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arXiv · 1302.4347

Large Neighborhood Local Search for the Maximum Set Packing Problem

Maxim Sviridenko·Justin Ward
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Abstract

In this paper we consider the classical maximum set packing problem where set cardinality is upper bounded by $k$. We show how to design a variant of a polynomial-time local search algorithm with performance guarantee $(k+2)/3$. This local search algorithm is a special case of a more general procedure that allows to swap up to $\Theta(\log n)$ elements per iteration. We also design problem instances with locality gap $k/3$ even for a wide class of exponential time local search procedures, which can swap up to $cn$ elements for a constant $c$. This shows that our analysis of this class of algorithms is almost tight.

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Maxim Sviridenko, Justin Ward. 2013-02-18. Large Neighborhood Local Search for the Maximum Set Packing Problem. https://arxiv.org/abs/1302.4347

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