On the multi-radius cover problem

Authors:
Julián Mestre
Affiliations:
Computer Science Department, University of Maryland, College Park, MD
Venue:
Information Processing Letters
Year:
2006

Citing 5
Cited 1

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The multi-radius cover problem

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WEA'05 Proceedings of the 4th international conference on Experimental and Efficient Algorithms

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Operations Research Letters

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Abstract

An instance of the multi-radius cover problem consists of a graph G = (V, E) with edge lengths l: E → R+. Each vertex u ∈ V represents a transmission station for which a transmission radius ru must be picked. Edges represent a continuum of demand points to be satisfied, that is, for every edge (u, v) ∈ E we ask that ru + rv ≥ luv. The cost of transmitting at radius r from vertex u is given by an arbitrary non-decreasing cost function cu (r). Our goal is to find a cover with minimum total cost Σu cu (ru).The multi-radius cover problem is NP-hard as it generalizes the well-known vertex cover problem. In this paper we present a 2-approximation algorithm for it.