Volume 36, Number 1, January-March 2002
|Page(s)||53 - 71|
|Published online||15 July 2002|
Primal-dual approximation algorithms for a packing-covering pair of problems
Department of Mathematics,
Maastricht University, P.O. Box 616, 6200 MD Maastricht, The
2 Department of Applied Economics, Katholieke Universiteit Leuven, Naamsestraat 69, 3000 Leuven, Belgium.
We consider a special packing-covering pair of problems. The packing problem is a natural generalization of finding a (weighted) maximum independent set in an interval graph, the covering problem generalizes the problem of finding a (weighted) minimum clique cover in an interval graph. The problem pair involves weights and capacities; we consider the case of unit weights and the case of unit capacities. In each case we describe a simple algorithm that outputs a solution to the packing problem and to the covering problem that are within a factor of 2 of each other. Each of these results implies an approximative min-max result. For the general case of arbitrary weights and capacities we describe an LP-based (2 + ε)-approximation algorithm for the covering problem. Finally, we show that, unless P = NP, the covering problem cannot be approximated in polynomial time within arbitrarily good precision.
Mathematics Subject Classification: 05A05
Key words: Primal-dual / approximation algorithms / packing-covering / intervals.
© EDP Sciences, 2002
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