Large neighborhood local search for the maximum set packing problem

Authors:
Maxim Sviridenko;Justin Ward
Affiliations:
Department of Computer Science, University of Warwick, UK;Department of Computer Science, University of Warwick, UK
Venue:
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
Year:
2013

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Abstract

In this paper we consider the classical maximum set packing problem where set cardinality is upper bounded by a constant 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 Θ(logn) 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.