Algebraic connectivity aided energy-efficient topology control in selfish ad hoc networks

Abstract

Topology control is a technique to assign per-node’s transmit parameters so as to get the network topology with the best possible network performance given some optimization criteria, such as energy-efficient connectivity. In this paper, we investigate energy-efficient topology control for wireless ad-hoc networks in the presence of selfish nodes. A non-cooperative game aided topology control approach is developed for minimizing the potential transmit power, whilst maintaining the network connectivity. The utility function is conceived by virtue of algebraic connectivity, which is a fine metric to measure the connectivity redundancy of a network. We prove the existence of Nash Equilibrium (NE) and demonstrate that the NE is Pareto optimal as well. Specifically, two fully distributed topology controls—algebraic connectivity-based Max-Improvement (ACMI) algorithm and $\delta$-Improvement (ACDI) algorithm—are proposed to find the NE topologies. Both ACMI and ACDI can easily construct the stable topologies with a low information-overhead of the order O(n), where n is the number of nodes. Simulations demonstrate that our algorithms observably eliminate the redundancy of the maximum power topology and embrace several other attractive topological features.