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.

The research was partially funded by the State Committee for Scientific Research (Poland) Grant 4 T11C 047 25, by the ANR-project “ALADDIN” (France), by the project “CEPAGE” of INRIA (France), and by European COST Action 293 “Graphs and Algorithms in Communication Networks” (GRAAL).