From: ali Date: Thu, 18 Dec 2014 00:51:42 +0000 (+0100) Subject: The Modifications have been finished by Ali X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/LiCO.git/commitdiff_plain/7faa23683c6117ff229363e291bcc97046907e22?ds=sidebyside;hp=--cc The Modifications have been finished by Ali --- 7faa23683c6117ff229363e291bcc97046907e22 diff --git a/LiCO_Journal.bib b/LiCO_Journal.bib index a2810af..3e67fc5 100644 --- a/LiCO_Journal.bib +++ b/LiCO_Journal.bib @@ -1025,3 +1025,83 @@ pages={1-4}, year={1999} } +@BOOK{AMPL, + AUTHOR = "Robert Fourer and David M. Gay and Brian W. Kernighan", + TITLE = "AMPL: A Modeling Language for Mathematical Programming", + PUBLISHER = "Cengage Learning", + YEAR = "November 12, 2002", + edition = "2nd", + +} + +@article{Deng2012, + title={Transforming Area Coverage to Target Coverage to Maintain Coverage and Connectivity for Wireless Sensor Networks}, + author={Xiu Deng and Jiguo Yu, Dongxiao Yu and Congcong Chen}, + journal={International Journal of Distributed Sensor Networks}, + volume={2012}, + year={2012}, + ee = {http://dx.doi.org/10.1155/2012/254318} +} + +@inproceedings{jaggi2006, + title={Energy-efficient Connected Covereage in Wireless Sensor Networks}, + author={N. Jaggi and A.A. Abouzeid}, + booktitle={Proceeding of 4th Asian International Mobile Computing Conference AMOC2006}, + year={2006} +} + +@inproceedings{yangnovel, + title={A Novel Distributed Algorithm for Complete Targets Coverage in Energy Harvesting Wireless Sensor Networks }, + author={Yang, Changlin and Chin, Kwan-Wu}, + booktitle={IEEE ICC 2014- Ad-hoc and Sensor Networking Symposium}, + pages={361--366}, + year={2014}, + organization={IEEE} +} + +@INPROCEEDINGS{5714480, +author={Xiaofei Xing and Jie Li and Guojun Wang}, +booktitle={Mobile Ad-hoc and Sensor Networks (MSN), 2010 Sixth International Conference on}, +title={Integer Programming Scheme for Target Coverage in Heterogeneous Wireless Sensor Networks}, +year={2010}, +month={Dec}, +pages={79-84}, +keywords={energy conservation;integer programming;wireless sensor networks;ETCA;clustered configurations;clusterheads;energy first algorithm;energy-efficient target coverage algorithm;heterogeneous wireless sensor networks;integer programming;network lifetime;polytype target coverage;sensor node;Algorithm design and analysis;Clustering algorithms;Energy consumption;Logic gates;Sensors;Simulation;Wireless sensor networks;Heterogeneous wireless sensor networks;network lifetime;optimization;target coverage}, +doi={10.1109/MSN.2010.18},} + +@article{Yang2014, + title={A Maximum Lifetime Coverage Algorithm Based on Linear Programming}, + author={Mengmeng Yang and Jie Liu}, + journal={Journal of Information Hiding an dMultimedia Signal Processing, Ubiquitous International}, + volume={5}, + number={2}, + pages={296-301}, + year={2014} +} + +@article{rossi2012exact, + title={An exact approach for maximizing the lifetime of sensor networks with adjustable sensing ranges}, + author={Rossi, Andr{\'e} and Singh, Alok and Sevaux, Marc}, + journal={Computers \& Operations Research}, + volume={39}, + number={12}, + pages={3166--3176}, + year={2012}, + publisher={Elsevier} +} + +@ARTICLE{glpk, +author = {Andrew Makhorin}, +title = {The GLPK (GNU Linear Programming Kit)}, +journal = {Available: https://www.gnu.org/software/glpk/}, +year = {2012}, +} + +@article{deschinkel2012column, + title={A Column Generation based Heuristic to Extend Lifetime in Wireless Sensor Network.}, + author={Deschinkel, Karine}, + journal={Sensors \& Transducers Journal}, + volume={14-2}, + pages={242--253}, + year={2012} +} \ No newline at end of file diff --git a/LiCO_Journal.tex b/LiCO_Journal.tex index 6842df2..cdd97c2 100755 --- a/LiCO_Journal.tex +++ b/LiCO_Journal.tex @@ -61,7 +61,7 @@ \begin{abstract} - One fundamental issue in Wireless Sensor Networks (WSNs) is the lifetime coverage optimization, which reflects how well a WSN is covered so that the network lifetime can be maximized. In this paper, a Lifetime Coverage Optimization Protocol (LiCO) in WSNs is proposed. The surveillance region is divided into subregions and LiCO protocol is distributed among sensor nodes in each subregion. LiC0 protocols works into periods, each period is divided into four stages: Information exchange, Leader Election, Optimization Decision, and Sensing. Schedules node activities (wakeup and sleep of sensors) is performed in each subregion by a leader whose selection is the result of cooperation between nodes within the same subregion. The novelty of the approach lies essentially in the formulation of a new mathematical optimization model based on perimeter coverage level to schedule sensors activities. Extensive simulation experiments have been performed using OMNeT++, the discrete event simulator, to demonstrate that LiCO is capable to extend the lifetime coverage of WSN as longer time as possible in comparison with some other protocols. + One fundamental issue in Wireless Sensor Networks (WSNs) is the lifetime coverage optimization, which reflects how well a WSN is covered so that the network lifetime can be maximized. In this paper, a Lifetime Coverage Optimization Protocol (LiCO) in WSNs is proposed. The surveillance region is divided into subregions and LiCO protocol is distributed among sensor nodes in each subregion. LiCO protocols works with periods, each period is divided into four stages: Information exchange, Leader Election, Optimization Decision, and Sensing. Schedules node activities (wakeup and sleep of sensors) is performed in each subregion by a leader whose selection is the result of cooperation between nodes within the same subregion. The novelty of approach lies essentially in the formulation of a new mathematical optimization model based on perimeter coverage level to schedule sensors activities. Extensive simulation experiments have been performed using OMNeT++, the discrete event simulator, to demonstrate that LiCO is capable to extend the lifetime coverage of WSN as longer time as possible in comparison with some other protocols. \end{abstract} @@ -80,7 +80,7 @@ Wireless Sensor Networks, Area Coverage, Network lifetime, Optimization, Schedul \section{\uppercase{Introduction}} \label{sec:introduction} -\noindent The great development in Micro Electro-Mechanical Systems (MEMS) and wireless communication hardware are being led to emerge networks of tiny distributed sensors called WSN~\cite{akyildiz2002wireless,puccinelli2005wireless}. WSN comprises of small, low-powered sensors working together for perform a typical mission by communicating with one another through multihop wireless connections. They can send the sensed measurements based on local decisions to the user by means of sink nodes. WSN has been used in many applications such as Military, Habitat, Environment, Health, industrial, and Business~\cite{yick2008wireless}.Typically, a sensor node contains three main parts~\cite{anastasi2009energy}: a sensing subsystem, for sense, measure, and gather the measurements from the real environment; processing subsystem, for measurements processing and storage; a communication subsystem, for data transmission and receiving. Moreover, the energy needed by the sensor node is supplied by a power supply, to accomplish the scheduled task. This power supply is composed of a battery with a limited lifetime. And it maybe be unsuitable or impossible to replace or recharge the batteries in most applications. It is then necessary to deploy the WSN with high density so as to increase the reliability and to exploit redundancy by using energy-efficient activity scheduling approaches. So, the main question is: how to extend the lifetime coverage of WSN as long time as possible while ensuring a high level of coverage? Many energy-efficient mechanisms have been suggested to retain energy and extend the lifetime of the WSNs~\cite{rault2014energy}. \\ +\noindent The great development in Micro Electro-Mechanical Systems (MEMS) and wireless communication hardware are being led to emerge networks of tiny distributed sensors called WSN~\cite{akyildiz2002wireless,puccinelli2005wireless}. WSN comprises of small, low-powered sensors working together for perform a typical mission by communicating with one another through multihop wireless connections. They can send the sensed measurements based on local decisions to the user by means of sink nodes. WSN has been used in many applications such as Military, Habitat, Environment, Health, industrial, and Business~\cite{yick2008wireless}. Typically, a sensor node contains three main parts~\cite{anastasi2009energy}: a sensing subsystem, for sense, measure, and gather the measurements from the real environment; processing subsystem, for measurements processing and storage; a communication subsystem, for data transmission and receiving. Moreover, the energy needed by the sensor node is supplied by a power supply, to accomplish the scheduled task. This power supply is composed of a battery with a limited lifetime. And it maybe be unsuitable or impossible to replace or recharge the batteries in most applications. It is then necessary to deploy the WSN with high density so as to increase the reliability and to exploit redundancy by using energy-efficient activity scheduling approaches. So, the main question is: how to extend the lifetime coverage of WSN as long time as possible while ensuring a high level of coverage? Many energy-efficient mechanisms have been suggested to retain energy and extend the lifetime of the WSNs~\cite{rault2014energy}. \\ %The sensor system ought to have a lifetime long enough to satisfy the application necessities. The lifetime coverage maximization is one of the fundamental requirements of any area coverage protocol in WSN implementation~\cite{nayak2010wireless}. In order to increase the reliability and prevent the possession of coverage holes (some parts are not covered in the area of interest) in the WSN, it is necessary to deploy the WSN with high density so as to increase the reliability and to exploit redundancy by using energy-efficient activity scheduling approaches. @@ -91,11 +91,11 @@ This paper makes the following contributions.\\ \begin{enumerate} \item We devise a framework to schedules nodes to be activated alternatively, such that the network lifetime may be prolonged ans certain coverage requirement can still be met. This framework is based on the division of the area of interest into several smaller subregions; on the division of timeline into periods of equal length. -One leader is elected for each subregion in an independent, distributed, and simultaneous way by the cooperation among the sensor nodes within each subregion, and this similar to cluster architecture +One leader is elected for each subregion in an independent, distributed, and simultaneous way by the cooperation among the sensor nodes within each subregion, and this is similar to cluster architecture \item We propose a new mathematical optimization model. Instead of trying to cover a set of specified points/targets as in most of the methods proposed in the literature, we formulate an integer program based on perimeter coverage of each sensor. The model involves integer variables to capture the deviations between the actual level of coverage and the required level. And a weighted sum of these deviations is minimized. -\item We conducted extensive simulation experiments using the discrete event simulator OMNeT++, to demonstrate the efficiency of our protocol, compared to two approaches found in the literature, DESK \ref{} and GAF \ref{}, and compared to our previous work using another optimization model for sensor scheduling. +\item We conducted extensive simulation experiments using the discrete event simulator OMNeT++, to demonstrate the efficiency of our protocol, compared to two approaches found in the literature, DESK \cite{ChinhVu} and GAF \cite{xu2001geography}, and compared to our previous work using another optimization model for sensor scheduling \cite{Idrees2}. \end{enumerate} @@ -118,14 +118,14 @@ coverage problem and distinguish our LiCO protocol from the works presented in the literature. The most discussed coverage problems in literature can be classified into three -types \cite{li2013survey}: area coverage \cite{Misra} where every point inside +types \cite{li2013survey}: area coverage \cite{Misra} where every point inside an area is to be monitored, target coverage \cite{yang2014novel} where the main objective is to cover only a finite number of discrete points called targets, -and barrier coverage \cite{Kumar:2005}\cite{kim2013maximum} to prevent intruders +and barrier coverage \cite{HeShibo}\cite{kim2013maximum} to prevent intruders from entering into the region of interest. In \cite{Deng2012} authors transform the area coverage problem to the target coverage problem taking into account the intersection points among disks of sensors nodes or between disk of sensor nodes -and boundaries. In \cite{Huang:2003:CPW:941350.941367} authors prove that if the perimeters of sensors are sufficiently covered, the whole area is sufficiently covered and they provide an algorithm in $O(n d log d)$ time to compute the perimeter-coverage of each sensor ($d$ the maximum number of sensors that are neighboring to a sensor, $n$ the total number of sensors in the network). {\it In LiCO protocol, rather than determining the level of coverage of a set of discrete points, our optimization model is based on checking the perimeter-coverage of each sensor to activate a minimal number of sensors.} +and boundaries. In \cite{Huang:2003:CPW:941350.941367} authors prove that if the perimeters of sensors are sufficiently covered, the whole area is sufficiently covered and they provide an algorithm in $O(nd~log~d)$ time to compute the perimeter-coverage of each sensor ($d$ the maximum number of sensors that are neighboring to a sensor, $n$ the total number of sensors in the network). {\it In LiCO protocol, instead of determining the level of coverage of a set of discrete points, our optimization model is based on checking the perimeter-coverage of each sensor to activate a minimal number of sensors.} The major approach to extend network lifetime while preserving coverage is to divide/organize the sensors into a suitable number of set covers (disjoint or @@ -238,14 +238,14 @@ Figure~\ref{pcmfig} illuminates the perimeter coverage of the sensor node $0$. O \begin{figure}[ht!] \centering -\includegraphics[width=75mm]{pcm.pdf} +\includegraphics[width=75mm]{pcm.jpg} \caption{Perimeter coverage of sensor node 0} \label{pcmfig} \end{figure} Figure~\ref{twosensors} demonstrates the way of locating the left and right points of a segment for a sensor node $u$ covered by a sensor node $v$. This figure assumes that the neighbor sensor node $v$ is located on the west of a sensor $u$. It is assumed that the two sensor nodes $v$ and $u$ are located in the positions $(v_x,v_y)$ and $(u_x,u_y)$, respectively. The distance between $v$ and $u$ is computed by $Dist(u,v) = \sqrt{\vert u_x - v_x \vert^2 + \vert u_y - v_y \vert^2}$. The angle $\alpha$ is computed through the formula $\alpha = arccos \left(\dfrac{Dist(u,v)}{2R_s} \right)$. So, the arch of sensor $u$ falling in the angle $[\pi - \alpha,\pi + \alpha]$, is said to be perimeter-covered by sensor node $v$. -The left and right points of each segment are placed on the line segment $[0,2\pi]$. Figure~\ref{pcmfig} illustrates the segments for the 9 neighbors of sensor $0$. The points reported on the line segment $[0,2\pi]$ separates it in intervals. For each interval, we sum up the number of parts of segments, and we deduce a level of coverage for each interval. For instance, the interval delimited by the points $5L$ and $6L$ contains three parts of segments. That means that this part of the perimeter of the sensor $0$ may be covered by three sensors, sensor $0$ itself and sensors $2$ and $5$. The level of coverage of this interval may reach $3$ if all previously mentioned sensors are active. Let say that sensors $0$, $2$ and $5$ are involved in the coverage of this interval. The table in figure~\ref{expcm} summarizes the level of coverage for each interval and the sensors involved in. +The left and right points of each segment are placed on the line segment $[0,2\pi]$. Figure~\ref{pcmfig} illustrates the segments for the 9 neighbors of sensor $0$. The points reported on the line segment $[0,2\pi]$ separates it in intervals as shown in figure~\ref{expcm}. For example, for each neighboring sensor of sensor 0, place the points $\alpha^ 1_L$, $\alpha^ 1_R$, $\alpha^ 2_L$, $\alpha^ 2_R$, $\alpha^ 3_L$, $\alpha^ 3_R$, $\alpha^ 4_L$, $\alpha^ 4_R$, $\alpha^ 5_L$, $\alpha^ 5_R$, $\alpha^ 6_L$, $\alpha^ 6_R$, $\alpha^ 7_L$, $\alpha^ 7_R$, $\alpha^ 8_L$, $\alpha^ 8_R$, $\alpha^ 9_L$, and $\alpha^ 9_R$; on the line segment $[0,2\pi]$, and then sort all these points in an ascending order into a list. Traverse the line segment $[0,2\pi]$ by visiting each point in the sorted list from left to right and determine the coverage level of each interval of the sensor 0 (see figure \ref{expcm}). For each interval, we sum up the number of parts of segments, and we deduce a level of coverage for each interval. For instance, the interval delimited by the points $5L$ and $6L$ contains three parts of segments. That means that this part of the perimeter of the sensor $0$ may be covered by three sensors, sensor $0$ itself and sensors $2$ and $5$. The level of coverage of this interval may reach $3$ if all previously mentioned sensors are active. Let say that sensors $0$, $2$ and $5$ are involved in the coverage of this interval. Table~\ref{my-label} summarizes the level of coverage for each interval and the sensors involved in for sensor node 0 in figure~\ref{pcmfig}. % to determine the level of the perimeter coverage for each left and right point of a segment. \begin{figure}[ht!] \centering @@ -254,6 +254,7 @@ The left and right points of each segment are placed on the line segment $[0,2\p \label{twosensors} \end{figure} + \begin{figure}[ht!] \centering \includegraphics[width=75mm]{expcm.pdf} @@ -261,8 +262,18 @@ The left and right points of each segment are placed on the line segment $[0,2\p \label{expcm} \end{figure} + + + + + + + + %For example, consider the sensor node $0$ in figure~\ref{pcmfig}, which has 9 neighbors. Figure~\ref{expcm} shows the perimeter coverage level for all left and right points of a segment that covered by a neighboring sensor nodes. Based on the figure~\ref{expcm}, the set of sensors for each left and right point of the segments illustrated in figure~\ref{ex2pcm} for the sensor node 0. +\iffalse + \begin{figure}[ht!] \centering \includegraphics[width=90mm]{ex2pcm.jpg} @@ -270,6 +281,37 @@ The left and right points of each segment are placed on the line segment $[0,2\p \label{ex2pcm} \end{figure} +\fi + + \begin{table}[h] + \caption{Coverage intervals and contributing sensors for sensor node 0.} +\begin{tabular}{|c|c|c|c|c|c|c|c|c|} +\hline +\begin{tabular}[c]{@{}c@{}}The angle \\ $\alpha$ \end{tabular} & \begin{tabular}[c]{@{}c@{}}Segment \\ Left (L) or\\ Right (R)\end{tabular} & \begin{tabular}[c]{@{}c@{}}Sensor \\ Node Id\end{tabular} & \begin{tabular}[c]{@{}c@{}}Interval \\ Coverage\\ Level\end{tabular} & \multicolumn{5}{c|}{\begin{tabular}[c]{@{}c@{}}The Set of Sensors\\ Involved in Interval \\ Coverage\end{tabular}} \\ \hline +0.0291 & L & 1 & 4 & 0 & 1 & 3 & 4 & \\ \hline +0.104 & L & 2 & 5 & 0 & 1 & 3 & 4 & 2 \\ \hline +0.3168 & R & 3 & 4 & 0 & 1 & 4 & 2 & \\ \hline +0.6752 & R & 4 & 3 & 0 & 1 & 2 & & \\ \hline +1.8127 & R & 1 & 2 & 0 & 2 & & & \\ \hline +1.9228 & L & 5 & 3 & 0 & 2 & 5 & & \\ \hline +2.3959 & L & 6 & 4 & 0 & 2 & 5 & 6 & \\ \hline +2.4258 & R & 2 & 3 & 0 & 5 & 6 & & \\ \hline +2.7868 & L & 7 & 4 & 0 & 5 & 6 & 7 & \\ \hline +2.8358 & L & 8 & 5 & 0 & 5 & 6 & 7 & 8 \\ \hline +2.9184 & R & 5 & 4 & 0 & 6 & 7 & 8 & \\ \hline +3.3301 & R & 7 & 3 & 0 & 6 & 8 & & \\ \hline +3.9464 & L & 9 & 4 & 0 & 6 & 8 & 9 & \\ \hline +4.767 & R & 6 & 3 & 0 & 8 & 9 & & \\ \hline +4.8425 & L & 3 & 4 & 0 & 3 & 8 & 9 & \\ \hline +4.9072 & R & 8 & 3 & 0 & 3 & 9 & & \\ \hline +5.3804 & L & 4 & 4 & 0 & 3 & 4 & 9 & \\ \hline +5.9157 & R & 9 & 3 & 0 & 3 & 4 & & \\ \hline +\end{tabular} + +\label{my-label} +\end{table} + + %The optimization algorithm that used by LiCO protocol based on the perimeter coverage levels of the left and right points of the segments and worked to minimize the number of sensor nodes for each left or right point of the segments within each sensor node. The algorithm minimize the perimeter coverage level of the left and right points of the segments, while, it assures that every perimeter coverage level of the left and right points of the segments greater than or equal to 1. In LiCO protocol, scheduling of sensor nodes'activities is formulated with an integer program based on coverage intervals and is detailed in section~\ref{cp}. @@ -461,7 +503,7 @@ relative importance of satisfying the associated level of coverage. For example, weights associated with coverage intervals of a specified part of a region may be given a relatively larger magnitude than weights associated -with another region. This kind of integer program is inspired from the model developed for brachytherapy treatment planning for optimizing dose distribution \ref{0031-9155-44-1-012}. The integer program must be solved by the leader in each subregion at the beginning of each sensing phase, whenever the environment has changed (new leader, death of some sensors). Note that the number of constraints in the model is constant (constraints of coverage expressed for all sensors), whereas the number of variables $X_k$ decreases over periods, since we consider only alive sensors (sensors with enough energy to be alive during one sensing phase) in the model. +with another region. This kind of integer program is inspired from the model developed for brachytherapy treatment planning for optimizing dose distribution \cite{0031-9155-44-1-012}. The integer program must be solved by the leader in each subregion at the beginning of each sensing phase, whenever the environment has changed (new leader, death of some sensors). Note that the number of constraints in the model is constant (constraints of coverage expressed for all sensors), whereas the number of variables $X_k$ decreases over periods, since we consider only alive sensors (sensors with enough energy to be alive during one sensing phase) in the model. \section{\uppercase{PERFORMANCE EVALUATION AND ANALYSIS}} @@ -517,6 +559,8 @@ for one period (3600 seconds), and adding the energy for the pre-sensing phases According to the interval of initial energy, a sensor may be active during at most 20 rounds. +The values of $\alpha^j_i$ and $\beta^j_i$ have been chosen in a way that ensuring a good network coverage and for a longer time during the lifetime of the WSN. We have given a higher priority for the undercoverage ( by setting the $\alpha^j_i$ with a larger value than $\beta^j_i$) so as to prevent the non-coverage for the interval i of the sensor j. On the other hand, we have given a little bit lower value for $\beta^j_i$ so as to minimize the number of active sensor nodes that contribute in covering the interval i in sensor j. + In the simulations, we introduce the following performance metrics to evaluate the efficiency of our approach: @@ -583,11 +627,11 @@ by the whole network in the sensing phase (active and sleeping nodes). %\end{enumerate} \subsection{Simulation Results} -In this section, we present the simulation results of LiCO protocol and the other protocols using a discrete event simulator OMNeT++ \cite{varga} to run different series of simulations. We implemented all protocols precisely on a laptop DELL with Intel Core~i3~2370~M (2.4 GHz) processor (2 cores) and the MIPS (Million Instructions Per Second) rate equal to 35330. To be consistent with the use of a sensor node with Atmels AVR ATmega103L microcontroller (6 MHz) and a MIPS rate equal to 6, the original execution time on the laptop is multiplied by 2944.2 $\left(\frac{35330}{2} \times \frac{1}{6} \right)$ so as to use it by the energy consumption model especially, after the computation and listening. Employing the modeling language ????\ref{}, the associated integer program instance is generated in a standard format, which is then read and solved by the optimization solver GLPK (GNU linear Programming Kit available in the public domain) \cite{glpk} through a Branch-and-Bound method. +In this section, we present the simulation results of LiCO protocol and the other protocols using a discrete event simulator OMNeT++ \cite{varga} to run different series of simulations. We implemented all protocols precisely on a laptop DELL with Intel Core~i3~2370~M (2.4 GHz) processor (2 cores) and the MIPS (Million Instructions Per Second) rate equal to 35330. To be consistent with the use of a sensor node with Atmels AVR ATmega103L microcontroller (6 MHz) and a MIPS rate equal to 6, the original execution time on the laptop is multiplied by 2944.2 $\left(\frac{35330}{2} \times \frac{1}{6} \right)$ so as to use it by the energy consumption model especially, after the computation and listening. Employing the modeling language for Mathematical Programming (AMPL)~\cite{AMPL}, the associated integer program instance is generated in a standard format, which is then read and solved by the optimization solver GLPK (GNU linear Programming Kit available in the public domain) \cite{glpk} through a Branch-and-Bound method. We compared LiCO protocol to three other approaches: the first, called DESK and proposed by ~\cite{ChinhVu} is a fully distributed coverage algorithm; the second, called GAF ~\cite{xu2001geography}, consists in dividing the region into fixed squares. During the decision phase, in each square, one sensor is -chosen to remain active during the sensing phase; the third, DiLCO protocol~\cite{Idrees2} is an improved version on the work presented in ~\cite{idrees2014coverage}. Note that the LiCO protocol is based on the same framework as that of DiLCO. For these two protocols, the division of the region of interest in 16 subregions was chosen since it produces the best results. The difference between the two protocols relies on the use of the integer programming to provide the set of sensors that have to be actived in each sensing phase. Whereas DilCO protocol tries to satisfy the coverage of a set of primary points, LiCO protocol tries to reach a desired level of coverage $l$ for each sensor's perimeter. In the experimentations, we chose a level of coverage equal to 1 ($l=1$). +chosen to remain active during the sensing phase; the third, DiLCO protocol~\cite{Idrees2} is an improved version on the work presented in ~\cite{idrees2014coverage}. Note that the LiCO protocol is based on the same framework as that of DiLCO. For these two protocols, the division of the region of interest in 16 subregions was chosen since it produces the best results. The difference between the two protocols relies on the use of the integer programming to provide the set of sensors that have to be activated in each sensing phase. Whereas DiLCO protocol tries to satisfy the coverage of a set of primary points, LiCO protocol tries to reach a desired level of coverage $l$ for each sensor's perimeter. In the experimentations, we chose a level of coverage equal to 1 ($l=1$). \subsubsection{\textbf{Coverage Ratio}} Figure~\ref{fig333} shows the average coverage ratio for 200 deployed nodes obtained with the four methods. @@ -600,7 +644,7 @@ Figure~\ref{fig333} shows the average coverage ratio for 200 deployed nodes obta \label{fig333} \end{figure} -DESK, GAF, and DiLCO provides a little better coverage ratio with 99.99\%, 99.91\%, and 99.02\% against 98.76\% produced by LiCO for the first periods. This is due to the fact that DiLCO protocol put in sleep mode redundant sensors using optimization (which lightly decreases the coverage ratio) while there are more active nodes in the case of others methods. But when the number of periods exceeds 70 periods, it clearly appears that LiCO provides a better coverage ratio and keeps a coverage ratio greater than 50\% for longer periods (15 more compared to DiLCO, 40 more compared to DESK). +DESK, GAF, and DiLCO provide a little better coverage ratio with 99.99\%, 99.91\%, and 99.02\% against 98.76\% produced by LiCO for the first periods. This is due to the fact that DiLCO protocol put in sleep mode redundant sensors using optimization (which lightly decreases the coverage ratio) while there are more active nodes in the case of others methods. But when the number of periods exceeds 70 periods, it clearly appears that LiCO provides a better coverage ratio and keeps a coverage ratio greater than 50\% for longer periods (15 more compared to DiLCO, 40 more compared to DESK). %When the number of periods increases, coverage ratio produced by DESK and GAF protocols decreases. This is due to dead nodes. However, DiLCO protocol maintains almost a good coverage from the round 31 to the round 63 and it is close to LiCO protocol. The coverage ratio of LiCO protocol is better than other approaches from the period 64. diff --git a/R/ASR.eps b/R/ASR.eps index 70dc1d4..def00e8 100644 --- a/R/ASR.eps +++ b/R/ASR.eps @@ -2,7 +2,7 @@ %%BoundingBox: 53 53 536 402 %%HiResBoundingBox: 54 53.5 535 401.5 %%Creator: gnuplot 4.6 patchlevel 0 -%%CreationDate: Tue Oct 21 11:55:00 2014 +%%CreationDate: Wed Dec 17 01:20:58 2014 %%EndComments % EPSF created by ps2eps 1.68 %%BeginProlog @@ -513,7 +513,7 @@ SDict begin [ /Author (ali) % /Producer (gnuplot) % /Keywords () - /CreationDate (Tue Oct 21 11:55:00 2014) + /CreationDate (Wed Dec 17 01:20:58 2014) /DOCINFO pdfmark end } ifelse @@ -800,7 +800,7 @@ LTb LT0 0.00 0.55 0.55 C LCb setrgbcolor 4316 3350 M -[ [(Helvetica) 110.0 0.0 true true 0 (DiLCO-16)] +[ [(Helvetica) 110.0 0.0 true true 0 (DiLCO)] ] -36.7 MRshow LT0 0.00 0.55 0.55 C 4382 3350 M diff --git a/R/ASR.pdf b/R/ASR.pdf index c0d70cf..566500b 100644 Binary files a/R/ASR.pdf and b/R/ASR.pdf differ diff --git a/R/CR.eps b/R/CR.eps index b81b919..44917e8 100644 --- a/R/CR.eps +++ b/R/CR.eps @@ -2,7 +2,7 @@ %%BoundingBox: 53 53 536 402 %%HiResBoundingBox: 54 53.5 535 401.5 %%Creator: gnuplot 4.6 patchlevel 0 -%%CreationDate: Tue Oct 21 18:32:31 2014 +%%CreationDate: Wed Dec 17 01:20:01 2014 %%EndComments % EPSF created by ps2eps 1.68 %%BeginProlog @@ -513,7 +513,7 @@ SDict begin [ /Author (ali) % /Producer (gnuplot) % /Keywords () - /CreationDate (Tue Oct 21 18:32:31 2014) + /CreationDate (Wed Dec 17 01:20:01 2014) /DOCINFO pdfmark end } ifelse @@ -800,7 +800,7 @@ LTb LT0 0.00 0.55 0.55 C LCb setrgbcolor 4382 3351 M -[ [(Helvetica) 110.0 0.0 true true 0 (DiLCO-16)] +[ [(Helvetica) 110.0 0.0 true true 0 (DiLCO)] ] -36.7 MRshow LT0 0.00 0.55 0.55 C 4448 3351 M diff --git a/R/CR.pdf b/R/CR.pdf index f10cbdd..b632dea 100644 Binary files a/R/CR.pdf and b/R/CR.pdf differ diff --git a/R/EC50.eps b/R/EC50.eps index aa569a8..3a916fc 100644 --- a/R/EC50.eps +++ b/R/EC50.eps @@ -2,7 +2,7 @@ %%BoundingBox: 53 53 545 402 %%HiResBoundingBox: 54 53.5 544.5 401.5 %%Creator: gnuplot 4.6 patchlevel 0 -%%CreationDate: Tue Oct 21 18:34:56 2014 +%%CreationDate: Wed Dec 17 01:23:08 2014 %%EndComments % EPSF created by ps2eps 1.68 %%BeginProlog @@ -513,7 +513,7 @@ SDict begin [ /Author (ali) % /Producer (gnuplot) % /Keywords () - /CreationDate (Tue Oct 21 18:34:56 2014) + /CreationDate (Wed Dec 17 01:23:08 2014) /DOCINFO pdfmark end } ifelse @@ -769,11 +769,11 @@ LTb 2.000 UL LT0 0.00 0.55 0.55 C LCb setrgbcolor -1163 3392 M -[ [(Helvetica) 110.0 0.0 true true 0 (DiLCO-16)] +1163 3275 M +[ [(Helvetica) 110.0 0.0 true true 0 (DiLCO)] ] -36.7 MRshow LT0 -0.00 0.55 0.55 C 1229 3392 M +0.00 0.55 0.55 C 1229 3275 M 327 0 V 1029 603 M 847 263 V @@ -785,18 +785,18 @@ LT0 2723 1067 TriUF 3570 1277 TriUF 4417 1537 TriUF -1392 3392 TriUF +1392 3275 TriUF % End plot #1 % Begin plot #2 1.000 UP 2.000 UL LT1 0.00 0.39 0.00 C LCb setrgbcolor -1163 3282 M +1163 3165 M [ [(Helvetica) 110.0 0.0 true true 0 (DESK)] ] -36.7 MRshow LT1 -0.00 0.39 0.00 C 1229 3282 M +0.00 0.39 0.00 C 1229 3165 M 327 0 V 1029 1513 M 847 293 V @@ -808,18 +808,18 @@ LT1 2723 2133 DiaF 3570 2711 DiaF 4417 3233 DiaF -1392 3282 DiaF +1392 3165 DiaF % End plot #2 % Begin plot #3 1.000 UP 2.000 UL LT2 0.50 0.00 0.00 C LCb setrgbcolor -1163 3172 M +1163 3055 M [ [(Helvetica) 110.0 0.0 true true 0 (GAF)] ] -36.7 MRshow LT2 -0.50 0.00 0.00 C 1229 3172 M +0.50 0.00 0.00 C 1229 3055 M 327 0 V 1029 1133 M 847 122 V @@ -831,18 +831,18 @@ LT2 2723 1372 Star 3570 1502 Star 4417 1643 Star -1392 3172 Star +1392 3055 Star % End plot #3 % Begin plot #4 1.000 UP 2.000 UL LT3 0.00 0.00 0.55 C LCb setrgbcolor -1163 3062 M +1163 2945 M [ [(Helvetica) 110.0 0.0 true true 0 (LiCO)] ] -36.7 MRshow LT3 -0.00 0.00 0.55 C 1229 3062 M +0.00 0.00 0.55 C 1229 2945 M 327 0 V 1029 491 M 847 76 V @@ -854,7 +854,7 @@ LT3 2723 688 CircleF 3570 811 CircleF 4417 1026 CircleF -1392 3062 CircleF +1392 2945 CircleF % End plot #4 1.000 UL LTb diff --git a/R/EC50.pdf b/R/EC50.pdf index 8e89657..123e681 100644 Binary files a/R/EC50.pdf and b/R/EC50.pdf differ diff --git a/R/EC95.eps b/R/EC95.eps index 3eae427..23a1571 100644 --- a/R/EC95.eps +++ b/R/EC95.eps @@ -2,7 +2,7 @@ %%BoundingBox: 53 53 545 402 %%HiResBoundingBox: 54 53.5 544.5 401.5 %%Creator: gnuplot 4.6 patchlevel 0 -%%CreationDate: Tue Oct 21 18:37:28 2014 +%%CreationDate: Wed Dec 17 01:24:57 2014 %%EndComments % EPSF created by ps2eps 1.68 %%BeginProlog @@ -513,7 +513,7 @@ SDict begin [ /Author (ali) % /Producer (gnuplot) % /Keywords () - /CreationDate (Tue Oct 21 18:37:28 2014) + /CreationDate (Wed Dec 17 01:24:57 2014) /DOCINFO pdfmark end } ifelse @@ -769,11 +769,11 @@ LTb 2.000 UL LT0 0.00 0.55 0.55 C LCb setrgbcolor -1163 3392 M -[ [(Helvetica) 110.0 0.0 true true 0 (DiLCO-16)] +1163 3261 M +[ [(Helvetica) 110.0 0.0 true true 0 (DiLCO)] ] -36.7 MRshow LT0 -0.00 0.55 0.55 C 1229 3392 M +0.00 0.55 0.55 C 1229 3261 M 327 0 V 1029 563 M 847 202 V @@ -785,18 +785,18 @@ LT0 2723 945 TriUF 3570 1161 TriUF 4417 1429 TriUF -1392 3392 TriUF +1392 3261 TriUF % End plot #1 % Begin plot #2 1.000 UP 2.000 UL LT1 0.00 0.39 0.00 C LCb setrgbcolor -1163 3282 M +1163 3151 M [ [(Helvetica) 110.0 0.0 true true 0 (DESK)] ] -36.7 MRshow LT1 -0.00 0.39 0.00 C 1229 3282 M +0.00 0.39 0.00 C 1229 3151 M 327 0 V 1029 1285 M 847 513 V @@ -808,18 +808,18 @@ LT1 2723 2170 DiaF 3570 2635 DiaF 4417 3229 DiaF -1392 3282 DiaF +1392 3151 DiaF % End plot #2 % Begin plot #3 1.000 UP 2.000 UL LT2 0.50 0.00 0.00 C LCb setrgbcolor -1163 3172 M +1163 3041 M [ [(Helvetica) 110.0 0.0 true true 0 (GAF)] ] -36.7 MRshow LT2 -0.50 0.00 0.00 C 1229 3172 M +0.50 0.00 0.00 C 1229 3041 M 327 0 V 1029 1408 M 847 77 V @@ -831,18 +831,18 @@ LT2 2723 1544 Star 3570 1713 Star 4417 1864 Star -1392 3172 Star +1392 3041 Star % End plot #3 % Begin plot #4 1.000 UP 2.000 UL LT3 0.00 0.00 0.55 C LCb setrgbcolor -1163 3062 M +1163 2931 M [ [(Helvetica) 110.0 0.0 true true 0 (LiCO)] ] -36.7 MRshow LT3 -0.00 0.00 0.55 C 1229 3062 M +0.00 0.00 0.55 C 1229 2931 M 327 0 V 1029 449 M 847 128 V @@ -854,7 +854,7 @@ LT3 2723 751 CircleF 3570 984 CircleF 4417 1295 CircleF -1392 3062 CircleF +1392 2931 CircleF % End plot #4 1.000 UL LTb diff --git a/R/EC95.pdf b/R/EC95.pdf index 66241a6..72ea08d 100644 Binary files a/R/EC95.pdf and b/R/EC95.pdf differ diff --git a/R/LT50.eps b/R/LT50.eps index f1f6eae..1a88388 100644 --- a/R/LT50.eps +++ b/R/LT50.eps @@ -2,7 +2,7 @@ %%BoundingBox: 53 53 545 402 %%HiResBoundingBox: 54 53.5 544.5 401.5 %%Creator: gnuplot 4.6 patchlevel 0 -%%CreationDate: Tue Oct 21 18:41:57 2014 +%%CreationDate: Wed Dec 17 01:27:20 2014 %%EndComments % EPSF created by ps2eps 1.68 %%BeginProlog @@ -513,7 +513,7 @@ SDict begin [ /Author (ali) % /Producer (gnuplot) % /Keywords () - /CreationDate (Tue Oct 21 18:41:57 2014) + /CreationDate (Wed Dec 17 01:27:20 2014) /DOCINFO pdfmark end } ifelse @@ -829,11 +829,11 @@ LTb 2.000 UL LT0 0.00 0.55 0.55 C LCb setrgbcolor -1112 3371 M -[ [(Helvetica) 110.0 0.0 true true 0 (DiLCO-16)] +1112 3288 M +[ [(Helvetica) 110.0 0.0 true true 0 (DiLCO)] ] -36.7 MRshow LT0 -0.00 0.55 0.55 C 1178 3371 M +0.00 0.55 0.55 C 1178 3288 M 327 0 V 969 1349 M 861 312 V @@ -845,18 +845,18 @@ LT0 2690 1972 TriUF 3550 2242 TriUF 4411 2450 TriUF -1341 3371 TriUF +1341 3288 TriUF % End plot #1 % Begin plot #2 1.000 UP 2.000 UL LT1 0.00 0.39 0.00 C LCb setrgbcolor -1112 3261 M +1112 3178 M [ [(Helvetica) 110.0 0.0 true true 0 (DESK)] ] -36.7 MRshow LT1 -0.00 0.39 0.00 C 1178 3261 M +0.00 0.39 0.00 C 1178 3178 M 327 0 V 969 1017 M 861 249 V @@ -868,18 +868,18 @@ LT1 2690 1495 DiaF 3550 1598 DiaF 4411 1723 DiaF -1341 3261 DiaF +1341 3178 DiaF % End plot #2 % Begin plot #3 1.000 UP 2.000 UL LT2 0.50 0.00 0.00 C LCb setrgbcolor -1112 3151 M +1112 3068 M [ [(Helvetica) 110.0 0.0 true true 0 (GAF)] ] -36.7 MRshow LT2 -0.50 0.00 0.00 C 1178 3151 M +0.50 0.00 0.00 C 1178 3068 M 327 0 V 969 1079 M 861 332 V @@ -891,18 +891,18 @@ LT2 2690 1723 Star 3550 1993 Star 4411 2242 Star -1341 3151 Star +1341 3068 Star % End plot #3 % Begin plot #4 1.000 UP 2.000 UL LT3 0.00 0.00 0.55 C LCb setrgbcolor -1112 3041 M +1112 2958 M [ [(Helvetica) 110.0 0.0 true true 0 (LiCO)] ] -36.7 MRshow LT3 -0.00 0.00 0.55 C 1178 3041 M +0.00 0.00 0.55 C 1178 2958 M 327 0 V 969 1391 M 861 498 V @@ -914,7 +914,7 @@ LT3 2690 2305 CircleF 3550 2699 CircleF 4411 2949 CircleF -1341 3041 CircleF +1341 2958 CircleF % End plot #4 1.000 UL LTb diff --git a/R/LT50.pdf b/R/LT50.pdf index 1c18c84..c3e47e1 100644 Binary files a/R/LT50.pdf and b/R/LT50.pdf differ diff --git a/R/LT95.eps b/R/LT95.eps index b5a22af..c5edb13 100644 --- a/R/LT95.eps +++ b/R/LT95.eps @@ -2,7 +2,7 @@ %%BoundingBox: 53 53 545 402 %%HiResBoundingBox: 54 53.5 544.5 401.5 %%Creator: gnuplot 4.6 patchlevel 0 -%%CreationDate: Tue Oct 21 18:44:01 2014 +%%CreationDate: Wed Dec 17 01:28:08 2014 %%EndComments % EPSF created by ps2eps 1.68 %%BeginProlog @@ -513,7 +513,7 @@ SDict begin [ /Author (ali) % /Producer (gnuplot) % /Keywords () - /CreationDate (Tue Oct 21 18:44:01 2014) + /CreationDate (Wed Dec 17 01:28:08 2014) /DOCINFO pdfmark end } ifelse @@ -769,11 +769,11 @@ LTb 2.000 UL LT0 0.00 0.55 0.55 C LCb setrgbcolor -1062 3344 M -[ [(Helvetica) 110.0 0.0 true true 0 (DiLCO-16)] +1062 3275 M +[ [(Helvetica) 110.0 0.0 true true 0 (DiLCO)] ] -36.7 MRshow LT0 -0.00 0.55 0.55 C 1128 3344 M +0.00 0.55 0.55 C 1128 3275 M 327 0 V 910 1425 M 873 520 V @@ -785,18 +785,18 @@ LT0 2657 2429 TriUF 3531 2845 TriUF 4404 3191 TriUF -1291 3344 TriUF +1291 3275 TriUF % End plot #1 % Begin plot #2 1.000 UP 2.000 UL LT1 0.00 0.39 0.00 C LCb setrgbcolor -1062 3234 M +1062 3165 M [ [(Helvetica) 110.0 0.0 true true 0 (DESK)] ] -36.7 MRshow LT1 -0.00 0.39 0.00 C 1128 3234 M +0.00 0.39 0.00 C 1128 3165 M 327 0 V 910 1356 M 873 139 V @@ -808,18 +808,18 @@ LT1 2657 1910 DiaF 3531 2187 DiaF 4404 2360 DiaF -1291 3234 DiaF +1291 3165 DiaF % End plot #2 % Begin plot #3 1.000 UP 2.000 UL LT2 0.50 0.00 0.00 C LCb setrgbcolor -1062 3124 M +1062 3055 M [ [(Helvetica) 110.0 0.0 true true 0 (GAF)] ] -36.7 MRshow LT2 -0.50 0.00 0.00 C 1128 3124 M +0.50 0.00 0.00 C 1128 3055 M 327 0 V 910 1010 M 873 485 V @@ -831,18 +831,18 @@ LT2 2657 1979 Star 3531 2256 Star 4404 2602 Star -1291 3124 Star +1291 3055 Star % End plot #3 % Begin plot #4 1.000 UP 2.000 UL LT3 0.00 0.00 0.55 C LCb setrgbcolor -1062 3014 M +1062 2945 M [ [(Helvetica) 110.0 0.0 true true 0 (LiCO)] ] -36.7 MRshow LT3 -0.00 0.00 0.55 C 1128 3014 M +0.00 0.00 0.55 C 1128 2945 M 327 0 V 910 1391 M 873 519 V @@ -854,7 +854,7 @@ LT3 2657 2325 CircleF 3531 2602 CircleF 4404 2914 CircleF -1291 3014 CircleF +1291 2945 CircleF % End plot #4 1.000 UL LTb diff --git a/R/LT95.pdf b/R/LT95.pdf index cbe4161..2c264b3 100644 Binary files a/R/LT95.pdf and b/R/LT95.pdf differ diff --git a/R/LTa.eps b/R/LTa.eps index e1fce4b..876a77d 100644 --- a/R/LTa.eps +++ b/R/LTa.eps @@ -2,7 +2,7 @@ %%BoundingBox: 53 53 536 402 %%HiResBoundingBox: 54 53.5 535 401.5 %%Creator: gnuplot 4.6 patchlevel 0 -%%CreationDate: Tue Oct 21 22:37:54 2014 +%%CreationDate: Wed Dec 17 01:57:52 2014 %%EndComments % EPSF created by ps2eps 1.68 %%BeginProlog @@ -513,7 +513,7 @@ SDict begin [ /Author (ali) % /Producer (gnuplot) % /Keywords () - /CreationDate (Tue Oct 21 22:37:54 2014) + /CreationDate (Wed Dec 17 01:57:52 2014) /DOCINFO pdfmark end } ifelse @@ -827,12 +827,12 @@ LTb % Begin plot #1 1.000 UL LT0 -0.00 0.55 0.55 C LCb setrgbcolor -1299 3309 M -[ [(Helvetica) 110.0 0.0 true true 0 (DiLCO-16/50)] +0.62 0.69 0.87 C LCb setrgbcolor +1156 3330 M +[ [(Helvetica) 110.0 0.0 true true 0 (DiLCO/50)] ] -36.7 MRshow LT0 -0.00 0.55 0.55 C 1.000 1365 3282 327 55 BoxColFill +0.62 0.69 0.87 C 1.000 1222 3303 327 55 BoxColFill 1.000 938 352 50 998 BoxColFill 1.000 1655 352 50 1310 BoxColFill 1.000 2372 352 50 1621 BoxColFill @@ -842,12 +842,12 @@ LT0 % Begin plot #2 1.000 UL LT1 -0.50 0.00 0.00 C LCb setrgbcolor -1299 3199 M +0.10 0.10 0.44 C LCb setrgbcolor +1156 3220 M [ [(Helvetica) 110.0 0.0 true true 0 (LiCO/50)] ] -36.7 MRshow LT1 -0.50 0.00 0.00 C 1.000 1365 3172 327 55 BoxColFill +0.10 0.10 0.44 C 1.000 1222 3193 327 55 BoxColFill 1.000 1003 352 50 1040 BoxColFill 1.000 1720 352 50 1538 BoxColFill 1.000 2437 352 50 1954 BoxColFill @@ -857,12 +857,12 @@ LT1 % Begin plot #3 1.000 UL LT2 -0.00 0.00 0.55 C LCb setrgbcolor -1299 3089 M -[ [(Helvetica) 110.0 0.0 true true 0 (DiLCO-16/80)] +1.00 0.75 0.80 C LCb setrgbcolor +1156 3110 M +[ [(Helvetica) 110.0 0.0 true true 0 (DiLCO/80)] ] -36.7 MRshow LT2 -0.00 0.00 0.55 C 1.000 1365 3062 327 55 BoxColFill +1.00 0.75 0.80 C 1.000 1222 3083 327 55 BoxColFill 1.000 1069 352 49 728 BoxColFill 1.000 1786 352 49 1081 BoxColFill 1.000 2503 352 49 1414 BoxColFill @@ -872,12 +872,12 @@ LT2 % Begin plot #4 1.000 UL LT3 -0.00 0.39 0.00 C LCb setrgbcolor -1299 2979 M +1.00 0.00 0.00 C LCb setrgbcolor +1156 3000 M [ [(Helvetica) 110.0 0.0 true true 0 (LiCO/80)] ] -36.7 MRshow LT3 -0.00 0.39 0.00 C 1.000 1365 2952 327 55 BoxColFill +1.00 0.00 0.00 C 1.000 1222 2973 327 55 BoxColFill 1.000 1134 352 50 749 BoxColFill 1.000 1851 352 50 1268 BoxColFill 1.000 2568 352 50 1580 BoxColFill @@ -887,12 +887,12 @@ LT3 % Begin plot #5 1.000 UL LT4 -0.50 0.00 0.50 C LCb setrgbcolor -1299 2869 M -[ [(Helvetica) 110.0 0.0 true true 0 (DiLCO-16/85)] +0.54 0.17 0.89 C LCb setrgbcolor +1156 2890 M +[ [(Helvetica) 110.0 0.0 true true 0 (DiLCO/85)] ] -36.7 MRshow LT4 -0.50 0.00 0.50 C 1.000 1365 2842 327 55 BoxColFill +0.54 0.17 0.89 C 1.000 1222 2863 327 55 BoxColFill 1.000 1199 352 50 707 BoxColFill 1.000 1916 352 50 1040 BoxColFill 1.000 2633 352 50 1351 BoxColFill @@ -902,12 +902,12 @@ LT4 % Begin plot #6 1.000 UL LT5 -1.00 0.27 0.00 C LCb setrgbcolor -1299 2759 M +0.18 0.55 0.34 C LCb setrgbcolor +1156 2780 M [ [(Helvetica) 110.0 0.0 true true 0 (LiCO/85)] ] -36.7 MRshow LT5 -1.00 0.27 0.00 C 1.000 1365 2732 327 55 BoxColFill +0.18 0.55 0.34 C 1.000 1222 2753 327 55 BoxColFill 1.000 1264 352 50 707 BoxColFill 1.000 1981 352 50 1081 BoxColFill 1.000 2698 352 50 1455 BoxColFill @@ -917,12 +917,12 @@ LT5 % Begin plot #7 1.000 UL LT6 -0.20 0.80 0.20 C LCb setrgbcolor -1299 2649 M -[ [(Helvetica) 110.0 0.0 true true 0 (DiLCO-16/90)] +1.00 0.00 1.00 C LCb setrgbcolor +1156 2670 M +[ [(Helvetica) 110.0 0.0 true true 0 (DiLCO/90)] ] -36.7 MRshow LT6 -0.20 0.80 0.20 C 1.000 1365 2622 327 55 BoxColFill +1.00 0.00 1.00 C 1.000 1222 2643 327 55 BoxColFill 1.000 1329 352 50 687 BoxColFill 1.000 2046 352 50 998 BoxColFill 1.000 2763 352 50 1310 BoxColFill @@ -932,12 +932,12 @@ LT6 % Begin plot #8 1.000 UL LT7 -1.00 0.00 1.00 C LCb setrgbcolor -1299 2539 M +0.00 0.55 0.55 C LCb setrgbcolor +1156 2560 M [ [(Helvetica) 110.0 0.0 true true 0 (LiCO/90)] ] -36.7 MRshow LT7 -1.00 0.00 1.00 C 1.000 1365 2512 327 55 BoxColFill +0.00 0.55 0.55 C 1.000 1222 2533 327 55 BoxColFill 1.000 1395 352 49 687 BoxColFill 1.000 2112 352 49 1019 BoxColFill 1.000 2829 352 49 1330 BoxColFill @@ -947,12 +947,12 @@ LT7 % Begin plot #9 1.000 UL LT8 -0.00 1.00 0.50 C LCb setrgbcolor -1299 2429 M -[ [(Helvetica) 110.0 0.0 true true 0 (DiLCO-16/95)] +0.50 1.00 0.83 C LCb setrgbcolor +1156 2450 M +[ [(Helvetica) 110.0 0.0 true true 0 (DiLCO/95)] ] -36.7 MRshow LT8 -0.00 1.00 0.50 C 1.000 1365 2402 327 55 BoxColFill +0.50 1.00 0.83 C 1.000 1222 2423 327 55 BoxColFill 1.000 1460 352 50 645 BoxColFill 1.000 2177 352 50 957 BoxColFill 1.000 2894 352 50 1247 BoxColFill @@ -962,12 +962,12 @@ LT8 % Begin plot #10 1.000 UL LT0 -0.18 0.31 0.31 C LCb setrgbcolor -1299 2319 M +0.50 0.00 0.00 C LCb setrgbcolor +1156 2340 M [ [(Helvetica) 110.0 0.0 true true 0 (LiCO/95)] ] -36.7 MRshow LT0 -0.18 0.31 0.31 C 1.000 1365 2292 327 55 BoxColFill +0.50 0.00 0.00 C 1.000 1222 2313 327 55 BoxColFill 1.000 1525 352 50 624 BoxColFill 1.000 2242 352 50 936 BoxColFill 1.000 2959 352 50 1185 BoxColFill diff --git a/ex2pcm.jpg b/ex2pcm.jpg deleted file mode 100644 index bce5d02..0000000 Binary files a/ex2pcm.jpg and /dev/null differ diff --git a/pcm.pdf b/pcm.pdf deleted file mode 100644 index f4b3022..0000000 Binary files a/pcm.pdf and /dev/null differ diff --git a/twosensors.jpg b/twosensors.jpg index 636b180..aa0ed5d 100644 Binary files a/twosensors.jpg and b/twosensors.jpg differ