Rewrite formulae to be shorter.

diff --git a/Heter_paper.tex b/Heter_paper.tex
index 0491692cc0205522bad90a1a75b8f00057bef0cc..9ac2e0c50bdac6fd055c1403e39490a94ee56851 100644 (file)
--- a/Heter_paper.tex
+++ b/Heter_paper.tex
@@ -648,7 +648,8 @@ maximum distance  between the  energy curve and  the performance curve  is while
           \State $F_i \gets F_i+\Fdiff_i,~i=1,\dots,N.$
     \EndIf 
     \State $\Told \gets max_{~i=1,\dots,N } (\Tcp_i+\Tcm_i)$
           \State $F_i \gets F_i+\Fdiff_i,~i=1,\dots,N.$
     \EndIf 
     \State $\Told \gets max_{~i=1,\dots,N } (\Tcp_i+\Tcm_i)$

-    \State $\Eoriginal \gets \sum_{i=1}^{N}{( \Pd_i \cdot  \Tcp_i)} +\sum_{i=1}^{N} {(\Ps_i \cdot \Told)}$
+    % \State $\Eoriginal \gets \sum_{i=1}^{N}{( \Pd_i \cdot  \Tcp_i)} +\sum_{i=1}^{N} {(\Ps_i \cdot \Told)}$
+    \State $\Eoriginal \gets \sum_{i=1}^{N}{( \Pd_i \cdot  \Tcp_i + \Ps_i \cdot \Told)}$

     \State $\Sopt_{i} \gets 1,~i=1,\dots,N. $
     \State $\Dist \gets 0 $
     \While {(all nodes not reach their  minimum  frequency)}
     \State $\Sopt_{i} \gets 1,~i=1,\dots,N. $
     \State $\Dist \gets 0 $
     \While {(all nodes not reach their  minimum  frequency)}


@@ -657,7 +658,8 @@ maximum distance  between the  energy curve and  the performance curve  is while
         \State $S_i \gets \frac{\Fmax_i}{F_i},~i=1,\dots,N.$
         \EndIf
        \State $\Tnew \gets max_\textit{~i=1,\dots,N} (\Tcp_{i} \cdot S_{i}) + \MinTcm $
         \State $S_i \gets \frac{\Fmax_i}{F_i},~i=1,\dots,N.$
         \EndIf
        \State $\Tnew \gets max_\textit{~i=1,\dots,N} (\Tcp_{i} \cdot S_{i}) + \MinTcm $

-       \State $\Ereduced \gets \sum_{i=1}^{N}{(S_i^{-2} \cdot \Pd_i \cdot  \Tcp_i)} + \sum_{i=1}^{N} {(\Ps_i \cdot \rlap{\Tnew)}} $
+%       \State $\Ereduced \gets \sum_{i=1}^{N}{(S_i^{-2} \cdot \Pd_i \cdot  \Tcp_i)} + \sum_{i=1}^{N} {(\Ps_i \cdot \rlap{\Tnew)}} $
+       \State $\Ereduced \gets \sum_{i=1}^{N}{(S_i^{-2} \cdot \Pd_i \cdot  \Tcp_i + \Ps_i \cdot \rlap{\Tnew)}} $

        \State $\Pnorm \gets \frac{\Told}{\Tnew}$
        \State $\Enorm\gets \frac{\Ereduced}{\Eoriginal}$
       \If{$(\Pnorm - \Enorm > \Dist)$}
        \State $\Pnorm \gets \frac{\Told}{\Tnew}$
        \State $\Enorm\gets \frac{\Ereduced}{\Eoriginal}$
       \If{$(\Pnorm - \Enorm > \Dist)$}