A 6/5-approximation algorithm for the maximum 3-cover problem

作者：Caragiannis Ioannis^*; Monaco Gianpiero

来源：Journal of Combinatorial Optimization, 2013, 25(1): 60-77.

DOI：10.1007/s10878-011-9417-z

• Maximum cover
• Set packing
• Approximation algorithms
• Local search

In the maximum cover problem, we are given a collection of sets over a ground set of elements and a positive integer w, and we are asked to compute a collection of at most w sets whose union contains the maximum number of elements from the ground set. This is a fundamental combinatorial optimization problem with applications to resource allocation. We study the simplest APX-hard variant of the problem where all sets are of size at most 3 and we present a 6/5-approximation algorithm, improving the previously best known approximation guarantee. Our algorithm is based on the idea of first computing a large packing of disjoint sets of size 3 and then augmenting it by performing simple local improvements.

• 出版日期2013-1