Two Connected Dominating Set Algorithms for Wireless Sensor Networks

1. Two Connected Dominating Set Algorithms for Wireless Sensor Networks Najla Al-Nabhan* ♦ Bowu Zhang** ♦ Mznah Al-Rodhaan* ♦ Abdullah Al-Dhelaan* Overview The Proposed Algorithms • Connected Dominating Set (CDS) • CDS is known to be an efficient strategy to control network topology, reduce overhead, and extend network lifetime. • CDS finds a minimum size subset of nodes that can collaboratively form a virtual backbone. • Definition • For a given connected graph (network) G = (V, E), a dominating set (DS) is a subset V' of V, where for each vertex (node) u of V, u is either in V' or at least one neighbor vertex of u is in V'. A DS is called a CDS if the sub-graph induced by the vertices in the DS is connected. • In this work, we present the design of two novel algorithms for CDS construction in WSNs. • Our algorithms are intended to minimize CDS size. The first algorithm has a performance factor of 5 from the optimal solution, which outperforms the best-published results (S-MIS algorithm) that has a performance factor =5.8+ ln4. The second algorithm is an improved version of the first algorithm. • We model a WSN using a unit disk graph (UDG). • We simplify the CDS construction by first finding a special independent set S1 satisfying the following condition: the hop-distance between any two complementary subsets S’ and S” of S1is exactly three. • Second, we find a small set of nodes S2 to dominate the multiple disconnected components resulted from constructing S1 in the first step. • Then, nodes in S2are connected with nodes in S1 in order to form the final CDS by adding more connecting nodes. • The above described technique is performed in two different ways in Approach-I and Approach-II. • For illustration purpose, we employ a coloring scheme to differentiate node states during the construction process. • Dominators (S1): black, dominatee: gray, (S1): red, connectors: blue. Other colors are temporary colors. Approach-I Approach-I • The newly colored black node (u ) dominates its 1-hop yellow, orange, and white nodes by coloring them gray. Furthermore, u marks its 2-hop white/orange nodes into yellow; and marks its 3-hops white nodes into orange. • Approach-I consists of 4 main phases to construct a CDS: • Phase-1: S1 Construction • given an arbitrary rooted spanning tree T, we define the tree level of a node u as the number of hops in T between u itself and i, where iis the root of T. All nodes are initially undominated and colored white. • The root node (i) initiates S1 construction by coloring itself black. Then: all white nodes that are 1-hop from iare colored gray; all white nodes that are 2-hop from iare colored yellow; all white nodes that are 3-hop from iare colored orange. • Next, the algorithm repeats the following steps until no orange/white nodes left in the graph. • Selects an orange node u to color it black. The selected orange node satisfies the following two conditions: i) its level is the lowest (closes to the root) among all orange nodes, and ii) it has the maximum number of 3-hop black neighbors. The selected node u is colored black. An exemplary graph G of 40 nodes after S1 construction • Phase-2: Covering Disconnected Regions (CDC) • We optimally compute a minimum dominating set for each connected yellow component. All the dominators computed from this phase are colored red and they form the set S2. • Phase-3: Connecting S2 Nodes to S1 Nodes. • Phase-4: Connecting S1 Nodes all Together. Simulation Results Approach-II • N𝝐 [36,400], the transmission range of each node R 𝝐 [200, 800], and the considered deployment schemes are: the uniform random and the partial random deployment models. • Results show that the sizes of CDSs generated by Approach-I and Approach-II are smaller than S-MIS as the network size increases. • Approach-II always outperforms both Approach-I and S-MIS in uniform random and grid-based deployments, and for small and large-scale networks. • Approach-II also has 4 phases. Phase-1, 3, and 4 are similar to their corresponding phases in Approach-I. • In Phase-2, we define the coverage factor of a yellow/gray node x as the number of its yellow neighbors. A gray/yellow node x that has the highest coverage factor is marked red. Then, x dominates its 1-hop yellow neighbors by coloring them gray. • In Phase-3: If a gray node u was marked red in Phase-2 of this approach, u is already connected to an S1 node and we do not need to introduce any connectors for u. Node density 𝝐 [28, 346] N 𝝐 [36, 225], R=400 Random network of 70 nodes Performance Analysis • Given any Minimum CDS (MCDS) of a unit-disk graph G, we show that: Approach-I produces a CDS with a size bounded by 5opt, where opt is the size of the MCDS. The proof of this theorem is provided in the paper. • For the simulation, we focused on CDS size as the main and most important performance measure. • We generated a total of N nodes in a fixed 1000*1000 2D square. Future Work • To implement distributed versions of the proposed algorithms. • To introduce more performance improvements. *{nalnabhan,rodhaan,dhelaan}@ksu.edu.sa , **{bowuzh}@gwmail.gwu.edu