Connectivity in Multi-interface Networks

Abstract

Let G = (V,E) be a graph which models a set of wireless devices (nodes V) that can communicate by means of multiple radio interfaces, according to proximity and common interfaces (edges E). In general, every node holds a subset of all the possible k interfaces. Such networks are known as multi-interface networks. In this setting, we study a basic problem called Connectivity, corresponding to the well-known Minimum Spanning Tree problem in graph theory. In practice, we need to cover a subgraph of G of minimum cost which contains a spanning tree of G. A connection is covered (activated) when the endpoints of the corresponding edge share at least one active interface.The connectivity problem turns out to be APX-hard in general and for many restricted graph classes, however it is possible to provide approximation algorithms: 2-approximation in general and \((2-\frac 1 k)\)-approximation for unit cost interfaces. We also consider the problem in special graph classes, such as graphs of bounded degree, planar graphs, graphs of bounded treewidth, complete graphs.KeywordsEnergy savingwireless networkmulti-interface networkapproximation algorithm