A Distributed Approximation for Multi-Hop Clustering Problem in Wireless Sensor Networks

In wireless sensor networks (WSNs), there is no predefined infrastructure. Nodes need to frequently flood messages to discover routes, which badly decreases the network performance. To overcome such drawbacks, WSNs are often grouped into several disjointed clusters, each with a representative cluster head (CH) in charge of the routing process. In order to further improve the efficiency of WSNs, it is crucial to find a cluster partition with minimum number of clusters and the distance between each node to its corresponding CH can be bounded by a constant number of hops. Finding such a partition is defined as minimum d-hop cluster head set (d-MCHS) problem, which is proved to be NP-hard. In this paper, we propose a distributed approximation algorithm, named d²-Cluster, to address d-MCHS problem and prove that the approximation ratio of d²-Cluster under unit disk graph (UDG) is a constant factor λ which is related to d. To the best of our knowledge, it is the first constant approximation ratio for d-MDS problem in UDG.