Regular Article
Greedy Local Improvement and Weighted Set Packing Approximation

https://doi.org/10.1006/jagm.2000.1155Get rights and content

Abstract

Given a collection of weighted sets, each containing at most k elements drawn from a finite base set, the k-set packing problem is to find a maximum weight sub-collection of disjoint sets. A greedy algorithm for this problem approximates it to within a factor of k, and a natural local search has been shown to approximate it to within a factor of roughly k  1. However, neither paradigm can yield approximations that improve on this.

We present an approximation algorithm for the weighted k-set packing problem that combines the two paradigms by starting with an initial greedy solution and then repeatedly choosing the best possible local improvement. The algorithm has a performance ratio of 2(k + 1)/3, which we show is asymptotically tight. This is the first asymptotic improvement over the straightforward ratio of k.

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An extended abstract of this paper appeared at SODA '99.

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