Cost Minimisation in Unbounded Multi-interface Networks

  • Adrian Kosowski
  • Alfredo Navarra
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4967)


Given a graph G = (V,E) with |V| = n and |E| = m, which models a set of wireless devices (nodes V) connected by multiple radio interfaces (edges E), the aim is to switch on the minimum cost set of interfaces at the nodes in order to satisfy all the connections. A connection is satisfied when the endpoints of the corresponding edge share at least one active interface. Every node holds a subset of all the possible k interfaces. The problem is called Cost Minimisation in Unbounded Multi-Interface Networks and in [1] the case with bounded k was studied. In this paper we generalise the model by considering the unbounded version of the problem, i.e., k is not set a priori but depends on the given instance. We distinguish two main variations of the problem by treating the cost of maintaining an active interface as uniform (i.e., the same for all interfaces), or non-uniform. In general, we prove that the problem is not approximable within O(logk) while it holds \(\min \{\lceil \frac {k+1} 2\rceil,\frac {2m} n\}\)-approximation factor for the uniform case and \(\min\{k-1, \sqrt{n}(1+\ln n) \}\)-approximation factor for the non-uniform case. Next, we also provide hardness and approximation results for several classes of networks: with bounded degree, trees, planar and complete graphs.


energy saving wireless network multi-interface network approximation algorithm 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Adrian Kosowski
    • 1
  • Alfredo Navarra
    • 2
  1. 1.Department of Algorithms and System ModelingGdańsk University of TechnologyGdańskPoland
  2. 2.Dipartimento di Matematica e InformaticaUniversitá degli Studi di PerugiaPerugiaItaly

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