The Complexity of Cluster-Connectivity of Wireless Sensor Networks

Abstract

Wireless sensor networks consist of sensor devices with limited computational capabilities and memory operating in bounded energy resources; hence, network optimisation and algorithmic development in minimising the total energy or power while maintaining the connectivity of the underlying network are crucial for their design and maintenance. We consider a generalised system model of wireless sensor networks whose node set is decomposed into multiple clusters, and show that the decision and the associated minimisation problems of the connectivity of clustered wireless sensor networks appear to be computationally intractable - completeness and hardness, respectively, for the non-deterministic polynomial-time complexity class. An approximation algorithm is devised to minimise the number of end nodes of inter-cluster edges within a factor of 2 of the optimum for the cluster-connectivity.