Connectivity in Multi-interface Networks

  • Authors:

  • Adrian Kosowski;Alfredo Navarra;Cristina M. Pinotti

  • Affiliations:

  • LaBRI - Université Bordeaux 1, Talence, France 33405 and Department of Algorithms and System Modeling, Gdańsk University of Technology, Gdańsk, Poland 80952;Dipartimento di Matematica e Informatica, Università degli Studi di Perugia, Perugia, Italy 06123;Dipartimento di Matematica e Informatica, Università degli Studi di Perugia, Perugia, Italy 06123

  • Venue:
  • Trustworthy Global Computing
  • Year:
  • 2009

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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.