CLUSTERING IN WIRELESS SENSOR NETWORKS: A GRAPH THEORY PERSPECTIVE in .NET framework

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CLUSTERING IN WIRELESS SENSOR NETWORKS: A GRAPH THEORY PERSPECTIVE
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(a) N (1) = {2, 3, 4}
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N (15) = {12, 13, 14, 16, 17, 18} N (20) = {9, 19}
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Figure 7.6. ACE cluster formation. (a) Initial state. (b) CHs dominating set.
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The nodes initiate actions at random intervals to avoid collisions. Each time that an action can be initiated for a node is called a node s iteration. The communication between nodes is local and do not require time synchronization. ACE distinguishes between three possible node states: unclustered (still during the cluster formation process), follower (a node that belongs to a cluster with a designated CH), or cluster head. The iteration interval, or time interval between iterations among nodes, is uniformly random distributed. All nodes in the sensor eld are initially in the unclustered state as shown in Figure 7.6a. When a node is unclustered at the beginning of its iteration, it assesses its surroundings and counts the number of loyal followers it would receive if it declared itself a CH of a new cluster. A loyal follower is a node that can belong only to the cluster that would be formed by the current node sensing its signal. If the number of loyal followers for the node is greater than or equal to its spawning threshold function, the node will span a new cluster. The Spanning Threshold Funct tion (fmin ) is given by the formula: fmin = (e k1 ( cI ) k2 )d, where l is the number of loyal followers in the network, c is the desired number of algorithm iterations, I is the expected length of the iteration interval, t is the time passed since the protocol began, d is the estimated average degree of a node in the network, and k1 and k2 are constants to determine the shape of the exponential graph. fmin is an exponentially decreasing function, where the nodes at the beginning of the algorithm have less probability of becoming a cluster head, since the number of loyal followers is usually going to be less than fmin , but the probability grows as the cluster formation process progresses. Based on the fmin function, the node will decide if it is becoming a cluster head or not. The set of CHs is a minimum dominating set in G (see Figure 7.6b). If at the beginning of the iteration interval a CH already exists, this will send a POLL message to all its followers to determine which of them is the best candidate to become the new leader of the cluster. The best candidate to become CH is the node that has the greatest number of possible followers while minimizing the amount of overlap with existing clusters. Once the best candidate is determined by the current
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cluster head, it will promote the best candidate as the new cluster head and abdicate its position as the old cluster head. In some cases, the best candidate can be the same node that was already acting as CH. When a node becomes a CH, it conserves the previous ID if it was promoted by a previous CH or generates a random cluster ID if it declared itself as CH. After generating the cluster ID, the CH broadcasts a RECRUIT message to its neighbors, who will become followers of the new cluster. A node can be a follower of more than one cluster while the protocol is running (it picks a single cluster for membership only at the end of the protocol). When the cluster head promotes a new node to CH, the position of the cluster will appear to migrate in the direction of the new CH because some of the former followers of the old CH are no longer part of the cluster, while some new nodes near the new CH become new followers of the cluster. Nodes that are not within one-hop radius of any CH can pick a clustered neighbor to act as their bridge to the CH, becoming two-hop followers. In the worst-case scenario, the loss of a CH in ACE would leave at most one cluster of the nodes unclustered. Listing 1 shows and outline of the algorithm used by the nodes during ACE s rst iteration, according to the pseudocode presented in reference 10. The number of iterations that the algorithm should execute is a non xed parameter that should be determined by the system using the algorithm, in order to determine a good tradeoff between communication overhead and cluster size. This algorithm only covers the aspects related to the clusters formation and does not include aspects related to data transmission after that. According to the simulations presented in the paper, the authors determined that 3 iterations were good for its execution, but they do not guarantee that this number is going to be the correct one for all executions of the protocol. LISTING 1. Pseudocode for the ACE Algorithm
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public class ACENode { int ID, clusterID, bestLeader; String state; //time since the node started the protocol double time; int expectedIterationLenght; int numLoyalFollowers, bestFollowerCount; public ACENode( ){ //All nodes initiate in an UnclusteredState state = Unclustered ; } public int ScaleOneIteration( ){ if (time > 3*expectedIterationLenght) {
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