X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/ThesisAli.git/blobdiff_plain/471e797ea207eea3a79a42ef48e6c3b14f3c004b..a5b27a679ef2809581fb27959ecfcf348dcbbe39:/SlidesAli/These.tex

diff --git a/SlidesAli/These.tex b/SlidesAli/These.tex
index 2e7b91c..94c4bef 100644
--- a/SlidesAli/These.tex
+++ b/SlidesAli/These.tex
@@ -111,7 +111,7 @@
 \end{figure}
 
  \begin{block}{\textcolor{white}{ MAIN QUESTION?}}
-  		\textcolor{black}{How to minimize the energy consumption and extend the network lifetime during covering a certain area?}
+  		\textcolor{black}{How to minimize the energy consumption and extend the network lifetime when covering a certain area?}
 \end{block}
  \end{frame}
 
@@ -121,19 +121,21 @@
 %%%%%%%%%%%%%%%%%%%% 
 \begin{frame}{Problem Definition, Solution, and Objectives}
 
-\begin{block}{\textcolor{white}{OUR SOLUTION}}
-\bf \textcolor{black}{The area of interest is divided into subregions using a divide-and conquer method and then combine two efficient techniques:}
+\begin{block}{\textcolor{white}{OUR SOLUTION: distributed optimization process}}
+\bf \textcolor{black}{Division into subregions}\\
+\bf \textcolor{black}{For each subregion:}
   	
  \begin{itemize}
-         \item \bf \textcolor{magenta}{Leader Election for each subregion.}
-        % \item Activity Scheduling based optimization is planned for each subregion.
+         \item \bf \textcolor{magenta}{Leader election}
+         \item \bf \textcolor{magenta}{Activity Scheduling based optimization}
          \end{itemize}
    		
-  		\end{block} 	
+  		\end{block}
+\vspace{-1.5em} 		 	
 \begin{figure}
-   \includegraphics[width=0.475\textwidth]{Figures/div}
-   \hfill
    \includegraphics[width=0.475\textwidth]{Figures/div2}
+   \hfill
+   \includegraphics[width=0.475\textwidth]{Figures/act2}
 \end{figure}
   	
 \end{frame}
@@ -141,39 +143,39 @@
 %%%%%%%%%%%%%%%%%%%%
 %%    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 \bf \textcolor{magenta}{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}
+%\begin{frame}{Problem Definition, Solution, and Objectives}
+%
+%\begin{block}{\textcolor{white}{OUR SOLUTION}}
+% \begin{itemize}
+%         %\item Leader Election for each subregion.
+%         \item \bf \textcolor{magenta}{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}{\bf \textcolor{white}{Dissertation Objectives}}
-\bf \textcolor{black}{Develop energy-efficient distributed optimization protocols that should be able to:}
- \begin{itemize}
-    \item \bf \textcolor{blue}{Schedule node activities by optimize both coverage and lifetime.}
-    \item \bf \textcolor{blue}{Combine two efficient techniques: leader election and sensor activity scheduling.}
-    \item \bf \textcolor{blue}{Perform a distributed optimization process.}
-  \end{itemize}
-   		
- \end{block} 	
-
-  	
-\end{frame}
+%\begin{frame}{Problem Definition, Solution, and Objectives}
+%
+%\begin{block}{\bf \textcolor{white}{Dissertation Objectives}}
+%\bf \textcolor{black}{Develop energy-efficient distributed optimization protocols that should be able to:}
+% \begin{itemize}
+%    \item \bf \textcolor{blue}{Schedule node activities by optimize both coverage and lifetime.}
+%    \item \bf \textcolor{blue}{Combine two efficient techniques: leader election and sensor activity scheduling.}
+%    \item \bf \textcolor{blue}{Perform a distributed optimization process.}
+%  \end{itemize}
+%   		
+% \end{block} 	
+%
+%  	
+%\end{frame}
 
 
 %%%%%%%%%%%%%%%%%%%%
@@ -211,9 +213,9 @@
     \begin{femtoBlock}	
 	{Sensor \\}
 		 \begin{itemize}
-  			\item  Electronic Low-cost tiny device.
-  			\item Sense, process and transmit data.
-  			\item Limited energy, memory and processing capabilities.
+  			\item  Electronic low-cost tiny device
+  			\item Sense, process and transmit data
+  			\item Limited energy, memory and processing capabilities
   		\end{itemize}
 	\end{femtoBlock}
 	 
@@ -226,18 +228,7 @@
      \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}
 
@@ -295,6 +286,8 @@
 
      \includegraphics[height = 5cm]{Figures/WSN-M.pdf}
  \end{figure} 
+ 
+ \bf \textcolor{blue} {Our approach: includes cluster architecture and scheduling schemes}
 \end{frame}
 
 %\begin{frame}{Energy-Efficient Mechanisms of a working WSN}
@@ -308,9 +301,9 @@
 %%%%%%%%%%%%%%%%%%%%
 %%    SLIDE 10    %%
 %%%%%%%%%%%%%%%%%%%%
-\begin{frame}{Network Lifetime}
+\begin{frame}{Network lifetime}
 \vspace{-1.5em}
-\begin{block}{\textcolor{white} {Some Network Lifetime Definitions:}}
+\begin{block}{\textcolor{white} {Some definitions:}}
 \small
 \begin{enumerate}[i)]
 \item \textcolor{black} {Time spent until death of the first sensor (or cluster head).}
@@ -318,12 +311,13 @@
 \item  \textcolor{black} {Time spent by WSN in covering each target by at least one sensor.}
 \item  \textcolor{black} {Time during which the area of interest is covered by at least k nodes.}
 \item \textcolor{black} {Elapsed time until losing the connectivity or the coverage.}
+\item \bf \textcolor{red} {Time elapsed until the coverage ratio becomes less than a predetermined threshold $\alpha$.}
 \end{enumerate}
 \end{block}
 
-\begin{block}{\textcolor{white} {Network lifetime In this dissertation:}}
-\textcolor{blue} {Time elapsed until the coverage ratio becomes less than a predetermined threshold $\alpha$.}
-\end{block}
+%\begin{block}{\textcolor{white} {Network lifetime In this dissertation:}}
+%\textcolor{blue} {Time elapsed until the coverage ratio becomes less than a predetermined threshold $\alpha$.}
+%\end{block}
 
 
 \end{frame}
@@ -333,15 +327,15 @@
 %%%%%%%%%%%%%%%%%%%%
 \begin{frame}{Coverage in Wireless Sensor Networks}
  
-\begin{block} <1-> {\textcolor{white} {Coverage Definition:}} 
+\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.
+\begin{block} <2-> {\textcolor{white} {Coverage types:}} 
+\begin{enumerate}[i)]
+\item \small  \textcolor{red} {Area coverage: every point inside an area has to be monitored.}
 \item  \textcolor{blue} {Target coverage:} only a finite number of discrete points called targets have to be monitored.
 
 \item  \textcolor{blue} {Barrier coverage:} detection of targets as they cross a barrier such as in intrusion detection and border surveillance applications.
@@ -350,70 +344,71 @@
  
 
  
-\begin{block} <3-> {\textcolor{white} {Coverage type in this dissertation:}} 
-The work presented in this dissertation deals with \textcolor{red} {area coverage}.
-\end{block}
+%\begin{block} <3-> {\textcolor{white} {Coverage type in this dissertation:}} 
+%The work presented in this dissertation deals with \textcolor{red} {area coverage}.
+%\end{block}
  
 \end{frame}
 
 %%%%%%%%%%%%%%%%%%%%
 %%    SLIDE 11    %%
 %%%%%%%%%%%%%%%%%%%% 
-\begin{frame}{Existing Works}
+\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{block}  {\textcolor{white} {Coverage approaches:}} 
+%Most existing coverage approaches in literature classified into
+\begin{enumerate}[i)]
+\item \textcolor{blue} { Full centralized coverage algorithms}
     \begin{itemize}
-    \item  Optimal or near optimal solution.
-    \item  low computation power for the sensors (except for base station).
-    \item  Higher energy consumption for communication in large WSN.
-    \item  Not scalable for large WSNs.
+    \item  Optimal or near optimal solution
+    \item  Low computation power for the sensors (except for base station)
+    \item  Higher energy consumption for communication in large WSN
+    \item  Not scalable for large WSNs
     \end{itemize}
-\item Full distributed coverage algorithms.
+\item \textcolor{blue} {Full distributed coverage algorithms}
+   \begin{itemize}
+    \item  Lower quality solution
+    \item Less energy consumption for communication in large WSN
+    \item  Reliable and scalable for large WSNs
+   \end{itemize}
+   \item  \textcolor{red} {Hybrid approaches}
    \begin{itemize}
-    \item  Lower quality solution.
-    \item less energy consumption for communication in large WSN.
-    \item  Reliable and scalable for large WSNs.
+   \item \textcolor{red} {Globally distributed and locally centralized}
    \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}
+%\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}
 
-\begin{frame}{Existing Works: DESK algorithm}
+\begin{frame}{Existing works: DESK algorithm (Vu et al.)}
 \vspace{-1.5em}
 \begin{figure}[!t]
-	   \includegraphics[height = 3.0cm]{Figures/DESK.eps}
+	   \includegraphics[height = 4.0cm]{Figures/DESK.eps}
     \end{figure}  
      \vspace{-2.5em}
      
      \begin{itemize}
-       \item \small developed by Vu et al.
-       \item  works in rounds.
-       \item requires only one-hop neighbor information.
-       \item each sensor decides its status (Active or Sleep) based on the perimeter coverage model.
-       \item whole area is K-covered if and only if the perimeters of all sensors
-are K-covered.
-       
+       \item Requires only one-hop neighbor information (fully distributed)
+       \item Each sensor decides its status (Active or Sleep) based on the perimeter coverage model without optimization
+              
      \end{itemize}
 
 
-\tiny \bf \textcolor{blue}{DESK is chosen for comparison because it works into rounds fashion similar to our approaches, as well as DESK is a full distributed coverage approach.}
+%\tiny \bf \textcolor{blue}{DESK is chosen for comparison because it works into rounds fashion similar to our approaches, as well as DESK is a full distributed coverage approach.}
 
 
 \end{frame}
 
-\begin{frame}{Existing Works: GAF algorithm}
-%\vspace{-0.3em}
+\begin{frame}{Existing works: GAF algorithm (Xu et al.)}
+
 \vspace{-3.3em}
  \begin{columns}[c]
   
@@ -423,33 +418,31 @@ are K-covered.
            \includegraphics[height = 2.7cm]{Figures/GAF1.eps}
     \end{figure}  
     \vspace{-2.5em}
-    \tiny
-	\begin{itemize}
-  	\item  developed by Xu et al.
-  	\item uses geographic location information to divide the area of interest into a fixed square grids.
-  	\item Within each grid, only one node staying awake to take the responsibility of sensing and communication.
-  	\item  the fixed grid is square with r units on a side.
-  	\item $r\leq \dfrac{R_c}{\sqrt{5}}$
-	 \item  Distance(2,5) $\leq$ Communication Range ($R_c$).
-  	\end{itemize}
+    \begin{figure}[!t]
+	   \includegraphics[height = 3.3cm]{Figures/GAF2.eps}
+    \end{figure}
 	 
 	\column{.52\textwidth}
-	 
-%	 \begin{itemize}
-%	 \end{itemize}
+	 \vspace{1.2em}
+\small
+	\begin{itemize}
+	\item Distributed energy-based scheduling approach
+  	\item Uses geographic location information to divide the area into a fixed square grids
+  	\item Nodes are in one of three sates: discovery, active, or sleep
+  	\item  Only one node staying active in grid
+  	\item  The fixed grid is square with r units on a side
+  	 \item  Nodes cooperate within each grid to choose the active node
+  	\end{itemize}
   	
-	 \begin{figure}[!t]
-	   \includegraphics[height = 3.3cm]{Figures/GAF2.eps}
-    \end{figure}  
-     \vspace{-2.5em}
-     
-     \begin{itemize}
-       \item \tiny enat: estimated node active time
-       \item enlt: estimated node lifetime
-       \item Td,Ta, Ts: discovery, active, and sleep timers
-       \item Ta = enlt/2 
-       \item Ts = [enat/2, enat]
-     \end{itemize}
+	   
+      
+%     \begin{itemize}
+%       \item \tiny enat: estimated node active time
+%       \item enlt: estimated node lifetime
+%       \item Td,Ta, Ts: discovery, active, and sleep timers
+%       \item Ta = enlt/2 
+%       \item Ts = [enat/2, enat]
+%     \end{itemize}
      
 
 	
@@ -457,182 +450,121 @@ are K-covered.
 
 \vspace{1.0em}
 
-\tiny \bf \textcolor{blue}{GAF is chosen for comparison because it is famous and easy to implement, as well as many authors referred to it in many publications.}
-
-
-
+%\tiny \bf \textcolor{blue}{GAF is chosen for comparison because it is famous and easy to implement, as well as many authors referred to it in many publications.}
 \end{frame}
 
-%%%%%%%%%%%%%%%%%%%%
-%%    SLIDE 12    %%
-%%%%%%%%%%%%%%%%%%%% 
-\section{\small {Distributed Lifetime Coverage Optimization Protocol (DiLCO)}}
-
+\section{\small {The main scheme for our protocols}}
 
-%%%%%%%%%%%%%%%%%%%%
-%%    SLIDE 13    %%
-%%%%%%%%%%%%%%%%%%%% 
-\begin{frame}{\small DiLCO Protocol $\blacktriangleright$ Assumptions and Network Model:}
-\vspace{-0.5cm}
 
+\begin{frame}{Assumptions for our protocols}
+\vspace{-0.1cm}
 
-\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{enumerate} [$\divideontimes$]
+  		    \item  Static wireless sensor, homogeneous in terms of: 
              \begin{itemize}
-             \item Sensing, Communication, and Processing capabilities
+             \item Sensing, communication, and processing capabilities
              \end{itemize}
-  			\item  Heterogeneous Energy.
-  			 \item Its $R_c\geq 2R_s$.
-  			 \item  Multi-hop communication.
+  			\item  Heterogeneous initial energy
+  			\item  High density uniform deployment 
+  			 \item Its $R_c\geq 2R_s$  for imply connectivity among active nodes during complete coverage (hypothesis proved by Zhang and Zhou)
+
+  			 \item  Multi-hop communication
   			 \item  Known location by:
     \begin{itemize}
-     \item Embedded GPS  or
-     \item Location Discovery Algorithm.           
+     \item Embedded GPS  or location discovery algorithm          
     \end{itemize}
-  		\end{enumerate}		
-  		
-	
-  		
-  	\column{.50\textwidth}
-  	\begin{enumerate} [$\divideontimes$]
-    	\item Using two kinds of packet: 
+    
+    \item Using two kinds of packets: 
         \begin{itemize}    	
-    	   \item INFO packet.
-    	   \item ActiveSleep packet.
+    	   \item INFO packet
+    	   \item ActiveSleep packet
         \end{itemize}
         \item Five status for each node:
         \begin{itemize}    	
-    	   \item  LISTENING, ACTIVE, SLEEP, COMPUTATION, and COMMUNICATION.
+    	   \item  \small 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{enumerate}		
   		
-  	\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}
+\begin{frame}{Assumptions for our protocols}
+  \vspace{-0.5cm}
+\begin{center}
+  	\includegraphics[height = 7.0cm]{Figures/Pmodels.pdf}  
+\end{center}
 
+\end{frame}
 
-\end{enumerate}
 
-\end{femtoBlock}
+
+
+\begin{frame}{Our general scheme}
+\vspace{-0.2cm}
+\begin{figure}[ht!]
+ \includegraphics[width=110mm]{Figures/GeneralModel.jpg}
+ \end{figure} 
+ 
+\begin{itemize}
+\item DiLCO and PeCO  $\blacktriangleright$ use one round sensing ($T=1$)
+\item MuDiLCO $\blacktriangleright$ uses multiple rounds sensing ($T=1\cdots T$)
+\end{itemize}
+
 \end{frame}
 
 
-%%%%%%%%%%%%%%%%%%%%
-%%    SLIDE 14.1    %%
-%%%%%%%%%%%%%%%%%%%% 
-\begin{frame}{\small DiLCO Protocol $\blacktriangleright$ Main Idea}
-%\vspace{-3.2cm}
-\begin{femtoBlock} {}%{Main Idea:\\}
+\begin{frame}{Our general scheme}
+  \vspace{-0.2cm}
+\begin{enumerate} [i)]
+\item \textcolor{blue}{\textbf{INFORMATION EXCHANGE}} $\blacktriangleright$ Sensors exchange through multi-hop communication, their
+\begin{itemize}
+\item \textcolor{magenta}{Position coordinates}, \textcolor{violet}{current remaining energy}, \textcolor{cyan}{sensor node ID}, and \textcolor{red}{number of its one-hop live neighbors}
+ 
+\end{itemize}
 
-\begin{enumerate} [2.]
 
-\item \textcolor{blue}{ \textbf{   LEADER ELECTION:}}\\
-The selection criteria are, in order of importance:
+\item \textcolor{blue}{\textbf{LEADER ELECTION}} $\blacktriangleright$ The selection criteria are, in order 
 \begin{itemize}
-\item   larger number of neighbors, 
-\item larger remaining energy, and then in case of equality, 
-\item larger ID. 
+\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:
+
+ 
+\item \textcolor{blue}{\textbf{DECISION}} $\blacktriangleright$ Leader solves an integer program 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.
+\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:
+
+ 
+\item \textcolor{blue}{\textbf{SENSING}} $\blacktriangleright$ 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.
+\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    %%
+%%    SLIDE 12    %%
 %%%%%%%%%%%%%%%%%%%% 
-\begin{frame}{\small DiLCO Protocol $\blacktriangleright$ Coverage Problem Formulation}
-\vspace{-0.3cm}
-\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*}
-\vspace{-0.3cm}
-\begin{itemize}
-\item \small $P$: the set of primary points.
-\item $J$: the set of sensors.
-\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).
-  \item $\alpha_{jp}$: denotes the indicator function of whether the primary point p is covered.
-\end{itemize}
+\section{\small {Distributed Lifetime Coverage Optimization Protocol (DiLCO)}}
 
 
+%%%%%%%%%%%%%%%%%%%%
+%%    SLIDE 15    %%
+%%%%%%%%%%%%%%%%%%%% 
+\begin{frame}{\small DiLCO Protocol $\blacktriangleright$ Coverage Problem Formulation}
+\vspace{0.2cm}
+\centering
+\includegraphics[height = 7.2cm]{Figures/modell1.pdf}
 
 \end{frame}
 
@@ -833,14 +765,14 @@ Network Simulator & Discrete Event Simulator OMNeT++
 %%%%%%%%%%%%%%%%%%%%
 %%    SLIDE 28    %%
 %%%%%%%%%%%%%%%%%%%% 
-\begin{frame}{\small MuDiLCO Protocol $\blacktriangleright$ Main Idea}
-\vspace{-0.2cm}
-\begin{figure}[ht!]
- \includegraphics[width=110mm]{Figures/GeneralModel.jpg}
-\caption{MuDiLCO protocol.}
-\label{fig2}
-\end{figure} 
-\end{frame}
+%\begin{frame}{\small MuDiLCO Protocol $\blacktriangleright$ Main Idea}
+%\vspace{-0.2cm}
+%\begin{figure}[ht!]
+% \includegraphics[width=110mm]{Figures/GeneralModel.jpg}
+%\caption{MuDiLCO protocol.}
+%\label{fig2}
+%\end{figure} 
+%\end{frame}
 
 
 %%%%%%%%%%%%%%%%%%%%
@@ -850,7 +782,7 @@ Network Simulator & Discrete Event Simulator OMNeT++
 \vspace{0.2cm}
 
 \centering
-\includegraphics[height = 7.2cm]{Figures/model2.pdf}
+\includegraphics[height = 7.2cm]{Figures/modell2.pdf}
 
 \end{frame}
 
@@ -964,8 +896,7 @@ Network Simulator & Discrete Event Simulator OMNeT++
 
 
 
-\section{\small {Perimeter-based Coverage Optimization (PeCO) to Improve Lifetime in WSNs
-}}
+\section{\small {Perimeter-based Coverage Optimization (PeCO)}}
 
 
 %%%%%%%%%%%%%%%%%%%%
@@ -1038,7 +969,7 @@ $$\alpha =  \arccos \left(\dfrac{Dist(u,v)}{2R_s}
 
 \begin{figure}[h!]
 \centering
-\includegraphics[scale=0.49]{Figures/model3.pdf}  
+\includegraphics[scale=0.49]{Figures/modell3.pdf}  
 \end{figure} 
 
 \end{frame}
