+\documentclass{beamer}
+\usepackage{beamerthemefemto}
+\usepackage[T1]{fontenc}
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+%\usepackage[section]{algorithm}
+%\usepackage{algorithmic}
+\usepackage{moreverb}
+\usepackage{verbatim}
+\usepackage{spverbatim}
+\usepackage{mdwlist}
+\usepackage{multirow}
+ \usepackage{animate}
+\usepackage{multido}
+ \usepackage{lmodern}
+ \usepackage{tikz}
+ \usepackage{booktabs}
+ \usepackage{pifont}
+ \usepackage{color}
+\usepackage{algorithmic}
+%\usepackage[ruled,english,boxed,linesnumbered]{algorithm2e}
+%\usepackage[english]{algorithme}
+\usepackage{subfigure}
+\usepackage{listings}
+
+\usepackage{array}
+\usepackage{picture}
+\usepackage{float}
+
+ \def\setgrouptext#1{\gdef\grouptext{#1}}
+\newenvironment{groupeditems}{\begin{displaymath}\left.\vbox\bgroup\setgrouptext}{%
+ \egroup\right\rbrace\hbox{\grouptext}\end{displaymath}}
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+
+\newcommand*{\twoelementtable}[3][l]%
+{%
+ \renewcommand{\arraystretch}{0.8}%
+ \begin{tabular}[t]{@{}#1@{}}%
+ #2\tabularnewline
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+\DeclareGraphicsExtensions{.jpg, .png , .pdf, .bmp, .pdftex}
+
+\setbeamertemplate{section in toc}[sections numbered]
+\setbeamertemplate{subsection in toc}[subsections numbered]
+
+\AtBeginSection[]
+{
+\begin{frame}
+\frametitle{Presentation Outline}
+\tableofcontents[currentsection]
+\end{frame}
+}
+
+
+\title{\textbf{Distributed Coverage Optimization Techniques for Improving Lifetime of Wireless Sensor Networks} \\\vspace{0.1cm}\hspace{2cm}\textbf{\textcolor{cyan}{\small PhD Dissertation Defense}}}
+\author{\textbf{\textcolor{green}{Ali Kadhum IDREES}} \\\vspace{0.5cm} \small Under Supervision: \\\textcolor{cyan}{\small Raphaël COUTURIER, Karine DESCHINKEL \& Michel SALOMON} \\\vspace{0.2cm} \textcolor{blue}{ University of Franche-Comté - FEMTO-ST - DISC Dept. - AND Team} \\\vspace{0.2cm}~~~~~~~~~~~~~~~~\textbf{\textcolor{green}{1 October 2015 }}}
+
+%\institute[FEMTO-ST, DISC]{\textit{FEMTO-ST - DISC Departement - AND Team}}
+
+\date{ }
+
+
+
+
+% ____ _____ ____ _ _ _____
+% | _ \| ____| __ )| | | |_ _|
+% | | | | _| | _ \| | | | | |
+% | |_| | |___| |_) | |_| | | |
+% |____/|_____|____/ \___/ |_|
+%
+
+\begin{document}
+
+%%%%%%%%%%%%%%%%%%%%
+%% SLIDE 01 %%
+%%%%%%%%%%%%%%%%%%%%
+\setbeamertemplate{background}{\titrefemto}
+\begin{frame}[plain]
+\begin{center}
+\titlepage
+\end{center}
+\end{frame}
+
+
+\setbeamertemplate{background}{\pagefemto}
+
+
+%%%%%%%%%%%%%%%%%%%%
+%% SLIDE 02 %%
+%%%%%%%%%%%%%%%%%%%%
+\begin{frame} {Problem Definition, Solution, and Objectives}
+ \vspace{-3.5em}
+ \begin{figure}
+ \includegraphics[width=0.475\textwidth]{Figures/6}
+ \hfill
+% \includegraphics[width=0.475\textwidth]{Figures/8}
+% \hfill
+ \includegraphics[width=0.475\textwidth]{Figures/10}
+% \hfill
+% \includegraphics[width=0.475\textwidth]{Figures/13}
+\end{figure}
+
+ \begin{block}{\textcolor{white}{ MAIN QUESTION?}}
+ How to reduce the redundancy while coverage preservation for prolong the network lifetime continuously and effectively when monitoring a certain area of interest?
+\end{block}
+ \end{frame}
+
+
+%%%%%%%%%%%%%%%%%%%%
+%% SLIDE 03 %%
+%%%%%%%%%%%%%%%%%%%%
+\begin{frame}{Problem Definition, Solution, and Objectives}
+
+\begin{block}{\textcolor{white}{OUR SOLUTION}}
+The area of interest is divided into subregions using a divide-and conquer method and then combine two efficient techniques :
+
+ \begin{itemize}
+ \item Leader Election for each subregion.
+ % \item Activity Scheduling based optimization is planned for each subregion.
+ \end{itemize}
+
+ \end{block}
+\begin{figure}
+ \includegraphics[width=0.475\textwidth]{Figures/div}
+ \hfill
+ \includegraphics[width=0.475\textwidth]{Figures/div2}
+\end{figure}
+
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%
+%% SLIDE 03.1 %%
+%%%%%%%%%%%%%%%%%%%%
+\begin{frame}{Problem Definition, Solution, and Objectives}
+
+\begin{block}{\textcolor{white}{OUR SOLUTION}}
+ \begin{itemize}
+ %\item Leader Election for each subregion.
+ \item Activity Scheduling based optimization is planned for each subregion.
+ \end{itemize}
+
+ \end{block}
+\begin{figure}
+ \includegraphics[width=0.775\textwidth]{Figures/act}
+
+\end{figure}
+
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%
+%% SLIDE 03.2 %%
+%%%%%%%%%%%%%%%%%%%%
+\begin{frame}{Problem Definition, Solution, and Objectives}
+
+\begin{block}{\textcolor{white}{Dissertation Objectives}}
+Develop energy-efficient distributed optimization protocols that should be able to:
+ \begin{itemize}
+ \item Schedule node activities by optimize both coverage and lifetime.
+ \item Combine two efficient techniques: leader election and sensor activity scheduling.
+ \item Perform a distributed optimization process.
+ \end{itemize}
+
+ \end{block}
+
+
+\end{frame}
+
+
+%%%%%%%%%%%%%%%%%%%%
+%% SLIDE 04 %%
+%%%%%%%%%%%%%%%%%%%%
+\begin{frame}
+ \frametitle{Presentation Outline}
+\begin{small}
+ \tableofcontents[section,subsection]
+\end{small}
+\end{frame}
+
+
+%%%%%%%%%%%%%%%%%%%%
+%% SLIDE 05 %%
+%%%%%%%%%%%%%%%%%%%%
+\section{\small {State of the Art}}
+
+
+%%%%%%%%%%%%%%%%%%%%
+%% SLIDE 06 %%
+%%%%%%%%%%%%%%%%%%%%
+\begin{frame}{Wireless Sensor Networks (WSNs)}
+\vspace{-3.5em}
+ \begin{columns}[c]
+
+\column{.58\textwidth}
+
+ \begin{figure}[!t]
+ \includegraphics[height = 3cm]{Figures/WSNT.jpg}
+ \end{figure}
+
+
+
+ \begin{femtoBlock}
+ {Sensor \\}
+ \begin{itemize}
+ \item Electronic Low-cost tiny device.
+ \item Sense, process and transmit data.
+ \item Limited energy, memory and processing capabilities.
+ \end{itemize}
+ \end{femtoBlock}
+
+ \column{.52\textwidth}
+
+ \begin{figure}[!t]
+ \includegraphics[height = 4.5cm]{Figures/WSN.jpg}
+ \end{figure}
+ \vspace{-3.5em}
+ \begin{figure}[!t]
+ \includegraphics[height = 2cm]{Figures/sn.jpg}
+ \end{figure}
+
+
+ % \begin{femtoBlock} {}% {SOME APPLICATIONS OF WSNs \\}
+
+% \includegraphics[height =1 cm]{1.png}
+% \includegraphics[height =1cm]{2.png}\\
+% \includegraphics[height =1cm]{5.jpg}
+% \includegraphics[height = 1cm]{traffic.jpg}
+% \includegraphics[height = 1cm]{3.png}
+%
+
+ % \end{femtoBlock}
+
+\end{columns}
+
+
+
+\end{frame}
+
+
+%%%%%%%%%%%%%%%%%%%%
+%% SLIDE 7 %%
+%%%%%%%%%%%%%%%%%%%%
+\begin{frame}{Types of Wireless Sensor Networks}
+
+\vspace{-1.5em}
+% \begin{columns}[c]
+%
+%\column{.52\textwidth}
+%\begin{itemize}
+% \item Terrestrial WSNs.
+% \item Underground WSNs.
+% \item Underwater WSNs.
+% \item Multimedia WSNs.
+% \item Mobile WSNs.
+% \item Flying WSNs.
+%\end{itemize}
+%
+% \column{.58\textwidth}
+ \begin{figure}[!t]
+ \includegraphics[height = 7cm]{Figures/typesWSN.pdf}
+ \end{figure}
+
+%\end{columns}
+\end{frame}
+
+
+%%%%%%%%%%%%%%%%%%%%
+%% SLIDE 08 %%
+%%%%%%%%%%%%%%%%%%%%
+\begin{frame}{Applications}
+\vspace{-1.5em}
+
+\begin{figure}[!t]
+ \includegraphics[height = 7cm]{Figures/WSNAP.pdf}
+ \end{figure}
+\end{frame}
+
+
+%%%%%%%%%%%%%%%%%%%%
+%% SLIDE 09 %%
+%%%%%%%%%%%%%%%%%%%%
+\begin{frame}{Energy-Efficient Mechanisms of a working WSN}
+\vspace{-2.5em}
+ \centering
+\begin{figure}[!t]
+
+ \includegraphics[height = 5cm]{Figures/WSN-M.pdf}
+ \end{figure}
+\end{frame}
+
+%\begin{frame}{Energy-Efficient Mechanisms of a working WSN}
+%\vspace{-1.5em}
+%
+%\begin{figure}[!t]
+% \includegraphics[height = 7cm]{Figures/WSN-S.pdf}
+% \end{figure}
+%\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%
+%% SLIDE 10 %%
+%%%%%%%%%%%%%%%%%%%%
+\begin{frame}{Network Lifetime}
+\vspace{-1.5em}
+\begin{block}{\textcolor{white} {Some network lifetime defintions:}}
+\begin{enumerate}[i)]
+\item \small Time spent until death of the first sensor ( or cluster head ).
+\item Time spent until death of all wireless sensor nodes in WSN.
+\item Time spent by WSN in covering each target by at least one sensor.
+\item Time during which the area of interest is covered by at least k nodes.
+\item Elapsed time until losing the connectivity or the coverage.
+\end{enumerate}
+\end{block}
+
+\begin{block}{\textcolor{white} {Network lifetime In this dissertation:}}
+Time elapsed until the coverage ratio becomes less than a predetermined threshold $\alpha$.
+\end{block}
+
+
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%
+%% SLIDE 10.1 %%
+%%%%%%%%%%%%%%%%%%%%
+\begin{frame}{Coverage in Wireless Sensor Networks}
+
+\begin{block} <1-> {\textcolor{white} {Coverage Definition:}}
+\textcolor{blue} {Coverage} reflects how well a sensor field is monitored efficiently using as less energy as possible.
+\end{block}
+
+
+
+\begin{block} <2-> {\textcolor{white} {Coverage Types:}}
+\begin{enumerate}
+\item \small \textcolor{blue} {Area coverage:} every point inside an area has to be monitored.
+\item \textcolor{blue} {Target coverage:} is to cover only a finite number of discrete points called targets.
+
+\item \textcolor{blue} {Barrier coverage:} is to detect targets as they cross a barrier such as in intrusion detection and border surveillance applications.
+\end{enumerate}
+\end{block}
+
+
+
+\begin{block} <3-> {\textcolor{white} {Coverage type in this dissertation:}}
+The work presented in this dissertation deals with area coverage.
+\end{block}
+
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%
+%% SLIDE 11 %%
+%%%%%%%%%%%%%%%%%%%%
+\begin{frame}{Existing Works}
+\vspace{-0.3em}
+\begin{block} {\textcolor{white} {Coverage Approaches:}}
+Most existing coverage approaches in literature classified into
+\begin{enumerate}[A)]
+\item Full centralized coverage algorithms.
+ \begin{itemize}
+ \item Optimal or near optimal solution.
+ \item low computation power for the sensors (except for base station).
+ \item High communication overhead.
+ \item Not scalable for large WSNs.
+ \end{itemize}
+\item Full distributed coverage algorithms.
+ \begin{itemize}
+ \item Lower quality solution.
+ \item High communication overhead especially for dense WSNs.
+ \item Reliable and scalable for large WSNs.
+ \end{itemize}
+\end{enumerate}
+
+\end{block}
+
+
+\begin{block} {\textcolor{white} {Coverage protocols in this dissertation:}}
+The protocols presented in this dissertation combine between the two above approaches.
+\end{block}
+
+
+\end{frame}
+
+
+%%%%%%%%%%%%%%%%%%%%
+%% SLIDE 12 %%
+%%%%%%%%%%%%%%%%%%%%
+\section{\small {Distributed Lifetime Coverage Optimization Protocol (DiLCO)}}
+
+
+%%%%%%%%%%%%%%%%%%%%
+%% SLIDE 13 %%
+%%%%%%%%%%%%%%%%%%%%
+\begin{frame}{\small DiLCO Protocol $\blacktriangleright$ Assumptions and Network Model:}
+\vspace{-0.5cm}
+
+
+\begin{femtoBlock} {} %{Assumptions and Network Model:}
+
+ \begin{columns}[c]
+
+ \column{.50\textwidth}
+
+ \vspace{-1.0cm}
+
+ \begin{enumerate} [$\divideontimes$]
+ \item Static Wireless Sensors.
+ \item Uniform deployment.
+ \item High density deployment.
+ \item Homogeneous in terms of:
+ \begin{itemize}
+ \item Sensing, Communication, and Processing capabilities
+ \end{itemize}
+ \item Heterogeneous Energy.
+ \item Its $R_c\geq 2R_s$.
+ \item Multi-hop communication.
+ \item Know Its location by:
+ \begin{itemize}
+ \item Embedded GPS or
+ \item Location Discovery Algorithm.
+ \end{itemize}
+ \end{enumerate}
+
+
+
+ \column{.50\textwidth}
+ \begin{enumerate} [$\divideontimes$]
+ \item Using two kinds of packet:
+ \begin{itemize}
+ \item INFO packet.
+ \item ActiveSleep packet.
+ \end{itemize}
+ \item Five status for each node:
+ \begin{itemize}
+ \item LISTENING, ACTIVE, SLEEP, COMPUTATION, and COMMUNICATION.
+ \end{itemize}
+ \end{enumerate}
+
+ \begin{femtoBlock} { \small Primary point coverage model}
+ \vspace{-1.2cm}
+ \begin{center}
+ \includegraphics[height = 4.0cm]{Figures/fig21.pdf}
+
+ \end{center}
+ \end{femtoBlock}
+
+ \end{columns}
+ \end{femtoBlock}
+
+\end{frame}
+
+
+%%%%%%%%%%%%%%%%%%%%
+%% SLIDE 14 %%
+%%%%%%%%%%%%%%%%%%%%
+\begin{frame}{\small DiLCO Protocol $\blacktriangleright$ Main Idea}
+%\vspace{-3.2cm}
+\begin{femtoBlock} {}%{Main Idea:\\}
+\centering
+\includegraphics[height = 2.5cm]{Figures/OneSensingRound.jpg}
+
+\vspace{1.2cm}
+\begin{enumerate}
+\item \textcolor{blue}{ \textbf{INFORMATION EXCHANGE:}}\\
+Sensors exchanges through multi-hop communication, their:
+\begin{itemize}
+\item Position coordinates,
+\item current remaining energy,
+\item sensor node ID, and
+\item number of its one-hop live neighbors.
+\end{itemize}
+
+
+\end{enumerate}
+
+\end{femtoBlock}
+\end{frame}
+
+
+%%%%%%%%%%%%%%%%%%%%
+%% SLIDE 14.1 %%
+%%%%%%%%%%%%%%%%%%%%
+\begin{frame}{\small DiLCO Protocol $\blacktriangleright$ Main Idea}
+%\vspace{-3.2cm}
+\begin{femtoBlock} {}%{Main Idea:\\}
+
+\begin{enumerate} [2.]
+
+\item \textcolor{blue}{ \textbf{ LEADER ELECTION:}}\\
+The selection criteria are, in order of importance:
+\begin{itemize}
+\item larger number of neighbors,
+\item larger remaining energy, and then in case of equality,
+\item larger ID.
+\end{itemize}
+\end{enumerate}
+
+\begin{enumerate} [3.]
+\item \textcolor{blue}{ \textbf{ DECISION:}} \\
+Leader solves an integer program(see next slide) to:
+\begin{itemize}
+\item Select which sensors will be activated in the sensing phase.
+\item Send Active-Sleep packet to each sensor in the subregion.
+\end{itemize}
+\end{enumerate}
+\begin{enumerate} [4.]
+\item \textcolor{blue}{ \textbf{ SENSING:}} \\
+Based on Active-Sleep Packet Information:
+\begin{itemize}
+\item Active sensors will execute their sensing task.
+\item Sleep sensors will wait a time equal to the period of sensing to wakeup.
+
+\end{itemize}
+
+\end{enumerate}
+
+\end{femtoBlock}
+\end{frame}
+
+
+%%%%%%%%%%%%%%%%%%%%
+%% SLIDE 15 %%
+%%%%%%%%%%%%%%%%%%%%
+\begin{frame}{\small DiLCO Protocol $\blacktriangleright$ Coverage Problem Formulation}
+\begin{femtoBlock} { }
+\noindent Our coverage optimization problem can then be formulated as follows:
+\begin{equation*} \label{eq:ip2r}
+\left \{
+\begin{array}{ll}
+\min \sum_{p \in P} (w_{\theta} \Theta_{p} + w_{U} U_{p})&\\
+\textrm{subject to :}&\\
+\sum_{j \in J} \alpha_{jp} X_{j} - \Theta_{p}+ U_{p} =1, &\forall p \in P\\
+%\label{c1}
+%\sum_{t \in T} X_{j,t} \leq \frac{RE_j}{e_t} &\forall j \in J \\
+%\label{c2}
+\Theta_{p}\in \mathbb{N}, &\forall p \in P\\
+U_{p} \in \{0,1\}, &\forall p \in P \\
+X_{j} \in \{0,1\}, &\forall j \in J
+\end{array}
+\right.
+\end{equation*}
+
+\begin{itemize}
+\item $X_{j}$ : indicates whether or not the sensor $j$ is actively sensing (1
+ if yes and 0 if not);
+\item $\Theta_{p}$ : {\it overcoverage}, the number of sensors minus one that
+ are covering the primary point $p$;
+\item $U_{p}$ : {\it undercoverage}, indicates whether or not the primary point
+ $p$ is being covered (1 if not covered and 0 if covered).
+\end{itemize}
+
+\end{femtoBlock}
+
+\end{frame}
+
+
+%%%%%%%%%%%%%%%%%%%%
+%% SLIDE 16 %%
+%%%%%%%%%%%%%%%%%%%%
+\begin{frame}{\small DiLCO Protocol $\blacktriangleright$ DiLCO Protocol Algorithm}
+%\begin{femtoBlock} {}
+\centering
+%\includegraphics[height = 7.2cm]{Figures/algo.jpeg}
+\includegraphics[height = 7.2cm]{Figures/Algo1.png}
+%\end{femtoBlock}
+
+\end{frame}
+
+
+
+
+%%%%%%%%%%%%%%%%%%%%
+%% SLIDE 18 %%
+%%%%%%%%%%%%%%%%%%%%
+\begin{frame}{\small DiLCO Protocol $\blacktriangleright$ Simulation Framework}
+\vspace{-0.8cm}
+\small
+\begin{table}[ht]
+\caption{Relevant parameters for network initializing.}
+\centering
+\begin{tabular}{c|c}
+\hline
+Parameter & Value \\ [0.5ex]
+\hline
+Sensing Field & $(50 \times 25)~m^2 $ \\
+Nodes Number & 50, 100, 150, 200 and 250~nodes \\
+Initial Energy & 500-700~joules \\
+Sensing Period & 60 Minutes \\
+$E_{th}$ & 36 Joules\\
+$R_s$ & 5~m \\
+$R_c$ & 10~m \\
+$w_{\Theta}$ & 1 \\
+$w_{U}$ & $|P|^2$ \\
+Modeling Language & A Mathematical Programming Language (AMPL) \\
+Optimization Solver & GNU linear Programming Kit (GLPK) \\
+Network Simulator & Discrete Event Simulator OMNeT++
+\end{tabular}
+\label{tablech4}
+\end{table}
+
+\end{frame}
+
+
+%%%%%%%%%%%%%%%%%%%%
+%% SLIDE 19 %%
+%%%%%%%%%%%%%%%%%%%%
+\begin{frame}{\small DiLCO Protocol $\blacktriangleright$ Energy Model \& Performance Metrics }
+%\vspace{-1.8cm}
+\begin{femtoBlock} {Energy Consumption Model}
+\vspace{-1.0cm}
+\begin{table}[h]
+%\centering
+\small
+%\caption{Power consumption values}
+\label{tab:EC}
+\begin{tabular}{|l||cccc|}
+ \hline
+ {\bf Sensor status} & MCU & Radio & Sensing & {\it Power (mW)} \\
+ \hline
+ LISTENING & On & On & On & 20.05 \\
+ ACTIVE & On & Off & On & 9.72 \\
+ SLEEP & Off & Off & Off & 0.02 \\
+ COMPUTATION & On & On & On & 26.83 \\
+ \hline
+ \multicolumn{4}{|l}{Energy needed to send or receive a 2-bit content message} & 0.515 \\
+ \hline
+\end{tabular}
+\end{table}
+
+\end{femtoBlock}
+\vspace{-0.5cm}
+\begin{femtoBlock} {Performance Metrics}
+\small
+\begin{enumerate}[$\mapsto$]
+\item {{\bf Network Lifetime}}
+\item {{\bf Coverage Ratio (CR)}}
+\item {{\bf Energy Consumption}}
+\item{{\bf Number of Active Sensors Ratio (ASR)}}
+\item {{\bf Execution Time}}
+%\item {{\bf Stopped Simulation Runs}}
+
+\end{enumerate}
+\end{femtoBlock}
+\end{frame}
+
+
+
+%%%%%%%%%%%%%%%%%%%%
+%% SLIDE 20 %%
+%%%%%%%%%%%%%%%%%%%%
+\begin{frame}{ \small DiLCO Protocol $\blacktriangleright$ Performance Comparison}
+
+\vspace{-0.5cm}
+\begin{figure}[h!]
+\centering
+ \includegraphics[scale=0.5] {Figures/R3/CR.eps}
+\caption{Coverage ratio for 150 deployed nodes}
+\label{Figures/ch4/R3/CR}
+\end{figure}
+
+
+
+\end{frame}
+
+
+
+%%%%%%%%%%%%%%%%%%%%
+%% SLIDE 20 %%
+%%%%%%%%%%%%%%%%%%%%
+\begin{frame}{ \small DiLCO Protocol $\blacktriangleright$ Performance Comparison}
+\vspace{-0.5cm}
+
+\begin{figure}[h!]
+\centering
+\includegraphics[scale=0.5]{Figures/R3/ASR.eps}
+\caption{Active sensors ratio for 150 deployed nodes }
+\label{Figures/ch4/R3/ASR}
+\end{figure}
+\end{frame}
+
+
+%%%%%%%%%%%%%%%%%%%%
+%% SLIDE 21 %%
+%%%%%%%%%%%%%%%%%%%%
+%\begin{frame}{ \small DiLCO Protocol $\blacktriangleright$ Performance Comparison}
+%\vspace{-0.5cm}
+%\begin{figure}[h!]
+%\centering
+%\includegraphics[scale=0.5]{Figures/R3/SR.eps}
+%\caption{Percentage of stopped simulation runs for 150 deployed nodes }
+%\label{Figures/ch4/R3/SR}
+%\end{figure}
+%\end{frame}
+
+
+%%%%%%%%%%%%%%%%%%%%
+%% SLIDE 22 %%
+%%%%%%%%%%%%%%%%%%%%
+\begin{frame}{ \small DiLCO Protocol $\blacktriangleright$ Performance Comparison}
+\vspace{-0.5cm}
+\begin{figure}%[h!]
+\begin{columns}[c]
+ \column{.50\textwidth}
+\includegraphics[scale=0.35]{Figures/R3/EC95.eps}
+\footnotesize \\~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(a)\\
+\column{.50\textwidth}
+\includegraphics[scale=0.35]{Figures/R3/EC50.eps}
+\footnotesize \\~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(b) \\
+\end{columns}
+\caption{Energy consumption for (a) $Lifetime_{95}$ and (b) $Lifetime_{50}$}
+\label{Figures/ch4/R3/EC}
+\end{figure}
+
+
+\end{frame}
+
+
+%%%%%%%%%%%%%%%%%%%%
+%% SLIDE 23 %%
+%%%%%%%%%%%%%%%%%%%%
+\begin{frame}{ \small DiLCO Protocol $\blacktriangleright$ Performance Comparison}
+\vspace{-0.5cm}
+\begin{figure}%[h!]
+\begin{columns}[c]
+ \column{.50\textwidth}
+\includegraphics[scale=0.35]{Figures/R3/LT95.eps}
+\footnotesize \\~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(a)\\
+\column{.50\textwidth}
+\includegraphics[scale=0.35]{Figures/R3/LT50.eps}
+\footnotesize \\~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(b) \\
+\end{columns}
+\caption{Network lifetime for (a) $Lifetime_{95}$ and (b) $Lifetime_{50}$}
+ \label{Figures/ch4/R3/LT}
+\end{figure}
+
+
+
+
+\end{frame}
+
+
+
+
+
+
+\section{\small{Multiround Distributed Lifetime Coverage Optimization Protocol (MuDiLCO)}}
+
+
+%%%%%%%%%%%%%%%%%%%%
+%% SLIDE 28 %%
+%%%%%%%%%%%%%%%%%%%%
+\begin{frame}{\small MuDiLCO Protocol $\blacktriangleright$ Main Idia}
+\vspace{-0.2cm}
+\begin{figure}[ht!]
+ \includegraphics[width=110mm]{Figures/GeneralModel.jpg}
+\caption{MuDiLCO protocol.}
+\label{fig2}
+\end{figure}
+\end{frame}
+
+
+%%%%%%%%%%%%%%%%%%%%
+%% SLIDE 29 %%
+%%%%%%%%%%%%%%%%%%%%
+\begin{frame}{\small MuDiLCO Protocol $\blacktriangleright$ Multiround Coverage Problem Formulation}
+\vspace{0.2cm}
+\small
+Our coverage optimization problem can then be formulated as follows
+\vspace{-0.2cm}
+\begin{equation*}
+ \min \sum_{t=1}^{T} \sum_{p=1}^{P} \left(W_{\theta}* \Theta_{t,p} + W_{U} * U_{t,p} \right) \label{eq15}
+\end{equation*}
+
+Subject to
+\vspace{-0.2cm}
+\begin{equation*}
+ \sum_{j=1}^{|J|} \alpha_{j,p} * X_{t,j} = \Theta_{t,p} - U_{t,p} + 1 \label{eq16} \hspace{6 mm} \forall p \in P, t = 1,\dots,T
+\end{equation*}
+
+\begin{equation*}
+ \sum_{t=1}^{T} X_{t,j} \leq \lfloor {RE_{j}/E_{th}} \rfloor \hspace{6 mm} \forall j \in J, t = 1,\dots,T
+ \label{eq144}
+\end{equation*}
+
+\begin{equation*}
+X_{t,j} \in \lbrace0,1\rbrace, \hspace{10 mm} \forall j \in J, t = 1,\dots,T \label{eq17}
+\end{equation*}
+
+\begin{equation*}
+U_{t,p} \in \lbrace0,1\rbrace, \hspace{10 mm}\forall p \in P, t = 1,\dots,T \label{eq18}
+\end{equation*}
+
+\begin{equation*}
+ \Theta_{t,p} \geq 0 \hspace{10 mm}\forall p \in P, t = 1,\dots,T \label{eq178}
+\end{equation*}
+
+
+
+
+
+
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%
+%% SLIDE 30 %%
+%%%%%%%%%%%%%%%%%%%%
+\begin{frame}{\small MuDiLCO Protocol $\blacktriangleright$ MuDiLCO Protocol Algorithm}
+%\vspace{0.2cm}
+\begin{femtoBlock} {}
+\centering
+%\includegraphics[height = 7.2cm]{Figures/algo2.jpeg}
+\includegraphics[height = 7.2cm]{Figures/Algo2.png}
+\end{femtoBlock}
+\end{frame}
+
+
+%%%%%%%%%%%%%%%%%%%%
+%% SLIDE 31 %%
+%%%%%%%%%%%%%%%%%%%%
+\begin{frame}{\small MuDiLCO Protocol $\blacktriangleright$ Results Analysis and Comparison}
+\vspace{-0.5cm}
+\begin{figure}[h!]
+\centering
+ \includegraphics[scale=0.5] {Figures/R1/CR.pdf}
+\caption{Average coverage ratio for 150 deployed nodes}
+\label{fig3}
+\end{figure}
+\end{frame}
+
+
+%%%%%%%%%%%%%%%%%%%%
+%% SLIDE 32 %%
+%%%%%%%%%%%%%%%%%%%%
+\begin{frame}{\small MuDiLCO Protocol $\blacktriangleright$ Results Analysis and Comparison}
+\vspace{-0.5cm}
+\begin{figure}[h!]
+\centering
+\includegraphics[scale=0.5]{Figures/R1/ASR.pdf}
+\caption{Active sensors ratio for 150 deployed nodes}
+\label{fig4}
+\end{figure}
+\end{frame}
+
+
+%%%%%%%%%%%%%%%%%%%%
+%% SLIDE 33 %%
+%%%%%%%%%%%%%%%%%%%%
+%\begin{frame}{\small MuDiLCO Protocol $\blacktriangleright$ Results Analysis and Comparison}
+%\vspace{-0.5cm}
+%\begin{figure}[t]
+%\centering
+%\includegraphics[scale=0.5]{Figures/R1/SR.pdf}
+%\caption{Cumulative percentage of stopped simulation runs for 150 deployed nodes }
+%\label{fig6}
+%\end{figure}
+%\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%
+%% SLIDE 34 %%
+%%%%%%%%%%%%%%%%%%%%
+\begin{frame}{\small MuDiLCO Protocol $\blacktriangleright$ Results Analysis and Comparison}
+\vspace{-0.5cm}
+\begin{figure}[h!]
+\centering
+\includegraphics[scale=0.5]{Figures/R1/T.pdf}
+\caption{Execution Time (in seconds)}
+\label{fig77}
+\end{figure}
+\end{frame}
+
+
+%%%%%%%%%%%%%%%%%%%%
+%% SLIDE 35 %%
+%%%%%%%%%%%%%%%%%%%%
+\begin{frame}{\small MuDiLCO Protocol $\blacktriangleright$ Results Analysis and Comparison}
+\vspace{-0.5cm}
+\begin{figure}%[h!]
+\begin{columns}[c]
+ \column{.50\textwidth}
+\includegraphics[scale=0.35]{Figures/R1/EC95.eps}
+\footnotesize \\~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(a)\\
+\column{.50\textwidth}
+\includegraphics[scale=0.35]{Figures/R1/EC50.eps}
+\footnotesize \\~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(b) \\
+\end{columns}
+\caption{Energy consumption for (a) $Lifetime_{95}$ and (b) $Lifetime_{50}$}
+\label{Figures/ch4t/R3/EC}
+\end{figure}
+\end{frame}
+
+
+%%%%%%%%%%%%%%%%%%%%
+%% SLIDE 36 %%
+%%%%%%%%%%%%%%%%%%%%
+\begin{frame}{\small MuDiLCO Protocol $\blacktriangleright$ Results Analysis and Comparison}
+\vspace{-0.5cm}
+\begin{figure}%[h!]
+\begin{columns}[c]
+ \column{.50\textwidth}
+\includegraphics[scale=0.35]{Figures/R1/LT95.eps}
+\footnotesize \\~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(a)\\
+\column{.50\textwidth}
+\includegraphics[scale=0.35]{Figures/R1/LT50.eps}
+\footnotesize \\~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(b) \\
+\end{columns}
+\caption{Network lifetime for (a) $Lifetime_{95}$ and (b) $Lifetime_{50}$}
+\label{Figures/ch4/Rh3/EC}
+\end{figure}
+
+\end{frame}
+
+
+
+
+\section{\small {Perimeter-based Coverage Optimization (PeCO) to Improve Lifetime in WSNs
+}}
+
+
+%%%%%%%%%%%%%%%%%%%%
+%% SLIDE 45 %%
+%%%%%%%%%%%%%%%%%%%%
+\begin{frame}{\small PeCO Protocol $\blacktriangleright$ Assumptions and Models}
+
+\vspace{-0.5cm}
+\begin{figure}%[h!]
+\begin{columns}[c]
+ \column{.50\textwidth}
+\includegraphics[scale=0.40]{Figures/ch6/pcm.jpg}
+\footnotesize \\~~~~~~~~~~~~~~~~~~~~~~~~~~(a)\\
+\column{.50\textwidth}
+$$\alpha = \arccos \left(\dfrac{Dist(u,v)}{2R_s}
+\right).$$
+\includegraphics[scale=0.40]{Figures/ch6/twosensors.jpg}
+\footnotesize \\~~~~~~~~~~~~~~~~~~~~~~~~~~(b) \\
+\end{columns}
+\caption{(a) Perimeter coverage of sensor node 0 and (b) finding the arc of
+ $u$'s perimeter covered by $v$.}
+ \label{pcm2sensors}
+\end{figure}
+\end{frame}
+
+
+%%%%%%%%%%%%%%%%%%%%
+%% SLIDE 46 %%
+%%%%%%%%%%%%%%%%%%%%
+\begin{frame}{\small PeCO Protocol $\blacktriangleright$ Assumptions and Models}
+
+\vspace{-0.5cm}
+\begin{figure}%[h!]
+\begin{columns}[c]
+ \column{.50\textwidth}
+\includegraphics[scale=0.33]{Figures/ch6/expcm2.jpg}
+\footnotesize \\~~~~~~~~~~~~~~~~~~~~~~~~~~(a)\\
+\column{.50\textwidth}
+\includegraphics[scale=0.38]{Figures/tbl.jpeg}
+\footnotesize \\~~~~~~~~~~~~~~~~~~~~~~~~~~(b) \\
+\end{columns}
+\caption{(a) Maximum coverage levels for perimeter of sensor node $0$. and (b) Coverage intervals and contributing sensors for sensor node 0.}
+ \label{pcm2sensors}
+\end{figure}
+
+
+\end{frame}
+
+
+
+%%%%%%%%%%%%%%%%%%%%
+%% SLIDE 47 %%
+%%%%%%%%%%%%%%%%%%%%
+\begin{frame}{\small PeCO Protocol $\blacktriangleright$ PeCO Protocol Algorithm}
+\vspace{-0.7cm}
+%\includegraphics[height = 7.2cm]{Figures/algo6.jpeg}
+
+\begin{figure}[h!]
+\centering
+ \includegraphics[height = 7.2cm]{Figures/Algo3.png}
+\end{figure}
+\end{frame}
+
+
+%%%%%%%%%%%%%%%%%%%%
+%% SLIDE 48 %%
+%%%%%%%%%%%%%%%%%%%%
+\begin{frame}{\small PeCO Protocol $\blacktriangleright$ Perimeter-based Coverage Problem Formulation}
+\vspace{-1.1cm}
+
+\begin{figure}[h!]
+\centering
+\includegraphics[scale=0.5]{Figures/ch6/formula6.png}
+\end{figure}
+
+\end{frame}
+
+
+
+%%%%%%%%%%%%%%%%%%%%
+%% SLIDE %%
+%%%%%%%%%%%%%%%%%%%%
+\begin{frame}{\small PeCO Protocol $\blacktriangleright$ Performance Evaluation and Analysis}
+\vspace{-0.5cm}
+\begin{figure}[h!]
+\centering
+ \includegraphics[scale=0.5] {Figures/ch6/R/CR.eps}
+\caption{Coverage ratio for 200 deployed nodes.}
+\label{fig333}
+\end{figure}
+
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%
+%% SLIDE %%
+%%%%%%%%%%%%%%%%%%%%
+\begin{frame}{\small PeCO Protocol $\blacktriangleright$ Performance Evaluation and Analysis}
+\vspace{-0.5cm}
+\begin{figure}[h!]
+\centering
+\includegraphics[scale=0.5]{Figures/ch6/R/ASR.eps}
+\caption{Active sensors ratio for 200 deployed nodes.}
+\label{fig444}
+\end{figure}
+
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%
+%% SLIDE %%
+%%%%%%%%%%%%%%%%%%%%
+\begin{frame}{\small PeCO Protocol $\blacktriangleright$ Performance Evaluation and Analysis}
+\vspace{-0.5cm}
+\begin{figure}%[h!]
+\begin{columns}[c]
+ \column{.50\textwidth}
+\includegraphics[scale=0.35]{Figures/ch6/R/EC95.eps}
+\footnotesize \\~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(a)\\
+\column{.50\textwidth}
+\includegraphics[scale=0.35]{Figures/ch6/R/EC50.eps}
+\footnotesize \\~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(b) \\
+\end{columns}
+\caption{Energy consumption per period for (a)~$Lifetime_{95}$ and (b)~$Lifetime_{50}$.}
+ \label{fig3EC}
+\end{figure}
+
+
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%
+%% SLIDE %%
+%%%%%%%%%%%%%%%%%%%%
+\begin{frame}{\small PeCO Protocol $\blacktriangleright$ Performance Evaluation and Analysis}
+\vspace{-0.5cm}
+\begin{figure}%[h!]
+\begin{columns}[c]
+ \column{.50\textwidth}
+\includegraphics[scale=0.35]{Figures/ch6/R/LT95.eps}
+\footnotesize \\~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(a)\\
+\column{.50\textwidth}
+\includegraphics[scale=0.35]{Figures/ch6/R/LT50.eps}
+\footnotesize \\~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(b) \\
+\end{columns}
+\caption{Network Lifetime for (a)~$Lifetime_{95}$ and (b)~$Lifetime_{50}$.}
+ \label{fig3LT}
+\end{figure}
+
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%
+%% SLIDE %%
+%%%%%%%%%%%%%%%%%%%%
+%\begin{frame}{\small PeCO Protocol $\blacktriangleright$ Performance Evaluation and Analysis}
+%\vspace{-0.5cm}
+%\begin{figure} [h!]
+%\centering \includegraphics[scale=0.5]{Figures/ch6/R/LTa.eps}
+%\caption{Network lifetime for different coverage ratios.}
+%\label{figLTALL}
+%\end{figure}
+%\end{frame}
+
+
+
+%%%%%%%%%%%%%%%%%%%%
+%% SLIDE %%
+%%%%%%%%%%%%%%%%%%%%
+\section{\small {Conclusion and Perspectives}}
+
+
+%%%%%%%%%%%%%%%%%%%%
+%% SLIDE 50 %%
+%%%%%%%%%%%%%%%%%%%%
+\begin{frame}{Conclusion}
+\begin{enumerate} [$\blacktriangleright$]
+
+\item Two-step approaches are proposed to optimize both coverage and lifetime performances, where:
+\begin{itemize}
+\item Sensing field is divided into smaller subregions using divide-and-conquer method.
+\item One of the proposed optimization protocols is applied in each subregion in a distributed parallel way.
+\end{itemize}
+\item The proposed protocols (DiLCO, MuDiLCO, PeCO) combine two efficient mechanisms:
+\begin{itemize}
+\item Network leader election, and
+\item Sensor activity scheduling based optimization.
+\end{itemize}
+\item Our protocols are periodic where each period consists of 4
+phases:
+\begin{itemize}
+\item Information exchange,
+\item Network leader election,
+\item Decision based optimization, and
+\item Sensing.
+\end{itemize}
+\end{enumerate}
+
+
+
+
+\end{frame}
+
+
+%%%%%%%%%%%%%%%%%%%%
+%% SLIDE 51 %%
+%%%%%%%%%%%%%%%%%%%%
+\begin{frame}{Conclusion}
+\begin{enumerate} [$\blacktriangleright$]
+
+\item DiLCO and PeCO provide a schedule for one round per period.
+\item MuDiLCO provides a schedule for multiple rounds per period.
+\item Comparison results show that DiLCO, MuDiLCO, and PeCO protocols:
+\begin{itemize}
+ \item maintain the coverage for a larger number of rounds.
+ \item use less active nodes to save energy efficiently during sensing.
+ \item are more powerful against network disconnections.
+ \item perform the optimization with suitable execution times.
+ \item consume less energy.
+ \item prolong the network lifetime.
+
+\end{itemize}
+\end{enumerate}
+\end{frame}
+
+
+%%%%%%%%%%%%%%%%%%%%
+%% SLIDE 52 %%
+%%%%%%%%%%%%%%%%%%%%
+\begin{frame}{Perspectives}
+\begin{enumerate} [$\blacktriangleright$]
+\item The optimal number of subregions will be investigated.
+\item Design a heterogeneous integrated optimization protocol to integrate coverage, routing, and data aggregation protocols.
+\item Extend PeCO protocol so that the schedules are planned for multiple
+sensing periods.
+\item We plan to consider particle swarm optimization or evolutionary algorithms to obtain quickly near optimal solutions.
+\item Improve our mathematical models to take into account heterogeneous sensors from both energy and node characteristics point of views.
+\item The cluster head will be selected in a distributed way and based on local information.
+\end{enumerate}
+
+
+\end{frame}
+
+
+%%%%%%%%%%%%%%%%%%%%
+%% SLIDE 53 %%
+%%%%%%%%%%%%%%%%%%%%
+%\begin{frame}{Mes perspectives}
+%
+%\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%
+%% SLIDE 54 %%
+%%%%%%%%%%%%%%%%%%%%
+\begin{frame}{Fin}
+\begin{center}
+\huge
+\textcolor{BleuFemto}{Thank You for Your Attention!}\\\vspace{2cm}
+\textcolor{BleuFemto}{Questions?}\\
+\end{center}
+\end{frame}
+\end{document}
+% _____ ___ _ _
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