A Heuristic for Minimum Connected Dominating Set With Local Repair for Wireless Sensor Networks Mritunjay Rai ABV-IIITM,Gwalior mrai@iiitm.ac.in S.Verma IIIT,Allahabad sverma@iiita.ac.in S.tapaswi ABV-IIITM,Gwalior stapaswi@iiitm.ac.in Abstract Connected Dominating Set (CDS) problem in unit disk graph has a significant impact on an efficient design of routing protocols in wireless sensor networks. In this paper, an algorithm is proposed for finding Minimum Connected Dominating Set (MCDS) using Dominating Set. Dominating Sets are connected by using Steiner tree. The algorithm goes through three phases. In first phase Dominating Set is found, in second phase connectors are identified, connected through Steiner tree. In third phase the CDS obtained in second phase is pruned to obtain a MCDS. MCDS so constructed needs to adapt to the continual topology changes due to deactivation of a node due to exhaustion of battery power. These topological changes due to power constraints are taken care by a local repair algorithm that reconstructs the MCDS using only neighbourhood information. Simulation results indicate both the heuristics are very efficient and result in near optimal MCDS. 1. Introduction A virtual backbone in a Wireless Sensor Network (WSN) reduces the communication overhead, increases the bandwidth efficiency, decreases the overall energy consumption and thus increases network operational life. Since the nodes themselves act as routers in this infrastructureless wireless network, the backbone that can be formed is virtual. A wireless sensor network can be modelled as a unit-disk graph, where vertices represent hosts and the unit distance corresponds to transmission range of wireless devices. A minimum connected dominating set (MCDS) [3][5][6] can be optimal as a virtual backbone in such networks. Only heuristics are possible, for the determination of MCDS in a graph is an NP Hard problem [2]. The CDS problem is defined as follows. Given a graph G (V, E), find a subset S of vertices, such that the sub-graph induced by S is connected and S forms a dominating set in G. The heuristics for CDS can be divided into two sets. The first set of heuristics strives to find disconnected, Maximum Independent Set (MIS) of nodes that are joined through minimum spanning tree or Steiner tree [3]. The second type of heuristics concentrates on evolving a CDS by growing a small trivial CDS [11]. Different techniques have been proposed for the MCDS problem in the recent years [1][3][4][5][6]. One set of algorithms [8] is based on the idea of creating a dominating set incrementally. The other set of algorithms uses initial set as CDS, recursively remove vertices using Steiner tree etc. [10]. Other approaches [7][12] try to construct a MCDS by finding a maximal independent set, which is then expanded to CDS by adding connected vertices i.e. connectors. An independent set in a graph G(V, E) is defined as a set I which is subset of V such that for each pair of vertices (u, v) ∈ I, (u, v) E. The MCDS constructed by these heuristics is not optimal. One of the goals of the present work is to construct a globally optimal MCDS. In general, a battery discharge varies directly as the rate of energy consumption. A sensor node in the MCDS carries a lot of traffic and tends to consume energy draining the battery quickly. A battery, however resumes if they are rested [13] [14]. To prolong battery life and maximize network lifetime, a node may be included and excluded from the MCDS at regular intervals of time. This necessitates modification in MCDS. An algorithm that reconstructs the MCDS for every iteration will consume unnecessary battery power and time. In order to optimize network performance, a battery aware energy efficient heuristic is required to repair the MCDS instead of globally optimum reconstruction 2009 Eighth International Conference on Networks 978-0-7695-3552-4/09 $25.00 © 2009 IEEE DOI 10.1109/ICN.2009.63 106