GRAPH-BASED APPROACHES FOR CLUSTERING IN WSN in .NET framework

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GRAPH-BASED APPROACHES FOR CLUSTERING IN WSN
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Graph Theory Approaches Used for Clustering in WSN
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Stationary Sensors
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Mobile Sensors
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Centralized algorithms & self elective protocols
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Localized protocols & emergent algorithms
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Distributed dominating setbased algorithms
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Combined & additional approaches
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Zone-based clustering
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Peer-to-peer generalized clustering model
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node degree [19] . Spanning tree [33, 4]
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. ACE [11]
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. Span [16] . DFS [17] . IDS [5] . LRG [24, 22]
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. Zonal algorithm [13, 18] . Vertex Cover [6] . Max-Min DCluster [2] . GHS [18] . Greedy set cover algorithm [12] . TASC [35] . Balanced Clusters [20]
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. Zonal weaklyconnected clustering algorithm [13, 15]
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. CDC [32]
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Figure 7.3. Graph theory approaches used for clustering in WSN.
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that often present an increased vulnerability to node failure in certain key parts of the network, usually near the root of the tree (if they use a spanning tree) or near the BS. Additionally, these protocols may require signi cant communications or computation overhead for very large networks. It is necessary to clarify that not all the clustering algorithms and protocols that have been proposed using graph theory concepts are suitable for WSN. For example, in reference 13, the authors propose a technique where each cluster forms a clique. However, they do not select a CH that makes the protocol unfeasible for WSN. Additionally, their createClusters() function has a relatively large overhead of O(d 3 ), where d is the density of the network (number of nodes per area unit). A group of clustering protocols called self-elective protocols use the Node ID and Node Degree to select the CH. In reference 14, Gerla and Tsai proposed two weightbased clustering algorithms, where each vertex v selects the node with optimal weight within N(v) as CH. In the rst algorithm, the optimal vertex is the one with lowest node ID as shown in Figure 7.4. The neighborhood of the node selected as CH is the cluster. A node that can hear two or more CHs is a gateway or border node. In the second clustering algorithm, the highest-degree node in a neighborhood is selected as the optimal node to be the CH and the neighbors are covered by it (see Figure 7.5). Although the algorithm is expected to perform well on many randomly de ned graphs, it may not produce any CH for graphs that do not have any node with the highest number of neighbors (like interval graphs). Thus, the algorithm must be completed by adding nontrivial tie resolution rules.
CLUSTERING IN WIRELESS SENSOR NETWORKS: A GRAPH THEORY PERSPECTIVE
1 12 2 3 4 6 19 18 5 Cluster 8 Cluster Head 9 7 20 11 10 16 17 13 14 15
Figure 7.4. Node ID clustering.
In references 15 and 16 the authors propose algorithms that control the size of each cluster and the number of hierarchical levels. However, these algorithms are not suitable for WSN, since they add a signi cant computation overhead to the nodes in the networks and incorrectly assume that the topology can be controlled and deployed in a regular organized basis. Additionally, they are unable to prevent two nodes that are just over one cluster radius apart from simultaneously electing themselves as CH, causing a large overlap in the network s clusters. This problem occurs suf ciently frequently to make the resultant cluster packing inef cient.
N(1)=1
N(2)=3
N(12)=3 N(11)=3 N(3)=3 12 (-1 outside (-1 outside the cluster) the cluster)
N(13)=2
N(14)=3
13 16
15 N(15)=2 17 N(17)=3
N(4)=3 (-1 outside the cluster) 4
N(10)=4
N(16)=3
N(19)=2 (-1 outside the cluster)
N(20)=2
N(6)=4 N(7)=1 N(5)=4
19 18
N(18)=2
N(9)=2
Cluster Border Nodes Cluster Head 8
N(8)=2
Figure 7.5. Node degree clustering.
GRAPH-BASED APPROACHES FOR CLUSTERING IN WSN
Zhang and Arora [17] present a centralized scheme to produce an approximate hexagonal close packing. However, they assume that each node knows their precise location, which may be dif cult to address in WSN. The clustering algorithms that use a centralized approach are generally based on the use of Spanning Trees to associate the vertices and to have several parent nodes in charge of the interactions with their child nodes and with their own parents in the superior level. A generalized clustering technique creating a tree-based construction for network partitioning is presented in reference 18. Thaler and Ravishankar propose to construct a top-down hierarchy based on an initial root node. However, the level of broadcasting messages used to create the tree is too large. Another tree-based clustering protocol is proposed by Banerjee and Khuller in reference 19. They use a Breadth First Search (BFS) algorithm to partition the network. However, a drawback for using their algorithm in WSN is that only one node initiates the clustering process, which can provoke the loss of an entire subtree if one of the higher-level nodes in the tree suffers a failure. Additionally, this protocol still requires O(n) time in linear networks, where n is the entire size of the network, which is outperformed by other protocols as we will show ahead. 7.3.2 Localized Protocols and Emergent Algorithms In contrast with centralized algorithms, localized algorithms are characterized by reducing the amount of central coordination necessary and only require each node to interact with its local neighbors. Emergent algorithms are a class of localized algorithms. The emerging localized algorithms have the additional characteristic that the individual agents (i.e., sensor nodes) only encode simple local behaviors and do not explicitly coordinate on the global scale. A localized protocol for a sensor network is a protocol in which each sensor node only communicates with a small set of other sensor nodes within close proximity in order to achieve a desired global objective. Locality reduces the chances for protocol failure due to transmission errors and node failure. In reference 20, the authors present an emergent algorithm called ACE (Algorithm for Cluster Establishment). The goal of ACE is to select the smallest set of cluster heads such that all nodes in the network belong to a cluster. The problem is similar to the minimum dominating set problem in graph theory. In ACE, the sensors are considered stationary and with uniformly random coordinates in the sensor eld. The proposed algorithm is completed in constant time regardless of the size of the network, and it consists of two logical parts: The rst part controls how clusters can spawn (by having a node elect itself to be leader), and the second part controls how clusters migrate dynamically to reduce overlap. The sensors continually compute the clusters, without the necessity of a speci c event. This makes the protocol suitable for proactive networks. ACE results in a highly uniform cluster formation that can achieve a packing ef ciency close to hexagonal close-packing, which minimizes the overlap between uniform circular clusters while ensuring full coverage. ACE is scaleindependent (it is completed in constant time regardless of the size of the network) and operates without requiring geographic knowledge of node positions or any kind of distance or direction estimation between nodes.