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Wireless Netw (2010) 16:10631073 DOI 10.1007/s11276-009-0188-8
Exploiting multi-interface networks: Connectivity and Cheapest Paths
Adrian Kosowski Alfredo Navarra Cristina M. Pinotti
Published online: 21 May 2009 Springer Science+Business Media, LLC 2009
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). The problem of switching on (activating) the minimum cost set of interfaces at the nodes in order to guarantee the coverage of G was recently studied. A connection is covered (activated) when the endpoints of the corresponding edge share at least one active interface. 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 two basic problems: Connectivity and Cheapest Path. The Connectivity problem corresponds 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. The problem turns out to be APX-hard in general and for many restricted graph classes, however it is possible to provide
approximation algorithms: a 2-approximation in general and a 2 1k-approximation for the unit cost interface
case, i.e. when the cost of activating an interface is unitary for any interface. We also consider the problem in special graph classes, such as graphs of bounded degree, planar graphs, graphs of bounded treewidth, complete graphs. The Cheapest Path problem corresponds to the well-known Shortest Path problem in graph theory. In the multi-interface setting this problem is still polynomially solvable, and we point out a simple Dijsktra-based algorithm with OkjEj kjVj logk jVj runtime in general and
O(k(|E| ? |V|)) runtime for the unit cost interface case.
Keywords Energy saving Wireless network
Multi-interface network
1 Introduction
As technology advances and more sophisticated and heterogeneous devices are released, special effort is required for managing new kinds of communication problems. Nowadays wireless devices hold multiple radio interfaces, and are capable of switching from one communication network to another according to required connectivity and related quality considerations. The selection of the most suitable radio interface for a specic connection might depend on various factors. Such factors include:...