Algorithms for A Connected Dominating Set in Wireless Networks

Transcription

1 Algorithms for A Connected Dominating Set in Wireless Networks Thesis submitted in Partial Fulfillment of the Requirements for the Award of the Degree of Master of Technology In Computer Science and Engineering By G.D.K.Viswanath Reddy [06CS6009] Under the guidance of Professor C.R.Mandal Department of Computer Science & Engineering Indian Institute of Technology, Kharagpur May 2008

2 Certificate May, 2008 This is to certify that the thesis entitled Algorithms For A Connected Dominating Set s in Wireless networks submitted to the Department of Computer Science and Engineering, Indian Institute of Technology, Kharagpur by G.D.K.Viswanath Reddy (Roll No. 06CS6009) for the partial fulfillment of the requirements for the award of degree of Master of Technology in Computer Science and Engineering is a bonafide record of the work carried out by him under my supervision and guidance. The research report and results embodied in this thesis have not been submitted for any other degree or diploma in any other University or Institute..... Prof. C.R.Mandal Dept. of Computer Science and Engineering Indian Institute of Technology Kharagpur

3 Acknowledgement I express my sincere gratitude to my respected project supervisor Prof. C.R.Mandal, Department of Computer Science And Engineering, Indian Institute of Technology, Kharagpur under whose supervision and guidance this work has been carried out. His whole hearted involvement, advice, support and constant encouragement throughout, have been responsible for carrying out this project work with confidence. I am also grateful to him for providing me with required infrastructural facilities that have been highly beneficial to me in undertaking the above mentioned project. I am sincerely grateful to Prof. Indranil Sen Gupta, Professor and Head, Department of Computer Science and Engineering, Indian Institute of Technology, Kharagpur for providing all necessary facilities for the successful completion of my project. I would like to extend my heartfelt thanks to my friends for their support and help to overcome the difficulties by always being with me in my ups and downs during the Project. I would also like to thank the supporting staff of Department of Computer Science and Engineering for their timely help and assistance. Place: Kharagpur Date:.. (G.D.K.Viswanath Reddy)

4 Dedicated to my parents

5 Abstract A wireless adhoc network is a collection of wireless mobile nodes forming a temporary network without the aid of any established infrastructure or centralized administration. A connection is achieved between two nodes through a single hop transmission if they are directly connected or multi-hop transmission if they are not. The wireless networks face challenges to form an optimal routing protocol. Some approaches are based on a dominating set, which has all the nodes either in the set or within its neighborhood. Efficient routing among a set of mobile hosts (also called nodes) is one of the most important functions in ad-hoc wireless networks. A set is dominating if all the nodes in the system are either in the set or neighbors of nodes in the set. Routing based on a connected dominating set is a Efficient approach, where the searching space for a route is reduced to nodes in the set, The proposed algorithm is an enhancement of the distributed algorithm proposed by Wu and Li. In this paper, we propose a simple and efficient distributed algorithm for calculating connected dominating set in ad-hoc wireless networks, where connections of nodes are determined by their geographical distances. We also propose an update/recalculation algorithm for the connected dominating set when the topology of the ad hoc wireless network changes dynamically. The simulation results from the new algorithm are compared to results from Wu and Li s algorithm. The simulation results show that the average dominating set of nodes decreased considerable after applying the new algorithm. Our approach can be potentially used in designing efficient routing algorithms based on a connected dominating set INDEX WORDS: Connected Dominating Set, Routing Protocol, Position-based Routing, Ad hoc wireless networks, Mobile computing, Simulation

6 CONTENTS Page No. ABSTRACT LIST OF TABLES LIST OF FIGURES CHAPTER INTRODUCTION TO CONNECTED DOMINATING SET Mobile Ad Hoc Wireless Networking Challenges And Status Of Routing Protocols Research Question Organization Of This Thesis... 6 CHAPTER LITERATURE REVIEW Traditional Routing Protocols Position-Based Routing Protocols Subgraph-Routing Protocols Summary... 9 CHAPTER RELATED WORK ON CONNECTED DOMINATING SET Dominating Set Problem And Definition Wu And Li s Algorithm Marking Process... 11

7 3.3 Problem With Wu s Algorithm Proposed Extension Rules Explanation Of New Extension Rules Algorithm For Finding Cds From Dominating Set Proposed Algorithm 1: Algorithm For Finding Cds In Wireless Network Proposed Algorithm2: Cds-Based-Routing In Wireless Network CHAPTER UPDATE/RECALCULATION OF THE CDS Mobile Host Switching On Mobile Host Switching Off movement Of A Node CHAPTER DISCUSSION OF SIMULATION AND RESULTS Simulation Procedure Results CHAPTER CONCLUSION BIBLIOGRAPHY... 45

8 List of Tables Table No. Page No. 5.1: Number of dominating set nodes relative to varying n for r = : Number of dominating set nodes relative to varying n for r = : Number of dominating set nodes relative to varying n for r = : Number of dominating set nodes relative to varying n for r = : Number of dominating set nodes relative to varying r for n = : Number of dominating set nodes relative to varying r for n = : Number of dominating set nodes relative to varying r for n = : Number of dominating set nodes relative to varying r for n =

9 Figure No. List of Figures Page No. 1.1: A simple wireless network of five wireless mobile hosts : Example for a Dominating set 4 3.1: The Represented graph of adhoc wireless network in Figure : Randomly Located 20 Nodes in 2D plane A Connected Graph A Connected graph with Basic Marking Rule A Connected Graph Marked with Extension Rule (i) A graph Marked with Extension Rule (ii) A graph Marked with New Extension Rule A gateway neighbor u A non-gateway neighbor w A gateway neighbor u A non-gateway neighbor w : Average number of dominate set nodes relative to varying n for r = : Average number of dominate set nodes relative to varying n for r = : Average number of dominate set nodes relative to varying n for r = : Average number of dominate set nodes relative to varying n for r = : Average number of dominate set nodes relative to varying r for n = : Average number of dominate set nodes relative to varying r for n = : Average number of dominate set nodes relative to varying r for n = : Average number of dominate set nodes relative to varying r for n =

10 CHAPTER 1 Introduction to Connected Dominating Set Recent advances in technology have provided portable computers with wireless interfaces that allow networked communication among mobile users. Wireless networks can provide mobile users with widespread communication capability and easy information access regardless of location. There are currently two variations of mobile wireless networks. The first kind is known as infrastructured networks, i.e., those networks with fixed and wired gateways, the bridges for these networks are known as stations. Typical applications of this kind of network are WLAN s and cellular networks. The second type of mobile wireless networks is the infrastructure less mobile network, known as self-organized network, and which is also referred to as Mobile Ad hoc Network. The resulting computing environment, which is often referred to as mobile computing [18], no longer requires users to maintain a fixed and universally known position in the network and enables almost unrestricted mobility. Self-organized networks consist of mobile radio nodes (hosts, routers or switches) forming a temporary network, without any aid of existing network infrastructure or centralized system administration. Network nodes, when out of the transmission range of each other, may communicate with intermediate nodes to forward their packets in a multi-hop mode. These networks are suitable in situations when an instant infrastructure is needed. A connection is achieved either through a single-hop radio transmission if two nodes are located within wireless transmission range of each other, or through relays by intermediate nodes that are willing to forward packets for them.

11 1.1 MOBILE AD HOC WIRELESS NETWORKING An ad hoc wireless network is a special type of wireless network in which a collection of mobile hosts with wireless network interfaces may form a temporary network, without the aid of any established infrastructure or centralized administration. If only two hosts, located closely together within wireless transmission range of each other, are involved in the ad hoc wireless network, no real routing protocol or decision is necessary. However, if two hosts that want to communicate are outside their wireless transmission ranges, they could communicate only if other hosts between them in the ad hoc wireless network are willing to forward packets for them. For example, in the network shown in Figure 1, mobile host C is outside the range of host A's wireless transmitter (indicated by the circle around A) and host A is also outside the range of host C's wireless transmitter. If A and C wish to exchange packets, they may use host B to forward packets for them, since B is within the overlap between A's and C's ranges. Figure 1: a simple wireless network of five wireless mobile hosts

12 We can use a simple graph G = (V,E) to represent an ad hoc wireless network, where V represents a set of wireless mobile hosts and E represents a set of edges. An edge between host pairs {v, u} indicates that both hosts v and u are within their wireless transmitter ranges. To simplify our discussion, we assume all mobile hosts are homogeneous, i.e., their wireless transmitter ranges are the same. In other word, if there is an edge e = {v,u} in E, it indicates u is within v's range and v is within u's range. Thus the corresponding graph will be an undirected graph. 1.2 CHALLENGES AND STATUS OF ROUTING PROTOCOLS Routing in ad hoc wireless networks poses special challenges. Routing problem is to find a route for sending a packet from a source to a given destination. There are two main classes of routing protocols. 1) Topology based 2) Position based Topology based routing protocols are based on information about the links. Position based routing protocols use additional information about physical positions. Shortest path algorithm does not work well in MANETS because some nodes may become temporarily inactive or nodes might move. Wireless networks require localized algorithms; traditional routing protocols that use link state or distance vector in wired networks are not suitable in ad hoc wireless networks [14]. Greedy routing, Face algorithm, combination of Greedy Face Greedy (GFG) algorithm are other position based algorithms. Dynamic source protocol (DSR) has also been proposed [17]. DSR allows the network to be

13 Completely self-organizing and self-configuring. The protocol includes two parts: Route Discovery and Route Maintenance. Some researches proposed a new approach where a sub-graph of the ad hoc wireless network is selected and then the sub-graph is searched for routing. This reduces the running time. Dominating set based routing is one such kind of sub graph routing. Wu and Li proposed an efficient algorithm to calculate connected dominating set [26]. Following are some of the characteristics of ad hoc wireless networks 1) Mobility 2) Each node has limited power 3) Low bandwidth Wireless networks deliver lower bandwidth than wired networks, and hence, the information collection (during the formation of a routing table) is expensive. Mobility of hosts, which causes topological changes of the underlying network, also increases the volatility of network information. In addition, the limitation of power leads users disconnect mobile unit frequently in order to save power consumption. This feature may also introduce mobile networks more failures (also called switching on/off), which can be considered as a special form of mobility. Definition: A dominating set in a graph G is a subset of the vertices of the graph, V(G), such that every vertex in V(G) is either in S or has an element of S as one of its neighbors. A real world application of this problem is to view the vertices as cities, and each city must be able to hear a radio station. A city will hear the radio station if it is located in the city itself or in a neighboring city. The standard optimal domination problem seeks a dominating set of minimum cardinality, i.e. S must be as small as possible. See Figure 2.1 for an example.

14 Figure 1.2 Example: Dominating set A dominating set, marked as black vertices. Each vertex v is either dominating (v is black) or has at least one dominating neighbor (v is white). Connected Dominating Set (CDS) Definition : A connected dominating set of a graph G = (V,E) is a set of vertices connected. such that is a dominating set of G, and the sub graph induced by is A dominating set of a graph is called connected dominating set if the induced graph of the dominating set is connected. The minimum connected dominating set problem is to find a connected dominating set of a graph with minimum cardinality. The concept of connected domination is used to find the upper bound of the domination number of a graph, since it is NP hard to determine a domination number of any arbitrary graph. The concept of connected domination is widely used in computer networks. The main advantage of connected-dominating-set-based routing is that it simplifies the routing process to the one in a smaller sub network generated from the connected dominating set. This means that only gateway hosts need to keep routing information. As long as changes in network topology do not affect this sub network there is no need to recalculate routing tables. Clearly, the efficiency of this approach depends largely on the process of finding a connected dominating set and the size of

15 the corresponding subnetwork. Unfortunately, finding a minimum connected dominating set is NP-complete for most graphs. In this paper, we propose a simple distributed algorithm that can quickly determine a connected dominating set in a given connected graph, which represents an ad hoc wireless network. Node connections in the ad hoc wireless network are determined based on their geographical distances in a 2-D space. That is, two nodes are connected if their geographical distance is within a given wireless transmission range. We study some properties of the derived connected dominating set. We show that proposed approach Is much efficient than a classical approach in terms of finding a small dominating set and does so quickly. We also discuss ways to update/recalculate the connected dominating set when the underlying graph changes with the movement of mobile host 1.3 RESEARCH QUESTION The research presented in this thesis implements Wu and Li s algorithm to calculate the connected dominating set nodes in ad hoc wireless networks and extends further by adding an extra extensional rule to decrease the size of dominating set nodes. The simulation results from the new algorithm are compared to results from Wu and Li s algorithm. The above discussion naturally leads us to the following question: does there exist fast local control distributed algorithms for CDS construction in wireless networks?

16 1.4 ORGANIZATION OF THIS THESIS This thesis is divided into six chapters: Introduction (Chapter1), Literature Review (Chapter 2), Related work on Connected Dominating sets (Chapter 3), Update and Recalculation Procedures of CDS (Chapter 4), Discussion of Simulation And Results (Chapter 5) and Conclusion (Chapter 6) Chapter 1 is an introduction for this thesis. It describes definition of mobile wireless network, ad hoc wireless network and its characteristics. The challenges ad hoc wireless network provide for finding a route. In addition to this a summary of status of routing protocols, the research question and overview of this thesis are outlined. Chapter 2 gives the literature survey about the status of routing protocols. Mainly there are two kinds of protocols, topology based routing protocol and position based routing protocol. The characteristics and disadvantage of some protocols are described in this chapter. Chapter 3 describes the definition of Dominating Set and Wu and Li s algorithm is introduced. Also the new extensional rule is described. Chapter 4 describes the process of Wu s algorithm and the new extensional rule. With update and recalculation procedures like switch on and switch off Chapter 5 presents simulation results and explanation. Tables and figures are provided based on the two parameters used to run the algorithms (number of nodes, transmission range). In Chapter 6 relevant conclusions are drawn. The contributions of this work are briefly discussed followed by future areas of research that might be investigated in order to build upon the work presented in this thesis.

17 CHAPTER 2 Literature Review Various routing protocols have been proposed in recent years to address the routing problem in ad hoc wireless networks. Mainly they are classified into two routing classes. One type is topology based routing protocol, based on the information about the links. The other is position based routing protocol that uses additional information about physical location. 2.1 TRADITIONAL ROUTING PROTOCOLS Distributed algorithms for Minimum Connected Dominating Set (MCDS) in mobile ad hoc networks were first developed by Das et al. [3, 10]. These algorithms provide distributed implementations of the two centralized algorithms given by Guha and Khuller [13]. The shortest path algorithm does not work very well in MANETS because some nodes maybe temporarily inactive or some might move. Wireless networks require localized algorithms in which nodes make routing decisions based on the neighboring nodes information. Other traditional routing protocols that use link state or distance vector in wired networks are not suitable for ad hoc wireless networks [14, 12, 17, 18]. Lower bandwidth in wireless networks makes information collection expensive. The power limitation leads users to get disconnected from mobile host frequently. Routing information needs to be localized to adapt quickly to topology changes caused by node movements. Link state routing algorithms are closer to the centralized shortest path algorithm. Each node maintains a view of the network topology with a cost for each link. Each node periodically floats the link cost between it and all other nodes. If a node gets the information, it updates its view of topology and applies shortest path

18 algorithm to select next hop. Although link state routing generally requires each node to know the entire topology, there are some link state algorithms where each node only maintains partial information of the network. The distance vector routing algorithms use the distributed version of Bellman- Ford algorithm (DBF), each node maintains for each destination a set of distances. A node selects next hop node if that node has the minimum distance for a destination. Compared to link state algorithm, it requires less storage space and less network bandwidth overhead. But this algorithm might be effective only when network topological changes are rare [12, 17, 18]. The details of these two routing protocols and their problems are discussed in the papers [16, 18]. 2.2 POSITION-BASED ROUTING PROTOCOLS In position-based routing protocols, forwarding decision of a node depends on the destination node s position and it s one hop neighbors position. One method, called Greedy routing algorithm, is a position based protocol. Each node forwards packet to its neighbor that is closet to destination based on the location information. The greedy algorithm may fail to find a path if the node does not have a neighbor that is closer to destination than the node itself. When that problem arises, the message needs to be forwarded to the node with the least backward distance; this introduces another problem of looping packets. Greedy algorithm s route is very close to the shortest path algorithm, but it has high failure rate because of loop or low degree graphs. To solve the local maximum problem, another algorithm called FACE algorithm is provided. It guarantees the package delivery in connected graph, but it has longer route. Face algorithm is to forward the packet on faces of the planar sub-graph, which are progressively closer to the destination. It also increases the hop count. GFG algorithm is a combination of these two algorithms. First Greedy algorithm is run, when it fails, face algorithm is run, and then greedy algorithm is run. The GFG algorithm combines the two algorithms advantages: it guarantees the package delivery and a relative short route [12].

19 2.3 SUBGRAPH-ROUTING PROTOCOLS Some researches try to find a sub-graph of ad hoc wireless network and search the routing in the sub-graph and reduce the running time. These approaches are known as dominating set based routing protocols. Another type of routing protocols known as Cluster based algorithm, divides a graph into several overlapping clusters [19]. Each cluster is a clique, which is a complete sub-graph. The routing protocol is completed in two phases: cluster formation and cluster maintenance. The routing process centralizes the whole network into a small connected sub-network so that if the network topological changes do not affect this centralized part of the network, there is no need to recalculate routing tables in the sub-network [21, 22]. Dominatingset-based routing is also one kind of sub-graph routing [1, 2, 21, and 25]. If every vertex not in the subset is adjacent to at least one vertex in this subset, the subset is called dominating set. The dominating-set-based routing is based on the theory of dominating theory. This approach reduces the routing and search process to a reduced sub-graph. The efficiency of the approach depends on the process of finding a connected dominating set and the size of the dominating set nodes. 2.4 SUMMARY All of these studies are based on different assumption and try to achieve different objectives. Quite a few algorithms are based on the dominating set based principle. This research focuses on the dominating-set-based routing protocol, particularly Wu and Li s algorithm [26].

20 CHAPTER 3 Related work on Connected Dominating set 3.1 DOMINATING SET PROBLEM AND DEFINITION A dominating set is a subset of nodes such that each node is either in dominating set or has a neighbor in dominating set. A dominating set is called a connected dominating set if there is a path between any two nodes in dominating set that does not use nodes that are not in dominating set. The standard connected dominating set problem is to find a connected dominating set with minimum cardinality of any arbitrary graph. Given an arbitrary undirected graph finding a minimum connected dominating set is a NP-hard problem.. Various algorithms have been proposed to address this problem. One such approach is dominating-set-based routing theory. Assume a wireless ad hoc network is deployed in a two-dimensional space where each node has equal maximum transmission range. Thus the topology of an ad hoc network can be described as a unit-disk graph (UDG). A graph is a unit graph if and only if its vertices can be put in one to one correspondence with equi-sized circles in a plane in such a way that two vertices are joined by an edge if and only if the corresponding circles intersect [5]. A wireless ad hoc network can be represented as a simple graph G (V, E), where V represents a set of mobile nodes and E represents a set of edges. An edge (u, v) in E indicates that nodes u and v are neighbors, and that u is within v s range of transmission, while v is within u s range. A dominating set (DS) is a subset of vertices of a graph G where every vertex that is not in the subset is adjacent to at least one vertex in the dominating set (DS) subset. A connected dominating set (CDS) is a dominating set that induces a connected sub-graph.

21 This approach reduces the routing and searching process to a reduced subgraph, therefore it simplifies the routing and search process. Several algorithms have been proposed based on the dominating set theory [2, 22]. 3.2 WU AND LI S ALGORITHM Wu [1,26] proposed a simple and efficient distributed algorithm that can quickly find a dominating set in a wireless network. Initially a marking process is required to construct a dominating set. The marking process marks every vertex in a given connected and simple graph G = (V, E). m(v) is a marker for node v in G, which is either T (marked) or F (unmarked). All marked nodes form a dominating set MARKING PROCESS 1. Initially assign marker F to every v in V. 2. Every v exchanges its open neighbor set N(v) with all its neighbors. 3. Every v assigns its marker m(v) to T if there exist two unconnected neighbors. Example: Figure 3.1 The Represented graph of adhoc wireless network in Figure 1

22 In the example of Figure 2, First finding the neighbors N(A) = {B,D}, N(B) = {A,C,D}, N(C) = {B,E}, N(D) ={A,B}, and N(E) = {C}. After Step 2 of the marking process, vertex A has N(B) and N(D), B has N(A), N(C), and N(D), C has N(B) and N(E), D has N(A) and N(B), and E has N(C).Based on Step 3, only vertices B and C are marked T. Using the basic marking rule, there are too many dominating set nodes. Then two extension rules can be performed to reduce the size of a dominating set generated from the marking process. A distinct id, id(v) is assigned to each node v in G. Extension rules are defined as: 1. Assume u, v are two marked nodes. If N[ v] N[ u] in G and id(v) < id{u), change m(v) to F. 2. Assume u and w are two marked neighbors of marked node v. If N[ v] N[ u] U N( w) in G and id(v) = min{id(v), id(u), id(w)}, then change m(v) to F. The main idea of the extensional rules is that if a dominating set node A and its all neighbors are dominated by another dominating set node(s) (B, C ) and A s id is the smaller, A can be unmarked to be a non dominating set node. By applying the extensional rules, some nodes can be unmarked and the size of the dominating set is reduced. The number of dominating set nodes is largely reduced and is proved by the simulation tests in this paper. The above algorithm proposed by Wu is distributed and constant number of rounds is needed for the marking process. The efficiency of the approach depends on the size of the dominating set nodes. Wu and Li also proved that the dominating set is connected and closed to minimum.

23 3.3 PROBLEM WITH WU S ALGORITHM After basic marking rule, the set of all marked nodes is a connected dominating set. The connectedness among all marked nodes in the induced graph of connected dominating set remains unaffected after the extension rule (i). But the extension rule (ii) may affect on the connectedness. This is shown through a counter example. In the Figure 3 represented below Fig: 3.2 is a domain with 20 nodes randomly located in a 2D plane Fig: 3.3 shows the graph is connected and then from Fig:3.4 onwards the results of Wu s algorithm using basic rule and extensional rules 1 and 2 are described. Figure 3.2 Randomly Located 20 Nodes in 2D plane

24 Figure 3.3 a Connected Graph Figure 3.3 shows connections between nodes. A connection is established if the distance between node A and node B is in the transmission range. For example, the distance between node 1 and node 8 is in the transmission range so a connection is established.

25 Figure 3.4 a Connected graph with Basic Marking Rule Figure 3.4 shows the graph after applying Basic Marking Rule. A node is marked red if that node has any two nodes that are not directly connected. For example node 4 has 14, 19 as neighbors. Since there is no direct connection between node 14 and node 19, node 4 can be marked red. The same rule is applied for all other nodes in the graph.

26 Figure 3.5 A Connected Graph Marked with Extension Rule (i) Figure 3.5 shows the graph after applying extensional rule (i) to the connected graph. A node is unmarked black if extensional rule 1 applies for that node. For example N[5] = {3,6,7,9,14}, N[7] = {3,5,6,9,14}, N[5] N[7] and id(5) < id(7), therefore 5 can be unmarked by extensional rule 1. In above example there are no other nodes where this rule satisfies. and the still the graph is connected.then now applying the extension rule (ii) we can see that the connected dominating set is no more connected as shown in the Fig:3.6

27 Figure 3.6 A graph Marked with Extension Rule (ii) Figure 3.6 shows the graph after applying extensional rule 2 to the connected graph. Applying extensional rule 2 proposed by Wu & Li, node 1can unmarked (marked blue). Node 1 can be unmarked by extensional rule 2 because it can be covered by other nodes (8,13),Node 3 is dominated by Nodes(7,12),Node 4 is dominated by (14,19),node 6 is dominated by (7,12),node 12 is dominated by (18,17) and finally Node 13 is dominated by (15,16) This is shown in Figure 3.6. Nodes that are unmarked by extensional rule 1 can also be unmarked by extensional rule 2. There is some overlap between extensional rule (i) and extension rule (ii).

28 There are 20 nodes randomly located in 2-D space. Nodes are connected if there are within the transmission range. Nodes are marked by red if the node has any twoneighbor nodes that are not connected directly. For example, Figure 3.4 shows the graph after applying Basic Marking Rule. A node is marked red if that node has any two nodes that are not directly connected. For example node 4 has 14, 19 as neighbors. Since there is no direct connection between node 14 and node 19, node 4 can be marked red.. In the figure nodes 2, 9,10,11,20 are not marked because all of their corresponding neighbors are connected. For example, Figure 3.5 shows the graph after applying extensional rule (i) to the connected graph. A node is unmarked black if extensional rule 1 applies for that node. For example N[5] = {3,6,7,9,14}, N[7] = {3,5,6,9,14}, N[5] N[7] and id(5) < id(7), therefore 5 can be unmarked by extensional rule (i). Applying extensional rule 2, node 1can unmarked (marked blue). Node 1 can be unmarked by extensional rule 2 because it can be covered by other nodes (8,13),Node 3 is dominated by Nodes(7,12),Node 4 is dominated by (14,19),node 6 is dominated by (7,12),node 12 is dominated by (18,17) and finally Node 13 is dominated by (15,16) This is shown in Figure 3.6. Nodes that are unmarked by extensional rule 1 can also be unmarked by extensional rule 2. There is some overlap between extensional rule (i) and extension rule (ii). 3.4 PROPOSED EXTENSION RULES There are two problems in Wu s algorithm: (i) the size of the dominating set is not optimum and (ii) finally a dominating set is established, which is not a connected dominating set. To overcome these problems we propose two more extension rules to reduce the size of the dominating set and an algorithm to form a connected dominating set depending on the dominating set formed by extension rules. New Extension Rule (iii): Assume u and w are two marked neighbors of marked

29 node v. If N[ v] N[ u] U N( w) in G and ID (u) <ID (v) < ID (w), then change m (v) to F. New Extension Rule (iv): Assume u and w are two marked neighbors of marked node v. If N[ v] N[ u] U N( w) in G and ID (v) = max {ID (v), ID (u), ID (w)}, then change m (v) to F Explanation of new extension rules We improved the existing algorithm proposed by Wu and Li. Wu and Li [26] proposed a simple and efficient distributed algorithm that can quickly find a DS in a mobile ad-hoc network. The basic rule of the algorithm proposed by Wu and Li is: A node is marked as dominating node it has two unconnected neighbors. Since this returns a large set of dominate set two extensional rules were proposed: In the First extension rule if a dominating set node can be covered by another dominating node with higher id, then it can be removed from dominating set of nodes. In the Second extension rule if a dominating set node can be covered by two dominating nodes with higher id's, then it can be removed from dominating set of nodes.

30 We implement the basic rule and the two extensional rules first and extend it further by introducing these two rules: In the New First extension rule If a dominating set node can be covered by two dominating nodes, one with higher ID and one with lower ID, then it can be removed from dominating set of nodes. In the New Second extension rule If a dominating set node can be covered by two dominating nodes with lower id s, then it can be removed from dominating set of nodes. Figure 3.7 a graph Marked with New Extension Rule

31 In the above figure 3.7 the representation of the previous example with the applied extension rules will further reduce the size of the dominating set.. Node 17 is covered by nodes 16 and 15 in extension rule(iii) extension rule(iv). 3.5 ALGORITHM FOR FINDING CDS FROM DOMINATING SET A connected dominating set is formed from a dominating set after adding some nodes into dominating set. The chance of an ordinary node to become a dominating node is high when it can connect more components of dominating set. Based on this concept we propose an algorithm to find a connected dominating set from a dominating set. Set Proposed Algorithm 1: To find a Connected Dominating Set from a Dominating Input: A dominating set D of graph G Output: A connected dominating set C of graph G Steps to The algorithm 1) Check whether the induced graph of dominating set is connected or disconnected. If it is connected then assign dominating set graph D to Connected dominating set Graph C and exit from the algorithm. 2) Find the connected components in the induced graph of dominating set graph D in G 3) Find H(u) for all node u belonging to outside of dominating set graph D in G. Where H(u) = the number of distinct components where u has neighbor 4) Find a node v such that H(v) H(u) for all u from outside of dominating set D in G

32 5) Update dominating set D by including the node v into dominating set graph D then goto Step1. Since the connectedness is checked before exit from the Algorithm1 in Step1, finally a connected dominating set is established in the proposed algorithm 3.6 ALGORITHM FOR FINDING CDS IN WIRELESS NETWORK After basic marking rule, a big sized connected dominating set is formed. Next two extension rules are applied to reduce the size of the dominating set. In this extension rules the connected dominating set is reduced to a dominating set. After these two extension rules, two proposed extension rules reduce further the size of the dominating set. Finally the proposed Algorithm1 gives a connected dominating set which is the required dominating set in the wireless network. Proposed Algorithm2: Finding a connected dominating set with minimum cardinality in a wireless network Input: A network topology G = (V, E) of the considered wireless network Output: A connected dominating set C of G 1) Apply basic marking rule on G 2) Apply Extension Rules (i), (ii),and New (iii), (iv) 3) Use Algorithm1 where the set of marked nodes formed in Step2 is the input and C is the output of Algorithm1.

33 3.7 CDS-BASED-ROUTING IN WIRELESS NETWORK The search space to establish a route is reduced to nodes in the current connected dominating set. Since the size of the connected dominating set is smaller than the size of the whole network, any all pair shortest path algorithm can be applied to find all paths among all nodes in connected dominating set. To find a path from a node u to node v, first find out the nearest nodes of u,v in connected dominating set then find out the path between these two nodes in connected dominating set.

34 CHAPTER 4 Update/Recalculation of the CDS One of the most important characteristics of the wireless network is mobility. Each host can move around in the network at any speed. Mobile hosts may switch off at any time and switch on anywhere in the network. We can summarize topological changes of an ad hoc wireless network into three different types: 1) Mobile host switching on 2) Mobile host switching off 3) Mobile host movement. The challenge here is when and how each vertex should update/recalculate gateway information. The gateway update means that only individual mobile hosts update their gateway status. The gateway recalculation means that the entire network recalculates gateway/non-gateway status. If many mobile hosts in the network are in movement, gateway recalculation might be a better approach, i.e., the connected dominating set is recalculated from scratch. On the other hand, if only few mobile hosts are in movement, then gateway information can be updated locally. The questions arise as exactly when to update gateways and when to recalculate gateways. In the following, we will focus only on the gateway update for three types of topology changes mentioned above. Without lost of generality, we assume that the underlying graph of an ad hoc wireless network always remains connected.

35 4.1 MOBILE HOST SWITCHING ON When a mobile host v switches on, only its non-gateway neighbors, along with host v, need to update their status, because any gateway neighbor will still remain as gateway after a new vertex v is added. For example, in Figure 6 (a), when host v switches on, the status of gateway neighbor host u is not affected, because at least two of the u's neighbors u1, u2, and u3 are not connected originally and these connections will not be affected by host v's switch on. Figure: 4.1 a gateway neighbor u On the other hand, in Figure 6 (b), host v's switch on might lead non-gateway neighbor host w to mark itself as gateway, depending on the connection between host v and w's neighbors w1, w2, and w3.

36 Figure: 4.2 a non-gateway neighbor w The corresponding update process can be the following, Consider a node v which is now going to switch on in the network i.e., v is entering into the network. The management to maintain the connected dominating set due to switch-on of v is depends on various situations and it is explained through following steps. 1) Check whether the location of v is unique or not. If it is not unique then v will not get the permission to switch on due to the conflict of location. 2) If the location of v is not in the range of any current existing node then v will not get the permission to switch on. 3) Find out the neighbors N(v) of v. 4) If there are two unconnected neighbors in N(v), assign m(v) to T otherwise assign m(v) to F. 5) Now consider all non-gateway neighbor w of node v, i.e., m(w) = F and w is neighbor of v. Assign m(v) to T if w has at least two unconnected neighbors. 6) If in Step3 and in Step4 any node becomes a dominating node then apply all Extension Rules on all distance-2 neighbors of v.

37 4.2 MOBILE HOST SWITCHING OFF When a mobile host v switches off, only gateway neighbors of that switched off host need to update their status, because any non-gateway neighbor will still remain as non-gateway after vertex v is deleted. For example, in Figure 6 (c), when v switches off, non-gateway neighbor w is not affected. Host w's neighbors w1, w2, and w3 are pairwise connected originally and these pairwise connections will not be affected by host v's switch off. Figure: 4.3 non-gateway neighbor w On the other hand, in Figure 6 (d), host v's switch off might change a gateway neighbor u to non-gateway, depending on the connection between its neighbor hosts u1, u2, and u3.

38 Figure: 4.4 gateway neighbor u The corresponding update process can be the following: Consider a node v which is going to switch off in the network. The management to maintain the connected dominating set due to switch on of v is depends on various situations and it is explained through following steps. 1) Check whether the whole network remains connected or not due to the switched off the node v. If the network remains connected then give permission to the node v to switch off otherwise v can not switch off. 2) For all neighbors w of v updates the neighborhood information of w by deleting v from its neighbor list. 3) Checks all neighbors of w. If its all neighbors are pairwise connected then assign m(w) to F otherwise m(w) to T. 4) Delete all information of v from the network and free its location. 5) Apply all Extension Rules on the network to reduce the size of the connected dominating set.

39 4.3 MOVEMENT OF A NODE A mobile host v's movement can be viewed as several simultaneous or non simultaneous link connections and disconnections. For example, when a mobile host moves, it may lead several link disconnections with its neighbor hosts, and at the same time, it may have new link connections to the hosts within its wireless transmission range, these new links may be disconnected again depending on the way host v moves. Consider a node v is now going to move towards its destination D. Assume that the node v will move on a path P from its current location S to destination D. The movement of v depends on its speed and a fixed time quantum T. The movement management to maintain the connected dominating set depends on various situations which are explained through following steps. 1) If there is any node on the path P then v will not get the permission of its movement on the path P. 2) If the network becomes disconnected due to the movement of v on the path P with given speed, this movement is not permissible. 3) Find out all the locations L where the node v will be after every T time interval on its paths to destination D depending on its speed. 4) After every T time interval update the neighborhood information of all the neighbors of v on its both current and previous locations due to the absence of v at its previous location and presence at its current location. Also update the neighborhood information of v due to the absence of v at its previous location and presence at its current location.

40 5) Consider all the previous and current neighbors of v and v itself. If there exists at least two unconnected neighbors of the considered node then its marker m(v) assigned to T otherwise to F. 6) Apply all extension rules on the network to reduce the size of the connected dominating set.

41 CHAPTER 5 Discussion of Simulation and Results In this chapter we present the implementation of the proposed algorithm, mobility management and the simulation results of our algorithm. Finally, we present the conclusions drawn from the simulation study. The goal of our simulations is the following: (i) Apply the proposed algorithm on varying nodes, (ii) perform comparison with Wu s algorithm, (iii) maintain the dynamic nature of the network through proposed mobility management. We model wireless network as a set of nodes deployed in a predefined rectangular area of dimension 100x100 square units called as deployment area. Each node has a unique ID. We use the uniform random number generator that chooses the x and y coordinates in deployment area A for nodes. For simulation experiments, we consider the network of varying sizes. We assume that each wireless node has the same transmission range r. The edge between any pair of nodes indicates that distance between them is at most radius r. Since the maximum transmission range r is fixed parameter of our experiments in the given network, thus the induced graph is unit disk graph. The simulation is carried out by varying the network size n, so that impact of network size can be observed on size of dominating set and size of connected dominating set. The simulation is carried out in GCC in UNIX/ LINUX platform.

42 5.1 SIMULATION PROCEDURE The flow of the simulation process for the proposed algorithm and mobility management in wireless network is expressed through the following steps. 1) Generate randomly distributed n nodes in the deployment area. 2) Connect two nodes if their distance is less than or equal to the transmission range r. 3) Find the number of connected components in the graph using DFS. If the number of connected components is more than one, goto Step1 4) Use basic marking rule to mark dominating set nodes and store the size of the dominating set. 5) Use extensional rule (i) to unmark some dominating set nodes, check whether the induced graph of marked nodes is connected or not and store the size of the dominating set. 6) Use extensional rule (ii) to unmark some dominating set nodes, check whether the induced graph of marked nodes is connected or not and store the size of the dominating set. 7) Use extensional rule (iii) and rule (iv) to unmark some dominating set nodes and store the size of the dominating set. 8) Implement Algorithm1 to find the connected dominating set from the marked nodes. 9) For Switching on a new node, first generate a unique node in the network and perform the switching on management on the network.

43 10) For Switching off a node, first take a permission to switch off the considered node. After permission, perform the switching off management on the network. 11) For movement of a node, first take the destination location and speed of the considered node to move. Perform the movement management on the network after taking the permission of the movement. 12) Apply the all pair shortest path process on the connected dominating set formed in Step8 13) Finally establish the routing based on the paths formed in Step RESULTS In this section we conducted the simulation study which computes the average size of the CDS derived from our algorithm and compared with results from existing Wu and Li s algorithm. We have simulated three algorithms: Wu and Li s basic rule, Wu and Li s extensional rules and our new algorithm. Our simulation results verify that Wu s algorithm results from using basic rule only is poor and generates a large dominating set. Wu s extensional rules 1 and 2 decrease the dominating set nodes considerably. But our proposed new two extension rules reduce the size of the dominating set more than Wu s extensional rules 1 and 2. Our simulation results verify the proposed mobility management for switch on, switch off, and movement of nodes in the network. The simulation is performed using the following parameters. Node n represents the number of mobile hosts in the network, and represents the number of gateways (the size of the dominating set) in the network, r represents the radius of mobile host's transmission area, Extension 1 and Extension 2 are the number of

44 dominating nodes calculated by Wu and Li algorithm two rules, New1 and New2 is the number of dominating nodes calculated by our algorithm with two proposed rules and finally CDS is the number of Connected Dominating nodes in the network,which we will be comparing it with the Extension 1 rile proposed by the Wu and Li. Random graphs are generated in a square units of a 2-D simulation area, by randomly throwing a certain number of mobile hosts. A 2-D simulation area resembles more an actual ad hoc wireless network where mobile hosts usually stay on ground. Assume that each mobile host has the same transmission radius, thus the generated graph is undirected. Then, set the radius of mobile host's transmission area to r. If the distance between any two nodes is less than radius r, then there is a link connection between these two nodes. The connected dominating set is calculated through the following steps. 1) Using a depth first search algorithm (DFS) to examine if the generated graph is connected or not. If the graph is disconnected, simply discard the graph; otherwise, continue the following step. 2) Applying three different algorithms to the generated random graph and calculate Extension1,Extension2,New1, New2,CDS, respectively. More precisely, we performed two groups of simulation. In the first group, we first generate random graphs according to the graph generation procedure above. Then, set the radius of the mobile host's transmission area r to four different values: 75, 100, 150, 200. In this way, we can control the density of generated graphs, since the density of generated graphs increases as r increases. If the distance between any two nodes is less than r, then there is a link connection between these two nodes and the resultant graph is a complete graph. For each r, we also vary the number of mobile nodes n from 100 to 500. we simply take the results of New1, New2, and CDS.

45 Table 5.1: Number of dominating set nodes relative to varying n for r = 75 No: of nodes Basic Marking Rule Extention Rule (i) Extension Rule (ii) New Rule (i) New rule (ii) CDS Figure 5.1: Average number of dominate set nodes relative to varying n for r = 75

46 Table 5.2: Number of dominating set nodes relative to varying n for r = 100 No: of nodes Basic Marking Rule Extention Rule (i) Extension Rule (ii) New Rule (i) New rule (ii) CDS Figure 5.2: Average number of dominate set nodes relative to varying n for r = 100