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Primal-dual approximation algorithms for a packing-covering pair of problems

Published online by Cambridge University Press:  15 July 2002

Sofia Kovaleva  and
Frits C.R. Spieksma
Sofia Kovaleva
Affiliation:
Department of Mathematics, Maastricht University, P.O. Box 616, 6200 MD Maastricht, The Netherlands; s.kovaleva@math.unimaas.nl.
Frits C.R. Spieksma
Affiliation:
Department of Applied Economics, Katholieke Universiteit Leuven, Naamsestraat 69, 3000 Leuven, Belgium.
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Abstract

We consider a special packing-covering pair of problems. Thepacking problem is a natural generalization of finding a(weighted) maximum independent set in an interval graph, thecovering problem generalizes the problem of finding a (weighted)minimum clique cover in an interval graph. The problem pairinvolves weights and capacities; we consider the case of unitweights and the case of unit capacities. In each case we describea simple algorithm that outputs a solution to the packing problemand to the covering problem that are within a factor of 2 of eachother. Each of these results implies an approximative min-maxresult. For the general case of arbitrary weights and capacitieswe describe an LP-based (2 + ε)-approximation algorithm forthe covering problem. Finally, we show that, unlessP = NP, the covering problem cannot be approximated inpolynomial time within arbitrarily good precision.

Keywords

Primal-dualapproximation algorithmspacking-coveringintervals.
Type
Research Article
Information
RAIRO - Operations Research , Volume 36 , Issue 1 , January 2002 , pp. 53 - 71
Copyright
© EDP Sciences, 2002

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