985A6117D3DFD2AC2D0F6EF8
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4313 224547 r(determine)S(a)S(subset)S
4323 109224 W(:)S(:)S(:)s o
4333 -18205 r(h)S(to)S(place)S(facilities)S(so)S(as)S(to)S
4392 226748 W(dimensional)S(geometric)S(instance)s
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4401 18205 r(cation)S(problem\))s o y u
4403 263185 W(a)S(set)S(of)S(p)s
4405 -18205 r(ts)S(that)S(corresp)T(ond)S(to)S(p)T(oin)s
4406 -18205 r(ts)S(in)s o y u
4410 186694 W(space)S(with)S(Euclidean)S(distance)S(as)s o y u
4412 218453 r(metric.)s o
4421 f7(-dimensional)S(ge)s
4422 -33497 r(ometric)s o y u
4423 17363435 r(instanc)s
4428 f7(-me)T(dian)S(pr)T(oblem)S(and)S(a)S(p)T
4435 334099 r(the)S(algorithm)S(develop)s
4438 -33497 r(ction)S(3.3)s o y u
4439 17363435 r(achieves)s
4440 256002 W(with)S(pr)s
4441 -33497 W(ob)S(ability)s
4448 f7(a)T(solution)T(of)s o y u
4451 218934 W(at)S(most)S
4457 f7(times)S(the)S(optimal)S(c)T(ost)S(in)s o y u
4476 f7(-dimensional)S(ge)s
4477 -33497 r(ometric)s o y u
4478 17363435 r(instanc)s
4480 282170 W(of)S(the)S(facility)S(lo)T(c)T(ation)S(pr)T
4481 (oblem)S(and)S(a)s o y u
4484 263353 X(r)S(e)S(al)T
4487 270573 r(the)T(algorithm)T(develop)S(e)S(d)T(in)T(Se)S
4490 289726 W(3.3.2)S(achieves)S(with)S(pr)s
4491 -33497 W(ob)S(ability)s
4499 17363435 r(solution)s
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4507 f7(times)S(the)S(op-)s o y u
4510 -33497 r(ost)S(in)S(time)S
4522 145635 W(algorithms)S(are)S(randomized,)s
4523 160199 r(and)S(so)S(the)S(prob-)s o y u
4524 17363435 r(abilities)s
4525 157957 W(in)S(all)S(our)S(theorems)S(are)S(o)s
4527 157957 W(the)S(random)s o y u
4530 263770 W(of)S(the)S(algorithm)S(\(and)S(hold)S(for)S(an)T
4534 204505 W(is)S(easy)S(to)S(restate)S(these)S(results)S(as)S
4541 f5(\)-appro)T(ximate)s
4542 172811 W(solution)S(in)S(ex-)s o y u
4555 360348 r(The)S(algorithm)S(hinges)S(on)s o y u
4558 -18205 X(harging)S(algorithm)S(that)S(generalizes)S(the)S(tec)T(h-)s o y u
4560 276933 W(of)S(Arora)S([)s u(1)s o
4561 327681 r(,)s u w(2)s o
4563 291553 r(and)S(should)S(b)s
4564 18205 r(e)S(of)S(inde-)s o y u
4568 250182 X(in)S(terest)T(for)T(other)T(geometric)T(optimiza-)s o y u
4570 315118 W(problems;)s
4571 363450 r(this)S(argumen)s
4572 -18205 X(t)S(is)S(dev)T(elop)s
4573 18205 r(ed)S(in)s o y u
4574 17363435 r(Section)s
4575 218453 r(2.1.)s o y u
4577 145635 W(in)S(section)S(3.3)S(w)s
4578 -18205 r(e)S(describ)s
4579 18205 X(e)S(quasi-p)T(olynomial)s o y u
4581 170674 W(algorithms)S(for)S
4583 f5(-dimensional)S(geometric)S(in-)s o y u
4584 17363435 r(stances)s
4585 318096 W(and)S(for)S(a)S(capacitated)S(v)s
4586 -18205 r(ersions)S(of)S(the)s o y u
4587 17363435 r(problems.)s o
4594 -20935 r(hniques)s o y u
4602 227217 W(a)S(geometric)S(division)S(of)S(the)S(plane)s o
4606 145635 W(a)S(hierarc)T(h)T(y)S(of)S(square)S(regions)S
4607 (\(see)S(Section)S(2\).)s o y u
4609 145635 W([)s u(2)s o
4610 327681 r(])S(uses)S(a)S(randomized)S(v)s
4612 -18205 r(t)S(of)S(the)S(quadtree.)s o y u
4615 -18205 W(atc)S(hing)s
4619 212603 W(that)S(the)s o y u
4623 285269 r(tour)S(can)S(b)s
4624 18205 X(e)S(mo)T(di\fed)S(|with)S(a)s o y u
4629 f5(factor)S(increase)S(in)S(cost|)S(suc)s
4630 -18205 r(h)S(that)S(the)s O O O
4645 187311 W(of)S(tour)S(edges)S(crossing)S(an)s
4646 -18205 r(y)S(region)S(in)S(the)s o
4648 2368143 r(quadtree)s
4655 554387 r(\(Note)S(that)S(this)S(is)s o y u
4657 264077 W(surprising)S(result,)s
4665 287891 W(crossing)S(edges)S(could)S(b)s
4666 18205 r(e)S(a)S(large)S(function)S(of)s o y u
4670 18205 W(er)T(of)T(no)S(des,)s
4682 521570 r(In)T(particular)s o y u
4685 -18205 r(ws)S(that)S(there)S
4688 f5(a)S(tour)S(of)S(cost)S(at)s o y u
4698 f5(that)T(crosses)T(ev)s
4699 -18205 r(ery)T(region)T(of)s o y u
4701 270124 W(quadtree)S(at)S(most)S
4708 270072 r(simple)s o y u
4710 236710 W(programming)S(\(whenev)s
4711 -18205 X(er)S(y)T(ou)S(divide)S(a)s o y u
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4713 229287 W(square)S(in)s
4714 -18205 r(to)S(four,)s
4715 231996 r(\\guess")S(the)S(tour)S(in-)s o y u
4719 -18205 W(w)S(een)T(the)T(four)T(subsquares)T(and)T(then)s o y u
4723 -18205 r(tly)S(in)S(the)S(subsquares\))S(can)S(\fnd)s o y u
4726 218453 W(a)S(tour.)s o
4730 255644 W(use)S(a)S(similar)S(quadtree-based)S(algorithm.)s o y u
4732 145635 W(main)S(di\013erence)S(is)S(that)S(the)S(P)s
4733 -18205 W(atc)S(hing)s
4734 145635 r(Lemma)s o y u
4737 192211 W(not)S(hold)S(for)S(our)S(problems)S(here,)s
4739 -18205 r(e)S(can-)s o y u
4741 211205 W(in)S(general)S(reduce)S(the)S(n)s
4744 211205 W(of)S(edges)S(that)s o y u
4747 18205 r(oundary)S(of)S(an)s
4748 -18205 r(y)S(quadtree)S(square.)s
4749 266999 r(Nev-)s o y u
4750 2368143 r(ertheless,)s
4753 340562 W(can)S(generalize)S(Arora's)S(c)T(harging)s o y u
4756 263483 W(|)S(whic)T(h)S(do)s
4757 18205 r(es)S(not)S(use)S(the)S(P)T(atc)T(hing)s o y u
4759 200604 W(|)S(to)S(argue)S(that)S(the)S(there)S(exists)S
4766 145635 W(solution)S(that)S(has)S(a)S(v)T(ery)S(restricted)s o y u
4770 18205 r(et)S(w)S(een)T(an)S(y)T(adjacen)S(t)T
4771 (squares)T(of)T(the)s o y u
4772 2368143 r(quadtree.)s
4774 18205 X(eci\fcally)s
4778 -18205 r(terface)S(b)T(elongs)S(to)s o y u
4790 -18205 X(terfaces,)s
4791 215202 r(all)S(of)S(whic)T(h)S(are)S(con-)s o y u
4794 -18205 X(y)S(our)S(algorithm.\))s
4795 585060 r(Th)T(us)S(w)T(e)S(can)S(use)s o y u
4797 218453 W(programming)S(to)S(\fnd)S(suc)s
4798 -18205 r(h)S(a)S(solution.)s o
4802 3498633 r(Quadtree)s
4803 243643 W(dissection)S(and)S(the)S(c)s
4804 -20935 r(harging)s o y u
4810 283680 W(section)S(describ)s
4811 18205 r(es)S(the)S(quadtree)S(dissection)s o y u
4813 253996 W(an)S(asso)s
4814 18205 r(ciated)S(c)s
4815 -18205 X(harging)S(argumen)T(t)S(that)S(ap-)s o y u
4818 -18205 X(y)S(set)S(of)S(line)S(segmen)T(ts)S(in)S
4819 (the)S(plane.)s o y u
4821 305667 W(dissection)S(is)S(the)S(same)S(as)S(in)S([)s u(2)s o
4823 327470 r(and)S(the)s o y u
4826 353818 X(argumen)S(t)T(is)T(a)T(general)T(statemen)S(t)T
4829 218453 W(of)S(the)S(calculations)S(in)S([)s u(2)s o
4837 f5(of)S(a)S(set)S(of)S(p)s
4839 -18205 r(ts)S(b)T(e)S(the)s o y u
4840 2368143 r(smallest)s
4841 229406 W(square)S(con)s
4842 -18205 r(taining)S(it.)s
4845 f5(denote)S(its)s o y u
4846 2368143 r(length.)s o z u
4854 18205 X(ounding)S(b)T(o)s
4855 -18205 r(x)S(is)S(a)S(recur-)s o y u
4858 208946 W(partitioning)S(in)T(to)S(smaller)S(squares.)s
4860 -54614 r(e)S(view)s o y u
4862 286042 W(as)S(a)S(4-ary)S(tree)S(whose)S(ro)s
4863 18205 X(ot)S(is)S(the)S(b)T(ounding)s o y u
4868 198878 W(square)S(in)S(the)S(tree)S(is)S(partitioned)S(in)s
4871 248594 W(equal)S(squares,)s
4873 -18205 X(h)S(are)S(its)S(c)T(hildren.)s
4877 170545 W(partitioning)S(a)S(square)S(if)S(it)S(has)S(size)S
4880 f5(1)S(\(and)s o y u
4881 2368143 r(therefore)s
4882 274714 W(at)S(most)S(one)S(no)s
4884 460055 r(Note)S(that)S(there)s o y u
4894 f5(\))S(no)T(des)S(in)S(the)S(tree)S(and)S
4895 (its)S(depth)S(is)s o y U
4906 297572 W(de\fned)S(similarly)s
4908 317352 r(except)s o y u
4911 312115 W(stop)S(the)S(recursiv)T(e)S(partitioning)S(as)S(so)s
4912 18205 r(on)S(as)s o y u
4914 279647 W(square)S(has)S(at)S(most)S(one)S(input)S(p)s
4917 474852 r(The)s o y u
4918 2368143 r(quadtree)s
4920 -18205 X(y)S(in)S(general)S(ha)T(v)T(e)S(few)T
4921 (er)S(squares)S(than)s o y u
4923 218453 W(dissection;)S(see)S(Figure)S(1.)s o z u
4929 -18205 r(tegers)S(in)S([0)s
4932 160199 r(then)S(the)s u w(\()s
4940 8695836 8525330 2170798 9406791 30522736 36969349 startTexFig
4942 %%BeginDocument: shift.eps
4943 %!PS-Adobe-3.0 EPSF-3.0
4944 %%BoundingBox: 33 143 464 562
4947 %%CreationDate: Sunday, January 19, 1997 22:54:50
4948 %%DocumentResources: procset Deneba_CanvasCustomColors
4949 %%+ procset Deneba_CanvasGraphics
4950 %%+ font Arial-BoldMT
4951 %%DocumentSuppliedResources: procset Deneba_CanvasCustomColors
4952 %%+ procset Deneba_CanvasGraphics
4953 %%+ font Arial-BoldMT
4954 %%DocumentProcessColors: Cyan Magenta Yellow Black
4955 %%Copyright: (C) 1996 Deneba Systems. All Rights Reserved
4958 %%BeginResource: procset Deneba_CanvasGraphics
4959 %%Title: Deneba standard graphics
4961 %%CreationDate: 10/1/94
4962 %%Copyright: (C) 1994 Deneba Systems. All Rights Reserved
4963 userdict /Deneba_CanvasGraphics 300 dict put
4964 Deneba_CanvasGraphics begin
4965 /invalidcolortable? true def
4966 /level2 /languagelevel where {pop languagelevel 2 ge}{false} ifelse def
4968 {Deneba_CanvasGraphics
4969 {dup xcheck{bind}if pop pop}forall
4970 currentscreen /_sp exch def /_sa exch def /_sf exch def
4971 /DefaultScreen{_sf _sa /_sp load}def
4972 /DefaultScreenProc{ /_sp load}def
4973 /setstrokeadjust where{pop true}{false}ifelse
4974 {/sa /setstrokeadjust load def
4975 /li /lineto load def
4976 /mt /moveto load def
4977 /ct /curveto load def
4978 /lh { currentpoint exch pop lineto}bind def
4979 /lv { currentpoint pop exch lineto}bind def}
4980 {/sa{{currentdict StrokeAdjustDict ne{StrokeAdjustDict begin}if}{ currentdict StrokeAdjustDict eq{end}if}ifelse} bind def
4981 userdict /StrokeAdjustDict 10 dict put
4982 StrokeAdjustDict begin
4985 .25 sub round .25 add exch
4986 .25 sub round .25 add exch
4989 /li{ _xl lineto}bind def
4990 /mt{ _xl moveto}bind def
4991 /ct{ _xl curveto}bind def
4992 /lh { dup _xl pop currentpoint exch pop lineto}bind def
4993 /lv { dup _xl pop currentpoint pop exch lineto}bind def
4994 /rp{_xl/cv_b xdf/cv_r xdf
4995 _xl/cv_t xdf/cv_l xdf
5004 {userdict /StrokeAdjustDict known {currentdict StrokeAdjustDict eq{end}if}if
5005 currentdict Deneba_CanvasGraphics eq{end}if}def
5007 /mxStk [mxMax {matrix} repeat]def
5009 /stm{mxStk mxIdx get currentmatrix pop
5010 /mxIdx mxIdx 1 add store}def
5011 /rtm{/mxIdx mxIdx 1 sub store
5012 mxStk mxIdx get setmatrix}def
5015 /_initmtx matrix def
5017 /min{2 copy gt{exch}if pop}def
5018 /max{2 copy lt{exch}if pop}def
5019 /CVvec 256 array def
5024 /_encodArr 10 array def
5045 /savehandler null def
5047 {dup /$eps exch not def{/savehandler errordict /handleerror get def
5049 /handleerror{$error begin
5050 newerror{/newerror false def
5053 /Helvetica findfont .2 scalefont setfont
5057 {dup type/stringtype ne
5058 {(converted error name will end up in this string)cvs}if
5061 (Offending Command: )show
5063 {dup type/stringtype ne
5064 {(converted command name will end up in this string)cvs}if
5069 {.25 currentpoint .2 sub exch pop moveto
5070 dup type/stringtype ne{dup type/integertype eq
5071 1 index type/realtype eq or
5072 1 index type/nametype eq or
5074 (converted stack will end up in this string)cvs}if
5077 Deneba_CanvasGraphics /savehandler get exec}if
5081 /lm{setmiterlimit}def
5087 /gs{gsave $psz dup $pix _penh put $pix 1 add _penv put /$pix $pix 2 add def}def
5088 /gr{grestore/$pix $pix 2 sub def $psz dup $pix get /_penh exch def $pix 1 add get /_penv exch def}def
5090 /lh{currentpoint exch pop lineto}def
5091 /lv{currentpoint pop exch lineto}def
5093 /mh{currentpoint exch pop moveto}def
5094 /mv{currentpoint pop exch moveto}def
5096 /rt{4 -2 roll moveto
5102 {{currentflat dup{gsave{eoclip}stopped{grestore 2 mul dup setflat dup 200 ge{pop pop exit}if}{grestore setflat exit}ifelse}loop eoclip setflat}
5103 {currentflat dup{gsave{clip}stopped{grestore 2 mul dup setflat dup 200 ge{pop pop exit}if}{grestore setflat exit}ifelse}loop clip setflat}}def
5105 /fg{$eps{systemdict /setgray get exec}{setgray}ifelse}def
5106 /setcmykcolor where {pop true}{false}ifelse
5107 {/f4{ setcmykcolor}def}{/f4{1 sub 4 1 roll 3{3 index add neg dup 0 lt{pop 0}if 3 1 roll}repeat setrgbcolor pop}def}ifelse
5108 /setcolorspace where {pop true}{false}ifelse
5109 {/scs{ dup setcolorspace /_cs exch def}def/f3{ _cs setcolorspace setcolor}def
5110 }{/f3{ setrgbcolor}def/scs{ pop}def}ifelse
5112 /findcmykcustomcolor where {pop true}{false}ifelse
5113 not {/findcmykcustomcolor{$cc astore}def}if
5114 /setcustomcolor where {pop true}{false}ifelse
5115 not{/setcustomcolor{exch aload pop pop 4{4 index mul 4 1 roll}repeat setcmykcolor pop}def}if
5116 /fc{6 1 roll findcmykcustomcolor exch setcustomcolor}def
5117 /setseparationgray where {pop true}{false}ifelse
5118 not{/setseparationgray {systemdict /setgray get exec} def}if
5119 /sg{ setseparationgray}def
5120 /sp{/_penv xdf/_penh xdf}def
5135 cv_l xradius add cv_t moveto
5136 cv_r xradius sub cv_t lineto
5137 _cvmtx currentmatrix pop
5138 currentpoint translate
5139 xradius yradius scale
5140 1 0 1 1 1 arcto 4{pop}repeat
5142 cv_r cv_b yradius sub lineto
5143 _cvmtx currentmatrix pop
5144 currentpoint translate
5145 xradius yradius scale
5146 0 1 -1 1 1 arcto 4{pop}repeat
5148 cv_l xradius add cv_b lineto
5149 _cvmtx currentmatrix pop
5150 currentpoint translate
5151 xradius yradius scale
5152 -1 0 -1 -1 1 arcto 4{pop}repeat
5154 cv_l cv_t yradius add lineto
5155 _cvmtx currentmatrix pop
5156 currentpoint translate
5157 xradius yradius scale
5158 0 -1 1 -1 1 arcto 4{pop}repeat
5161 /ep{_cvmtx currentmatrix pop
5167 _cvmtx setmatrix}def
5168 /wd{_cvmtx currentmatrix pop
5172 0 0 1 5 -2 roll arcn
5174 _cvmtx setmatrix}def
5175 /as{_cvmtx currentmatrix pop
5178 0 0 1 5 -2 roll arcn
5179 _cvmtx setmatrix}def
5181 {_penv _penh ne dup{stm _penh dup 0 le{pop 1}if _penv dup 0 le{pop 1}if scale}{_penh setlinewidth}ifelse stroke {rtm}if}def
5186 /_gst{ 9 dict begin level2{/_ccs currentcolorspace def /_cc [currentcolor] def}{/_cc [currentrgbcolor]def}ifelse {currentpoint}stopped {/_cp null def}{ 2 array astore /_cp exch def}ifelse /_cf currentfont def
5187 /_clw currentlinewidth def /_clc currentlinecap def /_clj currentlinejoin def /_cml currentmiterlimit def currentdict end}def
5188 /hs{newpath gsave stm}def
5189 /hc{/_hr load exch get exec newpath}def
5190 /he{_gstk _gstkc _gst put /_gstkc _gstkc 1 add store
5191 grestore rtm /_gstkc _gstkc 1 sub store _gstk _gstkc get level2{dup /_ccs get setcolorspace dup /_cc get aload pop setcolor}{dup /_cc get aload pop setrgbcolor}ifelse dup /_cp get dup null eq
5192 not{aload pop moveto}{pop}ifelse dup /_cf get setfont
5193 dup/_clw get setlinewidth dup/_clc get setlinecap dup/_clj get setlinejoin dup/_cml get setmiterlimit pop}def
5195 /_imatrix{_w 0 0 _h _id 0 ne{neg 0 _h}{0 0}ifelse _cvmtx astore}def
5196 % Copyright (C) 1990, 1991 by Adobe Systems Incorporated.
5197 % All rights reserved.
5198 level2 { save /dontloadlevel1 xdf }if
5199 /startnoload{{/noload save def} if}def
5200 /endnoload{{noload restore}if }def
5201 /testsystemdict{where{systemdict eq{true}{false}ifelse}{false}ifelse}def
5203 /colorimage where{pop true}{false}ifelse{/ncolors 0
5205 /processcolors where{pop pop processcolors}{/deviceinfo where{pop deviceinfo /Colors known
5206 {pop {deviceinfo /Colors get}}if}if}ifelse end def
5207 ncolors 0 ne{/colorimage testsystemdict
5208 /setcolortransfer testsystemdict
5209 /currentcolortransfer testsystemdict
5210 /currentcmykcolor testsystemdict
5211 and and and not{/ncolors 0 def}if}if}if
5212 ncolors dup 1 ne exch dup 3 ne exch 4 ne and and {/ncolors 0 def}if
5213 ncolors 1 eq dup dup not startnoload
5214 {/doclutimage{[{255 mul round cvi bwclut exch get 255 div} /exec load dup currenttransfer exch]
5215 cvx bind settransfer _w _h 8 _imatrix {currentfile st0 readhexstring pop}image}def}if
5217 ncolors dup 3 eq exch 4 eq or
5218 dup dup not startnoload
5219 {/nullproc{{}}def/concatutil{/exec load
5220 7 -1 roll /exec load}def
5222 {1 add getinterval def}def
5224 {/Dclut exch def/Cclut exch def/Bclut exch def/Aclut exch def/ncompute exch ld
5225 currentcolortransfer
5226 [{Aclut ncompute}concatutil] cvx
5227 [{Bclut ncompute}concatutil] cvx
5228 [{Cclut ncompute}concatutil] cvx
5229 [{Dclut ncompute}concatutil] cvx
5230 setcolortransfer}def
5232 {/bit3x rgbclut length 3 sub def
5233 /bit1x bit3x 3 idiv def/rclut rgbclut def
5234 /gclut rclut 1 bit3x defsubclut/bclut rclut 2 bit3x defsubclut}def}if not
5235 endnoload ncolors 3 eq dup dup not startnoload
5236 {/3compute{exch bit3x mul
5237 round cvi get 255 div}def
5238 /doclutimage{%/rgbclut xdf pop
5239 setuprgbcluts/3compute rclut gclut bclut dup
5240 spconcattransfer _w _h 8 _imatrix
5241 [{currentfile st0 readhexstring pop}/exec load
5243 nullproc nullproc true 3 colorimage}def}if not endnoload ncolors 4 eq dup dup not startnoload
5244 {/stuffclut{cmykindex 3 -1 roll put}def
5245 /ftoint{1 exch sub 255 mul round cvi}def
5246 /4compute { exch bit4x mul round cvi get 255 div } def
5247 /computecmykclut{setuprgbcluts/bit4x rgbclut length 3 idiv 4 mul 4 sub def
5248 /cmykclut bit4x 4 add string def
5250 /mclut cclut 1 bit4x defsubclut
5251 /yclut cclut 2 bit4x defsubclut
5252 /kclut cclut 3 bit4x defsubclut
5255 {dup /cmykindex exch bit1x exch sub 4 mul def
5256 3 mul dup rclut exch get 255 div exch dup gclut exch get 255 div
5257 exch bclut exch get 255 div
5258 setrgbcolor currentcmykcolor
5259 ftoint kclut stuffclut
5260 ftoint yclut stuffclut
5261 ftoint mclut stuffclut
5262 ftoint cclut stuffclut
5264 /doclutimage{invalidcolortable?{computecmykclut}if
5265 /4compute cclut mclut yclut kclut spconcattransfer
5266 _w _h 8 _imatrix[{currentfile st0 readhexstring pop}/exec load/dup load dup dup] cvx
5267 nullproc nullproc nullproc true 4 colorimage}def}if
5270 dup dup not startnoload
5271 {/colorexpand{mystringexp 0 rgbclut
5274 {3 mul 3 getinterval putinterval exch 3 add exch 3 copy}forall
5275 pop pop pop pop pop}def
5276 /createexpandstr{/mystringexp exch st0 length mul string def}def
5277 /doclutimage{/rgbclut xdf pop 3 createexpandstr _w _h 8 _imatrix
5278 [{currentfile st0 readhexstring pop} /exec load /colorexpand load /exec load] cvx
5279 false 3 colorimage}def}if not endnoload
5280 level2 { dontloadlevel1 restore }if
5281 level2 not{ save /dontloadlevel2 xdf }if
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6886 %%DSIBeginObject: #15 - Ref:17 Rectangle
6887 %bounds rect: 229. 395.5 374. 432.5
6888 %mag rect: 229 395 374 433
7031 229.5 396. 373.5 432. rp
7034 %%DSIBeginObject: #16 - Ref:18 Line
7035 %bounds rect: 175.5 442.0312 230.75 457.75
7036 %mag rect: 175 442 231 458
7052 %%DSIBeginObject: #17 - Ref:15 Line
7053 %bounds rect: 149.5313 394.75 165.25 432.
7054 %mag rect: 149 394 166 432
7071 %%DSIBeginObject: #18 - Ref:27 Group
7072 %bounds rect: 175.5 482.5312 374.75 562.5
7073 %mag rect: 175 482 375 563
7074 %%DSIBeginObject: #19 - Ref:19 Line
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7076 %mag rect: 175 482 375 499
7092 %%DSIBeginObject: #20 - Ref:24 Group
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7097 %mag rect: 222 508 311 537
7102 (a + L) 6 3 62.3274 tf
7104 %%DSIBeginObject: #22 - Ref:23 Text
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7106 %mag rect: 273 534 313 563
7112 %%DSIBeginObject: #23 - Ref:25 Line
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7126 %%DSIBeginObject: #24 - Ref:20 Line
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7130 % MiterAngle LineWidth MiterLimit: 0.1047 1. 19.1071
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7150 %mag rect: 190 454 231 483
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7171 (b + L) 6 3 63.6871 tf
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7175 %mag rect: 81 354 104 357
7177 % MiterAngle LineWidth MiterLimit: 0.1396 2. 14.3349
7185 %%DSIBeginObject: #29 - Ref:33 Text
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7187 %mag rect: 82 360 123 388
7198 dvidict /endTexFig get exec
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7208 297473 r(Only)S(the)s o
7212 -18205 X(hildren)S(of)S(the)S(ro)s
7213 18205 r(ot)S(are)S(sho)T(wn;)s
7214 177164 r(eac)T(h)S(is)S(iden-)s o y u
7217 -18205 X(y)S(a)S(distinctiv)T(e)S(shading.)s
7218 291093 r(Note)S(that)S(three)s o y u
7221 -18205 r(hildren)S(are)S(\\wrapp)s
7222 18205 r(ed-around")S(squares.)s O
7225 149559 W(the)S(dissection)S(is)S(de\fned)S(b)s
7226 -18205 r(y)S(shifting)S(the)S
7235 18205 X(ordinates)S(of)S(all)S(lines)S(b)s
7240 f5(resp)T(ec-)s o y u
7245 270832 W(then)S(reducing)S(mo)s
7249 448407 r(In)S(other)s o y u
7253 198414 W(middle)S(v)T(ertical)S(line)S(of)S(the)S(dissection)s o y u
7256 -18205 W(v)S(ed)T(from)T(the)T
7277 191738 W(the)S(middle)S(hor-)s o y u
7280 298222 W(line)S(from)S(the)S
7286 f5(2)S(to)S(the)s o y u
7303 293872 W(rest)S(of)S(the)s o y u
7304 17363435 r(dissection)s
7305 325184 W(is)S(then)S(\\wrapp)s
7306 18205 r(ed-around,")S(so)S(that)s o y u
7308 239520 W(left)S(edge)S(of)S(the)S(dissection)S(comes)S(to)S
7317 288818 r(and)S(the)S(lo)s
7319 274745 W(edge)S(of)S(the)s o y u
7320 17363435 r(dissection)s
7321 278068 W(comes)S(to)S(rest)S(at)S(the)S
7329 199375 W(Figure)S(2\).)s
7330 284912 r(Note)S(that)S(w)s
7331 -18205 r(e)S(treat)S(a)S(\\wrapp)s
7333 17363435 r(around")s
7334 312374 W(square)S(in)S(the)S(shifted)S(dissection)S(as)S(a)s o y u
7337 200279 r(this)S(will)S(greatly)S(simplify)S(notation)s o y u
7340 225216 W(reader)S(can)S(also)S(think)S(of)S(a)S(wrapp)s
7343 296155 W(square)S(as)S(a)S(disjoin)s
7344 -18205 r(t)S(union)S(of)S(2)S(\(or)S(4\))s o y u
7345 17363435 r(rectangles.)s o
7351 167480 W(with)S(shift)S
7355 f5(\))T(is)T(obtained)T(from)s o y u
7358 18205 r(onding)S(shifted)S(dissection)S(b)s
7359 -18205 r(y)S(cutting)s o y u
7361 173499 W(the)S(partitioning)S(at)S(squares)S(that)S(con)s
7362 -18205 r(tain)S(only)s o y u
7364 255946 W(input)S(p)s
7367 403751 r(It)S(is)S(easy)S(to)S(see)S(that)S(in)S
7370 310814 W(the)S(shifted)S(quadtree)S(has)S(a)S(v)s
7371 -18205 X(ery)S(di\013eren)T(t)s o y u
7372 17363435 r(structure)s
7373 218453 W(than)S(the)S(original)S(quadtree.)s o
7379 -20935 X(harging)S(argumen)T(t)s o y u
7383 233733 X(w)S(e)T(describ)s
7384 18205 r(e)T(our)T(c)S(harging)T(argumen)S(t.)s
7390 -18205 X(e)S(ha)T(v)T(e)S(a)S(collection)S
7393 f5(of)S(line)S(segmen)T(ts)S(in)s o y u
7397 18205 r(ose)S(the)S(minim)s
7398 -18205 r(um)S(length)S(of)S(a)s o y u
7404 f5(is)S(at)S(least)S(4)S(units,)s
7405 202494 r(and)S(the)S(sum)S(of)s o y u
7406 17363435 r(lengths)s
7407 172936 W(is)s u w(cost)s o
7412 276099 r(Consider)S(a)S(shifted)S(dissection)s o y u
7414 160889 W(random)S(shifts)S
7419 -18205 X(harging)S(argumen)T(t)s o y u
7422 320546 W(at)S(the)S(n)s
7423 -18205 W(um)S(b)T(er)s
7424 320546 W(of)S(times)S
7428 -36409 r(ari-)s o y u
7430 248120 W(squares)S(in)S(the)S(dissection,)s
7431 255536 r(and)S(allo)s
7432 -18205 r(ws)S(some)s o y u
7436 -18205 r(harged)S(in)S(prop)T(ortion)S(to)S(this)S(n)s
7437 -18205 r(um-)s o y u
7441 254487 W(main)S(lemma)S(b)T(ounds)S(from)S(ab)T(o)s
7443 254487 r(the)s O O O
7458 9974634 8525330 2960179 9406791 32298844 34403860 startTexFig
7460 %%BeginDocument: dissect2.eps
7461 %!PS-Adobe-3.0 EPSF-3.0
7462 %%BoundingBox: 45 143 491 523
7463 %%Title: dissect2.eps
7465 %%CreationDate: Sunday, January 19, 1997 22:55:17
7466 %%DocumentResources: procset Deneba_CanvasCustomColors
7467 %%+ procset Deneba_CanvasGraphics
7469 %%+ font Arial-BoldMT
7470 %%DocumentSuppliedResources: procset Deneba_CanvasCustomColors
7471 %%+ procset Deneba_CanvasGraphics
7473 %%+ font Arial-BoldMT
7474 %%DocumentProcessColors: Cyan Magenta Yellow Black
7475 %%Copyright: (C) 1996 Deneba Systems. All Rights Reserved
7478 %%BeginResource: procset Deneba_CanvasGraphics
7479 %%Title: Deneba standard graphics
7481 %%CreationDate: 10/1/94
7482 %%Copyright: (C) 1994 Deneba Systems. All Rights Reserved
7483 userdict /Deneba_CanvasGraphics 300 dict put
7484 Deneba_CanvasGraphics begin
7485 /invalidcolortable? true def
7486 /level2 /languagelevel where {pop languagelevel 2 ge}{false} ifelse def
7488 {Deneba_CanvasGraphics
7489 {dup xcheck{bind}if pop pop}forall
7490 currentscreen /_sp exch def /_sa exch def /_sf exch def
7491 /DefaultScreen{_sf _sa /_sp load}def
7492 /DefaultScreenProc{ /_sp load}def
7493 /setstrokeadjust where{pop true}{false}ifelse
7494 {/sa /setstrokeadjust load def
7495 /li /lineto load def
7496 /mt /moveto load def
7497 /ct /curveto load def
7498 /lh { currentpoint exch pop lineto}bind def
7499 /lv { currentpoint pop exch lineto}bind def}
7500 {/sa{{currentdict StrokeAdjustDict ne{StrokeAdjustDict begin}if}{ currentdict StrokeAdjustDict eq{end}if}ifelse} bind def
7501 userdict /StrokeAdjustDict 10 dict put
7502 StrokeAdjustDict begin
7505 .25 sub round .25 add exch
7506 .25 sub round .25 add exch
7509 /li{ _xl lineto}bind def
7510 /mt{ _xl moveto}bind def
7511 /ct{ _xl curveto}bind def
7512 /lh { dup _xl pop currentpoint exch pop lineto}bind def
7513 /lv { dup _xl pop currentpoint pop exch lineto}bind def
7514 /rp{_xl/cv_b xdf/cv_r xdf
7515 _xl/cv_t xdf/cv_l xdf
7524 {userdict /StrokeAdjustDict known {currentdict StrokeAdjustDict eq{end}if}if
7525 currentdict Deneba_CanvasGraphics eq{end}if}def
7527 /mxStk [mxMax {matrix} repeat]def
7529 /stm{mxStk mxIdx get currentmatrix pop
7530 /mxIdx mxIdx 1 add store}def
7531 /rtm{/mxIdx mxIdx 1 sub store
7532 mxStk mxIdx get setmatrix}def
7535 /_initmtx matrix def
7537 /min{2 copy gt{exch}if pop}def
7538 /max{2 copy lt{exch}if pop}def
7539 /CVvec 256 array def
7544 /_encodArr 10 array def
7565 /savehandler null def
7567 {dup /$eps exch not def{/savehandler errordict /handleerror get def
7569 /handleerror{$error begin
7570 newerror{/newerror false def
7573 /Helvetica findfont .2 scalefont setfont
7577 {dup type/stringtype ne
7578 {(converted error name will end up in this string)cvs}if
7581 (Offending Command: )show
7583 {dup type/stringtype ne
7584 {(converted command name will end up in this string)cvs}if
7589 {.25 currentpoint .2 sub exch pop moveto
7590 dup type/stringtype ne{dup type/integertype eq
7591 1 index type/realtype eq or
7592 1 index type/nametype eq or
7594 (converted stack will end up in this string)cvs}if
7597 Deneba_CanvasGraphics /savehandler get exec}if
7601 /lm{setmiterlimit}def
7607 /gs{gsave $psz dup $pix _penh put $pix 1 add _penv put /$pix $pix 2 add def}def
7608 /gr{grestore/$pix $pix 2 sub def $psz dup $pix get /_penh exch def $pix 1 add get /_penv exch def}def
7610 /lh{currentpoint exch pop lineto}def
7611 /lv{currentpoint pop exch lineto}def
7613 /mh{currentpoint exch pop moveto}def
7614 /mv{currentpoint pop exch moveto}def
7616 /rt{4 -2 roll moveto
7622 {{currentflat dup{gsave{eoclip}stopped{grestore 2 mul dup setflat dup 200 ge{pop pop exit}if}{grestore setflat exit}ifelse}loop eoclip setflat}
7623 {currentflat dup{gsave{clip}stopped{grestore 2 mul dup setflat dup 200 ge{pop pop exit}if}{grestore setflat exit}ifelse}loop clip setflat}}def
7625 /fg{$eps{systemdict /setgray get exec}{setgray}ifelse}def
7626 /setcmykcolor where {pop true}{false}ifelse
7627 {/f4{ setcmykcolor}def}{/f4{1 sub 4 1 roll 3{3 index add neg dup 0 lt{pop 0}if 3 1 roll}repeat setrgbcolor pop}def}ifelse
7628 /setcolorspace where {pop true}{false}ifelse
7629 {/scs{ dup setcolorspace /_cs exch def}def/f3{ _cs setcolorspace setcolor}def
7630 }{/f3{ setrgbcolor}def/scs{ pop}def}ifelse
7632 /findcmykcustomcolor where {pop true}{false}ifelse
7633 not {/findcmykcustomcolor{$cc astore}def}if
7634 /setcustomcolor where {pop true}{false}ifelse
7635 not{/setcustomcolor{exch aload pop pop 4{4 index mul 4 1 roll}repeat setcmykcolor pop}def}if
7636 /fc{6 1 roll findcmykcustomcolor exch setcustomcolor}def
7637 /setseparationgray where {pop true}{false}ifelse
7638 not{/setseparationgray {systemdict /setgray get exec} def}if
7639 /sg{ setseparationgray}def
7640 /sp{/_penv xdf/_penh xdf}def
7655 cv_l xradius add cv_t moveto
7656 cv_r xradius sub cv_t lineto
7657 _cvmtx currentmatrix pop
7658 currentpoint translate
7659 xradius yradius scale
7660 1 0 1 1 1 arcto 4{pop}repeat
7662 cv_r cv_b yradius sub lineto
7663 _cvmtx currentmatrix pop
7664 currentpoint translate
7665 xradius yradius scale
7666 0 1 -1 1 1 arcto 4{pop}repeat
7668 cv_l xradius add cv_b lineto
7669 _cvmtx currentmatrix pop
7670 currentpoint translate
7671 xradius yradius scale
7672 -1 0 -1 -1 1 arcto 4{pop}repeat
7674 cv_l cv_t yradius add lineto
7675 _cvmtx currentmatrix pop
7676 currentpoint translate
7677 xradius yradius scale
7678 0 -1 1 -1 1 arcto 4{pop}repeat
7681 /ep{_cvmtx currentmatrix pop
7687 _cvmtx setmatrix}def
7688 /wd{_cvmtx currentmatrix pop
7692 0 0 1 5 -2 roll arcn
7694 _cvmtx setmatrix}def
7695 /as{_cvmtx currentmatrix pop
7698 0 0 1 5 -2 roll arcn
7699 _cvmtx setmatrix}def
7701 {_penv _penh ne dup{stm _penh dup 0 le{pop 1}if _penv dup 0 le{pop 1}if scale}{_penh setlinewidth}ifelse stroke {rtm}if}def
7706 /_gst{ 9 dict begin level2{/_ccs currentcolorspace def /_cc [currentcolor] def}{/_cc [currentrgbcolor]def}ifelse {currentpoint}stopped {/_cp null def}{ 2 array astore /_cp exch def}ifelse /_cf currentfont def
7707 /_clw currentlinewidth def /_clc currentlinecap def /_clj currentlinejoin def /_cml currentmiterlimit def currentdict end}def
7708 /hs{newpath gsave stm}def
7709 /hc{/_hr load exch get exec newpath}def
7710 /he{_gstk _gstkc _gst put /_gstkc _gstkc 1 add store
7711 grestore rtm /_gstkc _gstkc 1 sub store _gstk _gstkc get level2{dup /_ccs get setcolorspace dup /_cc get aload pop setcolor}{dup /_cc get aload pop setrgbcolor}ifelse dup /_cp get dup null eq
7712 not{aload pop moveto}{pop}ifelse dup /_cf get setfont
7713 dup/_clw get setlinewidth dup/_clc get setlinecap dup/_clj get setlinejoin dup/_cml get setmiterlimit pop}def
7715 /_imatrix{_w 0 0 _h _id 0 ne{neg 0 _h}{0 0}ifelse _cvmtx astore}def
7716 % Copyright (C) 1990, 1991 by Adobe Systems Incorporated.
7717 % All rights reserved.
7718 level2 { save /dontloadlevel1 xdf }if
7719 /startnoload{{/noload save def} if}def
7720 /endnoload{{noload restore}if }def
7721 /testsystemdict{where{systemdict eq{true}{false}ifelse}{false}ifelse}def
7723 /colorimage where{pop true}{false}ifelse{/ncolors 0
7725 /processcolors where{pop pop processcolors}{/deviceinfo where{pop deviceinfo /Colors known
7726 {pop {deviceinfo /Colors get}}if}if}ifelse end def
7727 ncolors 0 ne{/colorimage testsystemdict
7728 /setcolortransfer testsystemdict
7729 /currentcolortransfer testsystemdict
7730 /currentcmykcolor testsystemdict
7731 and and and not{/ncolors 0 def}if}if}if
7732 ncolors dup 1 ne exch dup 3 ne exch 4 ne and and {/ncolors 0 def}if
7733 ncolors 1 eq dup dup not startnoload
7734 {/doclutimage{[{255 mul round cvi bwclut exch get 255 div} /exec load dup currenttransfer exch]
7735 cvx bind settransfer _w _h 8 _imatrix {currentfile st0 readhexstring pop}image}def}if
7737 ncolors dup 3 eq exch 4 eq or
7738 dup dup not startnoload
7739 {/nullproc{{}}def/concatutil{/exec load
7740 7 -1 roll /exec load}def
7742 {1 add getinterval def}def
7744 {/Dclut exch def/Cclut exch def/Bclut exch def/Aclut exch def/ncompute exch ld
7745 currentcolortransfer
7746 [{Aclut ncompute}concatutil] cvx
7747 [{Bclut ncompute}concatutil] cvx
7748 [{Cclut ncompute}concatutil] cvx
7749 [{Dclut ncompute}concatutil] cvx
7750 setcolortransfer}def
7752 {/bit3x rgbclut length 3 sub def
7753 /bit1x bit3x 3 idiv def/rclut rgbclut def
7754 /gclut rclut 1 bit3x defsubclut/bclut rclut 2 bit3x defsubclut}def}if not
7755 endnoload ncolors 3 eq dup dup not startnoload
7756 {/3compute{exch bit3x mul
7757 round cvi get 255 div}def
7758 /doclutimage{%/rgbclut xdf pop
7759 setuprgbcluts/3compute rclut gclut bclut dup
7760 spconcattransfer _w _h 8 _imatrix
7761 [{currentfile st0 readhexstring pop}/exec load
7763 nullproc nullproc true 3 colorimage}def}if not endnoload ncolors 4 eq dup dup not startnoload
7764 {/stuffclut{cmykindex 3 -1 roll put}def
7765 /ftoint{1 exch sub 255 mul round cvi}def
7766 /4compute { exch bit4x mul round cvi get 255 div } def
7767 /computecmykclut{setuprgbcluts/bit4x rgbclut length 3 idiv 4 mul 4 sub def
7768 /cmykclut bit4x 4 add string def
7770 /mclut cclut 1 bit4x defsubclut
7771 /yclut cclut 2 bit4x defsubclut
7772 /kclut cclut 3 bit4x defsubclut
7775 {dup /cmykindex exch bit1x exch sub 4 mul def
7776 3 mul dup rclut exch get 255 div exch dup gclut exch get 255 div
7777 exch bclut exch get 255 div
7778 setrgbcolor currentcmykcolor
7779 ftoint kclut stuffclut
7780 ftoint yclut stuffclut
7781 ftoint mclut stuffclut
7782 ftoint cclut stuffclut
7784 /doclutimage{invalidcolortable?{computecmykclut}if
7785 /4compute cclut mclut yclut kclut spconcattransfer
7786 _w _h 8 _imatrix[{currentfile st0 readhexstring pop}/exec load/dup load dup dup] cvx
7787 nullproc nullproc nullproc true 4 colorimage}def}if
7790 dup dup not startnoload
7791 {/colorexpand{mystringexp 0 rgbclut
7794 {3 mul 3 getinterval putinterval exch 3 add exch 3 copy}forall
7795 pop pop pop pop pop}def
7796 /createexpandstr{/mystringexp exch st0 length mul string def}def
7797 /doclutimage{/rgbclut xdf pop 3 createexpandstr _w _h 8 _imatrix
7798 [{currentfile st0 readhexstring pop} /exec load /colorexpand load /exec load] cvx
7799 false 3 colorimage}def}if not endnoload
7800 level2 { dontloadlevel1 restore }if
7801 level2 not{ save /dontloadlevel2 xdf }if
7802 /rgbclut 0 def/doclutimage{/hival 255 def
7803 [/Indexed /DeviceRGB hival rgbclut] setcolorspace
7804 _imagedict dup begin
7807 /Decode [0 hival] def
7808 /ImageMatrix _imatrix def
7809 /DataSource{currentfile st0 readhexstring pop}def
7810 /BitsPerComponent 8 def
7811 /Interpolate false def
7813 level2 not{ dontloadlevel2 restore }if
7815 /_imagedict 12 dict begin /ImageType 1 def/BitsPerComponent 8 def/Interpolate false def currentdict end def
7816 /$rhs0 {currentfile st0 readhexstring pop}def
7817 /$rhs1 {currentfile st1 readhexstring pop}def
7818 /$rhs2 {currentfile st2 readhexstring pop}def
7819 /$rhs3 {currentfile st3 readhexstring pop}def
7820 /$rhs4 {currentfile st4 readhexstring pop}def
7821 /$rs0 {currentfile st0 readstring pop}def
7822 /$rs1 {currentfile st1 readstring pop}def
7823 /$rs2 {currentfile st2 readstring pop}def
7824 /$rs3 {currentfile st3 readstring pop}def
7825 /$rs4 {currentfile st4 readstring pop}def
7828 {pop deviceinfo /Colors known
7829 {deviceinfo /Colors get exec 1 gt}
7832 {pop statusdict /processcolors known
7833 {statusdict /processcolors get exec 1 gt}
7834 {false} ifelse}{false} ifelse}ifelse
7836 /level2 systemdict /languagelevel known
7837 {languagelevel 2 ge}{false}ifelse def
7838 /foureq {4 index eq 8 1 roll
7842 pop pop pop pop and and and} def
7844 /_settransfer systemdict /settransfer get def
7845 /_currenttransfer systemdict /currenttransfer get def
7846 /_image systemdict /image get def
7847 /blank 0 _currenttransfer exec
7848 1 _currenttransfer exec eq def
7849 /negative blank{0 _currenttransfer exec 0.5 lt}
7850 {0 _currenttransfer exec 1 _currenttransfer exec gt}ifelse def
7851 /inverted? negative def
7852 /_currentgray systemdict /currentgray get def
7853 hascolor{/$b 0 def} {/$b 5 def} ifelse
7854 /setcmykcolor where{pop 1 0 0 0 setcmykcolor _currentgray 1 exch sub
7855 0 1 0 0 setcmykcolor _currentgray 1 exch sub
7856 0 0 1 0 setcmykcolor _currentgray 1 exch sub
7857 0 0 0 1 setcmykcolor _currentgray 1 exch sub
7859 1 0 0 0 foureq{/$b 1 store}if
7860 0 1 0 0 foureq{/$b 2 store}if
7861 0 0 1 0 foureq{/$b 3 store}if
7862 0 0 0 1 foureq{/$b 4 store}if
7863 0 0 0 0 foureq{/$b 6 store}if}if
7864 blank{/$b 6 store}if
7865 $b 0 eq $b 5 eq or{/$dt 0 def}if/$dt -1 def grestore}def
7867 1 index 0 eq{dup dup/Width get exch /Decode get length 2 div mul cvi}{dup/Width get}ifelse
7868 /st0 exch string def
7870 /MultipleDataSources false def
7871 dup 0 eq{pop/DataSource {$rhs0} def}
7872 {1 eq{/DataSource {$rs0} def}{/DataSource currentfile /ASCII85Decode filter def}ifelse}ifelse
7875 Width Height BitsPerComponent ImageMatrix
7877 {/DataSource load end image}{
7879 {MultipleDataSources{DataSource 0 get DataSource 1 get DataSource 2 get}{/DataSource load}ifelse
7880 MultipleDataSources 3 end DSIColorImage}{
7881 Decode length 8 eq{MultipleDataSources{DataSource 0 get DataSource 1 get
7882 DataSource 2 get DataSource 3 get}{/DataSource load}ifelse
7883 MultipleDataSources 4 end DSIColorImage}if}ifelse
7886 /dt{/rgbclut xdf /bwclut xdf}def
7887 /cl{pop gsave $i setmatrix translate scale
7888 cvi/_h xdf cvi/_w xdf/st0 _w string def pop doclutimage grestore}def
7889 /c3{/imagesave save def
7890 /$src xdf $i setmatrix translate scale cvi/_h xdf cvi/_w xdf
7891 level2{_cs setcolorspace}if
7895 /ImageMatrix _imatrix def
7896 /Decode [0 1 0 1 0 1]def
7897 currentdict end exch
7899 imagesave restore}def
7900 /ca{/imagesave save def
7901 /$src xdf $i setmatrix translate scale cvi/_h xdf cvi/_w xdf
7902 level2{_cs setcolorspace}if
7904 /Decode[0 100 -128 127 -128 127]def
7907 /ImageMatrix _imatrix def
7908 currentdict end exch
7910 imagesave restore}def
7911 /c4{/imagesave save def
7912 /$src xdf $i setmatrix translate scale cvi/_h xdf cvi/_w xdf
7913 level2 {/DeviceCMYK setcolorspace}if
7915 /Decode [0 1 0 1 0 1 0 1] def
7918 /ImageMatrix _imatrix def
7919 currentdict end exch
7921 imagesave restore}def
7922 /im{/imagesave save def
7923 pop $i setmatrix translate scale cvi/_h xdf cvi/_w xdf
7924 level2{/DeviceGray setcolorspace}if
7929 /ImageMatrix _imatrix def
7930 currentdict end exch
7932 imagesave restore}def
7933 /colorimage where{pop/DSIColorImage {colorimage} def}{/DSIColorImage{
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8876 %bounds rect: 359.5 287.5 432.5 360.5
8877 %mag rect: 359 287 433 361
8878 %%DSIBeginObject: #73 - Ref:75 Rectangle
8879 %bounds rect: 359.5 287.5 396.5 324.5
8880 %mag rect: 359 287 397 325
8883 360. 288. 396. 324. rp
8887 360. 288. 396. 324. rp
8890 %%DSIBeginObject: #74 - Ref:76 Rectangle
8891 %bounds rect: 395.5 287.5 432.5 324.5
8892 %mag rect: 395 287 433 325
8895 396. 288. 432. 324. rp
8899 396. 288. 432. 324. rp
8902 %%DSIBeginObject: #75 - Ref:77 Rectangle
8903 %bounds rect: 395.5 323.5 432.5 360.5
8904 %mag rect: 395 323 433 361
8907 396. 324. 432. 360. rp
8911 396. 324. 432. 360. rp
8914 %%DSIBeginObject: #76 - Ref:78 Rectangle
8915 %bounds rect: 359.5 323.5 396.5 360.5
8916 %mag rect: 359 323 397 361
8919 360. 324. 396. 360. rp
8923 360. 324. 396. 360. rp
8927 %%DSIBeginObject: #77 - Ref:79 Group
8928 %bounds rect: 287.5 359.5 360.5 432.5
8929 %mag rect: 287 359 361 433
8930 %%DSIBeginObject: #78 - Ref:80 Rectangle
8931 %bounds rect: 287.5 359.5 324.5 396.5
8932 %mag rect: 287 359 325 397
8935 288. 360. 324. 396. rp
8939 288. 360. 324. 396. rp
8942 %%DSIBeginObject: #79 - Ref:81 Rectangle
8943 %bounds rect: 323.5 359.5 360.5 396.5
8944 %mag rect: 323 359 361 397
8947 324. 360. 360. 396. rp
8951 324. 360. 360. 396. rp
8954 %%DSIBeginObject: #80 - Ref:82 Rectangle
8955 %bounds rect: 323.5 395.5 360.5 432.5
8956 %mag rect: 323 395 361 433
8959 324. 396. 360. 432. rp
8963 324. 396. 360. 432. rp
8966 %%DSIBeginObject: #81 - Ref:83 Rectangle
8967 %bounds rect: 287.5 395.5 324.5 432.5
8968 %mag rect: 287 395 325 433
8971 288. 396. 324. 432. rp
8975 288. 396. 324. 432. rp
8979 %%DSIBeginObject: #82 - Ref:84 Group
8980 %bounds rect: 359.5 359.5 432.5 432.5
8981 %mag rect: 359 359 433 433
8982 %%DSIBeginObject: #83 - Ref:85 Rectangle
8983 %bounds rect: 359.5 359.5 396.5 396.5
8984 %mag rect: 359 359 397 397
8987 360. 360. 396. 396. rp
8991 360. 360. 396. 396. rp
8994 %%DSIBeginObject: #84 - Ref:86 Rectangle
8995 %bounds rect: 395.5 359.5 432.5 396.5
8996 %mag rect: 395 359 433 397
8999 396. 360. 432. 396. rp
9003 396. 360. 432. 396. rp
9006 %%DSIBeginObject: #85 - Ref:87 Rectangle
9007 %bounds rect: 395.5 395.5 432.5 432.5
9008 %mag rect: 395 395 433 433
9011 396. 396. 432. 432. rp
9015 396. 396. 432. 432. rp
9018 %%DSIBeginObject: #86 - Ref:88 Rectangle
9019 %bounds rect: 359.5 395.5 396.5 432.5
9020 %mag rect: 359 395 397 433
9023 360. 396. 396. 432. rp
9027 360. 396. 396. 432. rp
9033 %%DSIBeginObject: #87 - Ref:89 Text
9034 %bounds rect: 252.875 247.5 347. 328.5
9035 %mag rect: 252 247 347 329
9041 %%DSIBeginObject: #88 - Ref:90 Text
9042 %bounds rect: 180.875 207. 275. 288.
9043 %mag rect: 180 207 275 288
9049 %%DSIBeginObject: #89 - Ref:91 Text
9050 %bounds rect: 144.875 175.5 239. 256.5
9051 %mag rect: 144 175 239 257
9057 %%DSIBeginObject: #90 - Ref:92 Text
9058 %bounds rect: 320.375 180. 414.5 261.
9059 %mag rect: 320 180 415 261
9065 %%DSIBeginObject: #91 - Ref:93 Text
9066 %bounds rect: 396.875 283.5 491. 364.5
9067 %mag rect: 396 283 491 365
9073 %%DSIBeginObject: #92 - Ref:94 Text
9074 %bounds rect: 288.875 315. 383. 396.
9075 %mag rect: 288 315 383 396
9081 %%DSIBeginObject: #93 - Ref:95 Text
9082 %bounds rect: 216.875 279. 311. 360.
9083 %mag rect: 216 279 311 360
9090 %%DSIBeginObject: #94 - Ref:2 Line
9091 %bounds rect: 285. 144. 291. 432.
9092 %mag rect: 285 144 291 432
9094 % MiterAngle LineWidth MiterLimit: 0.1396 6. 14.3349
9102 %%DSIBeginObject: #95 - Ref:96 Line
9103 %bounds rect: 144. 285. 432. 291.
9104 %mag rect: 144 285 432 291
9110 %%DSIBeginObject: #96 - Ref:100 Line
9111 %bounds rect: 144. 214.5 432. 217.5
9112 %mag rect: 144 214 432 218
9119 %%DSIBeginObject: #97 - Ref:101 Line
9120 %bounds rect: 144. 358.5 432. 361.5
9121 %mag rect: 144 358 432 362
9127 %%DSIBeginObject: #98 - Ref:97 Line
9128 %bounds rect: 214.5 144. 217.5 432.
9129 %mag rect: 214 144 218 432
9135 %%DSIBeginObject: #99 - Ref:102 Line
9136 %bounds rect: 358.5 144. 361.5 432.
9137 %mag rect: 358 144 362 432
9143 %%DSIBeginObject: #100 - Ref:107 Group
9144 %bounds rect: 144. 446.5312 288.25 523.
9145 %mag rect: 144 446 289 523
9146 %%DSIBeginObject: #101 - Ref:98 Line
9147 %bounds rect: 144. 446.5312 288.25 462.25
9148 %mag rect: 144 446 289 463
9150 % MiterAngle LineWidth MiterLimit: 0.1047 1. 19.1071
9168 %%DSIBeginObject: #102 - Ref:106 Group
9169 %bounds rect: 189. 459. 236. 523.
9170 %mag rect: 189 459 236 523
9171 %%DSIBeginObject: #103 - Ref:103 Text
9172 %bounds rect: 195.125 459. 236. 487.
9173 %mag rect: 195 459 236 487
9179 %%DSIBeginObject: #104 - Ref:104 Text
9180 %bounds rect: 195.125 495. 235. 523.
9181 %mag rect: 195 495 235 523
9187 %%DSIBeginObject: #105 - Ref:105 Line
9188 %bounds rect: 189. 489.5 225. 491.5
9189 %mag rect: 189 489 225 492
9191 % MiterAngle LineWidth MiterLimit: 0.1396 2. 14.3349
9201 %%DSIBeginObject: #106 - Ref:112 Group
9202 %bounds rect: 45. 287.7501 114.75 432.
9203 %mag rect: 45 287 115 432
9204 %%DSIBeginObject: #107 - Ref:99 Line
9205 %bounds rect: 100.5313 287.7501 114.75 432.
9206 %mag rect: 100 287 115 432
9208 % MiterAngle LineWidth MiterLimit: 0.1047 1. 19.1071
9217 107.6854 287.7501 mt
9219 107.6854 294.4319 li
9221 107.6854 287.7501 li
9226 %%DSIBeginObject: #108 - Ref:108 Group
9227 %bounds rect: 45. 328.5 92. 392.5
9228 %mag rect: 45 328 92 393
9229 %%DSIBeginObject: #109 - Ref:109 Text
9230 %bounds rect: 51.125 328.5 92. 356.5
9231 %mag rect: 51 328 92 357
9237 %%DSIBeginObject: #110 - Ref:110 Text
9238 %bounds rect: 51.125 364.5 91. 392.5
9239 %mag rect: 51 364 91 393
9245 %%DSIBeginObject: #111 - Ref:111 Line
9246 %bounds rect: 45. 359. 81. 361.
9247 %mag rect: 45 359 81 361
9249 % MiterAngle LineWidth MiterLimit: 0.1396 2. 14.3349
9264 dvidict /endTexFig get exec
9272 9633622 8525330 3552215 7038648 36114186 35785277 startTexFig
9274 %%BeginDocument: quad.eps
9275 %!PS-Adobe-3.0 EPSF-3.0
9276 %%BoundingBox: 54 107 549 544
9279 %%CreationDate: Sunday, January 19, 1997 22:55:40
9280 %%DocumentResources: procset Deneba_CanvasCustomColors
9281 %%+ procset Deneba_CanvasGraphics
9283 %%+ font Arial-BoldMT
9284 %%DocumentSuppliedResources: procset Deneba_CanvasCustomColors
9285 %%+ procset Deneba_CanvasGraphics
9287 %%+ font Arial-BoldMT
9288 %%DocumentProcessColors: Cyan Magenta Yellow Black
9289 %%Copyright: (C) 1996 Deneba Systems. All Rights Reserved
9292 %%BeginResource: procset Deneba_CanvasGraphics
9293 %%Title: Deneba standard graphics
9295 %%CreationDate: 10/1/94
9296 %%Copyright: (C) 1994 Deneba Systems. All Rights Reserved
9297 userdict /Deneba_CanvasGraphics 300 dict put
9298 Deneba_CanvasGraphics begin
9299 /invalidcolortable? true def
9300 /level2 /languagelevel where {pop languagelevel 2 ge}{false} ifelse def
9302 {Deneba_CanvasGraphics
9303 {dup xcheck{bind}if pop pop}forall
9304 currentscreen /_sp exch def /_sa exch def /_sf exch def
9305 /DefaultScreen{_sf _sa /_sp load}def
9306 /DefaultScreenProc{ /_sp load}def
9307 /setstrokeadjust where{pop true}{false}ifelse
9308 {/sa /setstrokeadjust load def
9309 /li /lineto load def
9310 /mt /moveto load def
9311 /ct /curveto load def
9312 /lh { currentpoint exch pop lineto}bind def
9313 /lv { currentpoint pop exch lineto}bind def}
9314 {/sa{{currentdict StrokeAdjustDict ne{StrokeAdjustDict begin}if}{ currentdict StrokeAdjustDict eq{end}if}ifelse} bind def
9315 userdict /StrokeAdjustDict 10 dict put
9316 StrokeAdjustDict begin
9319 .25 sub round .25 add exch
9320 .25 sub round .25 add exch
9323 /li{ _xl lineto}bind def
9324 /mt{ _xl moveto}bind def
9325 /ct{ _xl curveto}bind def
9326 /lh { dup _xl pop currentpoint exch pop lineto}bind def
9327 /lv { dup _xl pop currentpoint pop exch lineto}bind def
9328 /rp{_xl/cv_b xdf/cv_r xdf
9329 _xl/cv_t xdf/cv_l xdf
9338 {userdict /StrokeAdjustDict known {currentdict StrokeAdjustDict eq{end}if}if
9339 currentdict Deneba_CanvasGraphics eq{end}if}def
9341 /mxStk [mxMax {matrix} repeat]def
9343 /stm{mxStk mxIdx get currentmatrix pop
9344 /mxIdx mxIdx 1 add store}def
9345 /rtm{/mxIdx mxIdx 1 sub store
9346 mxStk mxIdx get setmatrix}def
9349 /_initmtx matrix def
9351 /min{2 copy gt{exch}if pop}def
9352 /max{2 copy lt{exch}if pop}def
9353 /CVvec 256 array def
9358 /_encodArr 10 array def
9379 /savehandler null def
9381 {dup /$eps exch not def{/savehandler errordict /handleerror get def
9383 /handleerror{$error begin
9384 newerror{/newerror false def
9387 /Helvetica findfont .2 scalefont setfont
9391 {dup type/stringtype ne
9392 {(converted error name will end up in this string)cvs}if
9395 (Offending Command: )show
9397 {dup type/stringtype ne
9398 {(converted command name will end up in this string)cvs}if
9403 {.25 currentpoint .2 sub exch pop moveto
9404 dup type/stringtype ne{dup type/integertype eq
9405 1 index type/realtype eq or
9406 1 index type/nametype eq or
9408 (converted stack will end up in this string)cvs}if
9411 Deneba_CanvasGraphics /savehandler get exec}if
9415 /lm{setmiterlimit}def
9421 /gs{gsave $psz dup $pix _penh put $pix 1 add _penv put /$pix $pix 2 add def}def
9422 /gr{grestore/$pix $pix 2 sub def $psz dup $pix get /_penh exch def $pix 1 add get /_penv exch def}def
9424 /lh{currentpoint exch pop lineto}def
9425 /lv{currentpoint pop exch lineto}def
9427 /mh{currentpoint exch pop moveto}def
9428 /mv{currentpoint pop exch moveto}def
9430 /rt{4 -2 roll moveto
9436 {{currentflat dup{gsave{eoclip}stopped{grestore 2 mul dup setflat dup 200 ge{pop pop exit}if}{grestore setflat exit}ifelse}loop eoclip setflat}
9437 {currentflat dup{gsave{clip}stopped{grestore 2 mul dup setflat dup 200 ge{pop pop exit}if}{grestore setflat exit}ifelse}loop clip setflat}}def
9439 /fg{$eps{systemdict /setgray get exec}{setgray}ifelse}def
9440 /setcmykcolor where {pop true}{false}ifelse
9441 {/f4{ setcmykcolor}def}{/f4{1 sub 4 1 roll 3{3 index add neg dup 0 lt{pop 0}if 3 1 roll}repeat setrgbcolor pop}def}ifelse
9442 /setcolorspace where {pop true}{false}ifelse
9443 {/scs{ dup setcolorspace /_cs exch def}def/f3{ _cs setcolorspace setcolor}def
9444 }{/f3{ setrgbcolor}def/scs{ pop}def}ifelse
9446 /findcmykcustomcolor where {pop true}{false}ifelse
9447 not {/findcmykcustomcolor{$cc astore}def}if
9448 /setcustomcolor where {pop true}{false}ifelse
9449 not{/setcustomcolor{exch aload pop pop 4{4 index mul 4 1 roll}repeat setcmykcolor pop}def}if
9450 /fc{6 1 roll findcmykcustomcolor exch setcustomcolor}def
9451 /setseparationgray where {pop true}{false}ifelse
9452 not{/setseparationgray {systemdict /setgray get exec} def}if
9453 /sg{ setseparationgray}def
9454 /sp{/_penv xdf/_penh xdf}def
9469 cv_l xradius add cv_t moveto
9470 cv_r xradius sub cv_t lineto
9471 _cvmtx currentmatrix pop
9472 currentpoint translate
9473 xradius yradius scale
9474 1 0 1 1 1 arcto 4{pop}repeat
9476 cv_r cv_b yradius sub lineto
9477 _cvmtx currentmatrix pop
9478 currentpoint translate
9479 xradius yradius scale
9480 0 1 -1 1 1 arcto 4{pop}repeat
9482 cv_l xradius add cv_b lineto
9483 _cvmtx currentmatrix pop
9484 currentpoint translate
9485 xradius yradius scale
9486 -1 0 -1 -1 1 arcto 4{pop}repeat
9488 cv_l cv_t yradius add lineto
9489 _cvmtx currentmatrix pop
9490 currentpoint translate
9491 xradius yradius scale
9492 0 -1 1 -1 1 arcto 4{pop}repeat
9495 /ep{_cvmtx currentmatrix pop
9501 _cvmtx setmatrix}def
9502 /wd{_cvmtx currentmatrix pop
9506 0 0 1 5 -2 roll arcn
9508 _cvmtx setmatrix}def
9509 /as{_cvmtx currentmatrix pop
9512 0 0 1 5 -2 roll arcn
9513 _cvmtx setmatrix}def
9515 {_penv _penh ne dup{stm _penh dup 0 le{pop 1}if _penv dup 0 le{pop 1}if scale}{_penh setlinewidth}ifelse stroke {rtm}if}def
9520 /_gst{ 9 dict begin level2{/_ccs currentcolorspace def /_cc [currentcolor] def}{/_cc [currentrgbcolor]def}ifelse {currentpoint}stopped {/_cp null def}{ 2 array astore /_cp exch def}ifelse /_cf currentfont def
9521 /_clw currentlinewidth def /_clc currentlinecap def /_clj currentlinejoin def /_cml currentmiterlimit def currentdict end}def
9522 /hs{newpath gsave stm}def
9523 /hc{/_hr load exch get exec newpath}def
9524 /he{_gstk _gstkc _gst put /_gstkc _gstkc 1 add store
9525 grestore rtm /_gstkc _gstkc 1 sub store _gstk _gstkc get level2{dup /_ccs get setcolorspace dup /_cc get aload pop setcolor}{dup /_cc get aload pop setrgbcolor}ifelse dup /_cp get dup null eq
9526 not{aload pop moveto}{pop}ifelse dup /_cf get setfont
9527 dup/_clw get setlinewidth dup/_clc get setlinecap dup/_clj get setlinejoin dup/_cml get setmiterlimit pop}def
9529 /_imatrix{_w 0 0 _h _id 0 ne{neg 0 _h}{0 0}ifelse _cvmtx astore}def
9530 % Copyright (C) 1990, 1991 by Adobe Systems Incorporated.
9531 % All rights reserved.
9532 level2 { save /dontloadlevel1 xdf }if
9533 /startnoload{{/noload save def} if}def
9534 /endnoload{{noload restore}if }def
9535 /testsystemdict{where{systemdict eq{true}{false}ifelse}{false}ifelse}def
9537 /colorimage where{pop true}{false}ifelse{/ncolors 0
9539 /processcolors where{pop pop processcolors}{/deviceinfo where{pop deviceinfo /Colors known
9540 {pop {deviceinfo /Colors get}}if}if}ifelse end def
9541 ncolors 0 ne{/colorimage testsystemdict
9542 /setcolortransfer testsystemdict
9543 /currentcolortransfer testsystemdict
9544 /currentcmykcolor testsystemdict
9545 and and and not{/ncolors 0 def}if}if}if
9546 ncolors dup 1 ne exch dup 3 ne exch 4 ne and and {/ncolors 0 def}if
9547 ncolors 1 eq dup dup not startnoload
9548 {/doclutimage{[{255 mul round cvi bwclut exch get 255 div} /exec load dup currenttransfer exch]
9549 cvx bind settransfer _w _h 8 _imatrix {currentfile st0 readhexstring pop}image}def}if
9551 ncolors dup 3 eq exch 4 eq or
9552 dup dup not startnoload
9553 {/nullproc{{}}def/concatutil{/exec load
9554 7 -1 roll /exec load}def
9556 {1 add getinterval def}def
9558 {/Dclut exch def/Cclut exch def/Bclut exch def/Aclut exch def/ncompute exch ld
9559 currentcolortransfer
9560 [{Aclut ncompute}concatutil] cvx
9561 [{Bclut ncompute}concatutil] cvx
9562 [{Cclut ncompute}concatutil] cvx
9563 [{Dclut ncompute}concatutil] cvx
9564 setcolortransfer}def
9566 {/bit3x rgbclut length 3 sub def
9567 /bit1x bit3x 3 idiv def/rclut rgbclut def
9568 /gclut rclut 1 bit3x defsubclut/bclut rclut 2 bit3x defsubclut}def}if not
9569 endnoload ncolors 3 eq dup dup not startnoload
9570 {/3compute{exch bit3x mul
9571 round cvi get 255 div}def
9572 /doclutimage{%/rgbclut xdf pop
9573 setuprgbcluts/3compute rclut gclut bclut dup
9574 spconcattransfer _w _h 8 _imatrix
9575 [{currentfile st0 readhexstring pop}/exec load
9577 nullproc nullproc true 3 colorimage}def}if not endnoload ncolors 4 eq dup dup not startnoload
9578 {/stuffclut{cmykindex 3 -1 roll put}def
9579 /ftoint{1 exch sub 255 mul round cvi}def
9580 /4compute { exch bit4x mul round cvi get 255 div } def
9581 /computecmykclut{setuprgbcluts/bit4x rgbclut length 3 idiv 4 mul 4 sub def
9582 /cmykclut bit4x 4 add string def
9584 /mclut cclut 1 bit4x defsubclut
9585 /yclut cclut 2 bit4x defsubclut
9586 /kclut cclut 3 bit4x defsubclut
9589 {dup /cmykindex exch bit1x exch sub 4 mul def
9590 3 mul dup rclut exch get 255 div exch dup gclut exch get 255 div
9591 exch bclut exch get 255 div
9592 setrgbcolor currentcmykcolor
9593 ftoint kclut stuffclut
9594 ftoint yclut stuffclut
9595 ftoint mclut stuffclut
9596 ftoint cclut stuffclut
9598 /doclutimage{invalidcolortable?{computecmykclut}if
9599 /4compute cclut mclut yclut kclut spconcattransfer
9600 _w _h 8 _imatrix[{currentfile st0 readhexstring pop}/exec load/dup load dup dup] cvx
9601 nullproc nullproc nullproc true 4 colorimage}def}if
9604 dup dup not startnoload
9605 {/colorexpand{mystringexp 0 rgbclut
9608 {3 mul 3 getinterval putinterval exch 3 add exch 3 copy}forall
9609 pop pop pop pop pop}def
9610 /createexpandstr{/mystringexp exch st0 length mul string def}def
9611 /doclutimage{/rgbclut xdf pop 3 createexpandstr _w _h 8 _imatrix
9612 [{currentfile st0 readhexstring pop} /exec load /colorexpand load /exec load] cvx
9613 false 3 colorimage}def}if not endnoload
9614 level2 { dontloadlevel1 restore }if
9615 level2 not{ save /dontloadlevel2 xdf }if
9616 /rgbclut 0 def/doclutimage{/hival 255 def
9617 [/Indexed /DeviceRGB hival rgbclut] setcolorspace
9618 _imagedict dup begin
9621 /Decode [0 hival] def
9622 /ImageMatrix _imatrix def
9623 /DataSource{currentfile st0 readhexstring pop}def
9624 /BitsPerComponent 8 def
9625 /Interpolate false def
9627 level2 not{ dontloadlevel2 restore }if
9629 /_imagedict 12 dict begin /ImageType 1 def/BitsPerComponent 8 def/Interpolate false def currentdict end def
9630 /$rhs0 {currentfile st0 readhexstring pop}def
9631 /$rhs1 {currentfile st1 readhexstring pop}def
9632 /$rhs2 {currentfile st2 readhexstring pop}def
9633 /$rhs3 {currentfile st3 readhexstring pop}def
9634 /$rhs4 {currentfile st4 readhexstring pop}def
9635 /$rs0 {currentfile st0 readstring pop}def
9636 /$rs1 {currentfile st1 readstring pop}def
9637 /$rs2 {currentfile st2 readstring pop}def
9638 /$rs3 {currentfile st3 readstring pop}def
9639 /$rs4 {currentfile st4 readstring pop}def
9642 {pop deviceinfo /Colors known
9643 {deviceinfo /Colors get exec 1 gt}
9646 {pop statusdict /processcolors known
9647 {statusdict /processcolors get exec 1 gt}
9648 {false} ifelse}{false} ifelse}ifelse
9650 /level2 systemdict /languagelevel known
9651 {languagelevel 2 ge}{false}ifelse def
9652 /foureq {4 index eq 8 1 roll
9656 pop pop pop pop and and and} def
9658 /_settransfer systemdict /settransfer get def
9659 /_currenttransfer systemdict /currenttransfer get def
9660 /_image systemdict /image get def
9661 /blank 0 _currenttransfer exec
9662 1 _currenttransfer exec eq def
9663 /negative blank{0 _currenttransfer exec 0.5 lt}
9664 {0 _currenttransfer exec 1 _currenttransfer exec gt}ifelse def
9665 /inverted? negative def
9666 /_currentgray systemdict /currentgray get def
9667 hascolor{/$b 0 def} {/$b 5 def} ifelse
9668 /setcmykcolor where{pop 1 0 0 0 setcmykcolor _currentgray 1 exch sub
9669 0 1 0 0 setcmykcolor _currentgray 1 exch sub
9670 0 0 1 0 setcmykcolor _currentgray 1 exch sub
9671 0 0 0 1 setcmykcolor _currentgray 1 exch sub
9673 1 0 0 0 foureq{/$b 1 store}if
9674 0 1 0 0 foureq{/$b 2 store}if
9675 0 0 1 0 foureq{/$b 3 store}if
9676 0 0 0 1 foureq{/$b 4 store}if
9677 0 0 0 0 foureq{/$b 6 store}if}if
9678 blank{/$b 6 store}if
9679 $b 0 eq $b 5 eq or{/$dt 0 def}if/$dt -1 def grestore}def
9681 1 index 0 eq{dup dup/Width get exch /Decode get length 2 div mul cvi}{dup/Width get}ifelse
9682 /st0 exch string def
9684 /MultipleDataSources false def
9685 dup 0 eq{pop/DataSource {$rhs0} def}
9686 {1 eq{/DataSource {$rs0} def}{/DataSource currentfile /ASCII85Decode filter def}ifelse}ifelse
9689 Width Height BitsPerComponent ImageMatrix
9691 {/DataSource load end image}{
9693 {MultipleDataSources{DataSource 0 get DataSource 1 get DataSource 2 get}{/DataSource load}ifelse
9694 MultipleDataSources 3 end DSIColorImage}{
9695 Decode length 8 eq{MultipleDataSources{DataSource 0 get DataSource 1 get
9696 DataSource 2 get DataSource 3 get}{/DataSource load}ifelse
9697 MultipleDataSources 4 end DSIColorImage}if}ifelse
9700 /dt{/rgbclut xdf /bwclut xdf}def
9701 /cl{pop gsave $i setmatrix translate scale
9702 cvi/_h xdf cvi/_w xdf/st0 _w string def pop doclutimage grestore}def
9703 /c3{/imagesave save def
9704 /$src xdf $i setmatrix translate scale cvi/_h xdf cvi/_w xdf
9705 level2{_cs setcolorspace}if
9709 /ImageMatrix _imatrix def
9710 /Decode [0 1 0 1 0 1]def
9711 currentdict end exch
9713 imagesave restore}def
9714 /ca{/imagesave save def
9715 /$src xdf $i setmatrix translate scale cvi/_h xdf cvi/_w xdf
9716 level2{_cs setcolorspace}if
9718 /Decode[0 100 -128 127 -128 127]def
9721 /ImageMatrix _imatrix def
9722 currentdict end exch
9724 imagesave restore}def
9725 /c4{/imagesave save def
9726 /$src xdf $i setmatrix translate scale cvi/_h xdf cvi/_w xdf
9727 level2 {/DeviceCMYK setcolorspace}if
9729 /Decode [0 1 0 1 0 1 0 1] def
9732 /ImageMatrix _imatrix def
9733 currentdict end exch
9735 imagesave restore}def
9736 /im{/imagesave save def
9737 pop $i setmatrix translate scale cvi/_h xdf cvi/_w xdf
9738 level2{/DeviceGray setcolorspace}if
9743 /ImageMatrix _imatrix def
9744 currentdict end exch
9746 imagesave restore}def
9747 /colorimage where{pop/DSIColorImage {colorimage} def}{/DSIColorImage{
9748 /$nc xdf pop /proc0 xdf 3 index 2 index mul 7 add 8 div cvi string /st1 xdf
9749 $nc 3 eq{{proc0 dup/st0 xdf 0 exch 3 exch length 3 sub
9750 {dup st0 exch get .3 mul 1 index 1 add st0 exch get .59 mul add 1 index 2 add st0 exch get .11 mul add
9751 cvi exch 3 div cvi exch st1 3 1 roll put}for st1}}{{proc0 dup/st0 xdf 0 exch 4 exch length 4 sub{dup
9753 1 index 1 add st0 exch get .59 mul add
9754 1 index 2 add st0 exch get .11 mul add
9755 1 index 3 add st0 exch get add dup 255.0 gt{pop 255.0}if
9758 st1 3 1 roll put}for st1}}ifelse
9762 /bi{scale translate $i currentmatrix pop translate scale setupbands}def
9763 /ei{$i setmatrix}def
9764 /ik{gsave $i setmatrix translate scale cvi/_h xdf cvi/_w xdf
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11210 215367 r(eac)S(h)s o
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11320 309530 r(where)s o y u
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11327 -18205 X(w)S(the)S(segmen)T(ts)S(forming)S(the)S(sp)s
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11332 18205 r(end)S(and)S(pass)S(through)S(a)S(set)S(of)s o y u
11336 -18205 r(ts)T(called)T
11349 18205 X(e)S(a)S(p)T(ositiv)s
11350 -18205 X(e)S(in)T(teger.)s
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11389 18205 r(oundary)S(of)S(an)s
11390 -18205 r(y)S(square)S(of)S(the)S(dis-)s o y u
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11422 195305 X(pr)S(oblem,)s
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11433 f7(-light)T(solution)T(with)T(r)S(e-)s o y u
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11437 -33497 X(ction)S(with)S(shift)s
11442 f7(with)S(c)T(ost)s o y u
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11500 254672 r(so)S(a)S(p)T(ortal)s o y u
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11513 (in)S(more)S(than)s o y u
11515 218453 W(direction)S(for)S(that)S(square.)s o y u
11517 335598 W(that)S(if)S(the)S(length)S(of)S(the)S(side)S
11519 17363435 r(square)s
11524 -18205 X(e)S(need)S(to)S(de\rect)S(an)S(edge)S(b)T
11531 -18205 r(e)S(it)S(pass)S(through)S(a)S(p)s
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11536 -18205 r(harge)S(this)S(cost)S(to)S(the)S(corresp)s
11537 18205 r(onding)S(side)s o y u
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11541 145635 W(that)S(w)s
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11605 f5(-ligh)T(t)S(so-)s o y u
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12021 f5(is)S(within)S(distance)s o y u
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12046 f5(\))S(b)T(e)S(the)S(n)s
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12680 512710 r(If)S(no)S(suc)T(h)S(w)T(a)T(y)S
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12711 290251 r(\(One)S(could)s o y u
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12815 4670993 r(Initial)s
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12821 184126 X(w)S(e)T(indicate)T(wh)S(y)T(the)T(input)T
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12829 -18205 r(ts)S(of)S(an)S
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12851 235655 W([)s u(4)s o
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12879 f5(Using)S(argumen)s
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12893 -18205 r(t)S(squares)S(of)S(size)S(2)s
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12903 18205 r(oin)T(t)s o y u
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12913 283368 r(This)S(increases)s o y u
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12942 -18205 r(xes)S(with)S(side)S(length)S
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12973 18205 r(olynomial)S(time)s o y u
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12981 2368143 r(quadtree)s
12983 18205 r(osition)S(is)S(easily)S(generalized)S(so)s o y u
12985 177921 W(the)S(space)S(is)S(recursiv)s
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12987 18205 r(er-)s o y u
12991 237901 X(b)S(y)T(h)S(yp)s
12992 18205 r(erplanes.)s
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13001 196005 W(solution)S(that)s o y u
13011 -18205 X(t)S(with)S(resp)s
13012 18205 r(ect)S(to)S(an)T(y)S(h)T(yp)s
13013 18205 r(erplane)s o y u
13015 237996 W(is)S(used)S(in)S(the)S(quadtree)S(decomp)s
13016 18205 r(osition)S(for)s o y u
13033 18205 r(ceed)S(with)S(a)S(dynamic)S(program)S(analo-)s o
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13052 145635 W(running)S(time)S(of)S(the)S(DP)s
13058 f9(\(\()s u(log)s o
13077 20935 r(cation)s o y u
13081 209810 W(can)S(\fnd)S(a)S(\(1)s
13085 209810 W(times)S(optimal)S(solution)S(to)s o
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13099 400596 r(Sa)T(y)S(the)S(facilit)T(y)S(cost)s o y u
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13104 f5(and)S(the)S(service)S(cost)S(is)S
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13132 258538 W(service)S(cost)S(\(1)s
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13158 251220 W(for)S(few)S(medians.)s o y u
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13182 17363435 r(consists)s
13188 f5(p)T(ositions)S(from)S(an)S
13195 f5(regular)S(spaced)S(grid)S(placed)S(inside)S(the)S(square.)s o y u
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13218 268604 W(can)S(th)s
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13224 17363435 r(algorithm)s
13225 176096 W(for)S(the)S
13228 f5(-median)S(algorithm)S(with)S(run-)s o y u
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13256 251220 W(to)S(Capacitated)s o y u
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13263 145635 W(capacitated)S
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13268 f5(-medians)s o y u
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13282 -18205 r(y)S(fa-)s o y u
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13294 17363435 r(dynamic)s
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13298 368449 r(ho)T(w-)s o y u
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13304 18205 r(ounds)s o y u
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13309 -18205 r(e)S(dynamic)s o y u
13310 17363435 r(programming)s
13312 -18205 r(ulation)S(where)S(the)S(subprob-)s o y u
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13315 -18205 r(umerate)S(partitions)S(of)S(ex-)s o y u
13318 -18205 X(y)S(a)T(v)s
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13365 f5(time)S(algorithm)s o y u
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13413 f7(Minimum-)s o y u
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13527 216689 W(Bern)S(and)S(D.)S(Eppstein.)s
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13542 3715275 r(Submitted)s
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13627 3715275 r(1992.)s o y U u
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13655 326406 r(mining)s o y u
13659 -33497 X(dge)S(disc)T(overy)s
13661 218453 W(1\(2\),)S(1997.)s o y U u
13662 17363435 r([13])s O
13664 271722 W(B.)S(Shmo)s
13667 -54614 r(ardos)S(and)S(K.)S(Aardal.)s o y u
13669 -18205 X(ximation)s
13670 317732 W(algorithms)S(for)S(facilit)T(y)S(lo-)s o y u
13671 18710567 r(cation)s
13672 162908 W(problems)S(\(extended)S(abstract\).)S
13674 -33497 W(o)S(c.)s o y u
13677 -16749 r(CM)S(STOC)s
13679 218453 W(265{274,)S(1997.)s O O O