Packing-Based Approximation Algorithm for the k-Set Cover Problem

We present a packing-based approximation algorithm for the k-Set Cover problem. We introduce a new local search-based k-set packing heuristic, and call it Restricted k-Set Packing. We analyze its tight approximation ratio via a complicated combinatorial argument. Equipped with the Restricted k-Set Packing algorithm, our k-Set Cover algorithm is composed of the k-Set Packing heuristic [7] for k ≥ 7, Restricted k-Set Packing for k = 6, 5, 4 and the semi-local (2, 1)improvement [2] for 3-Set Cover. We show that our algorithm obtains a tight approximation ratio of Hk − 0.6402 + Θ( 1 k ), where Hk is the k-th harmonic number. For small k, our results are 1.8667 for k = 6, 1.7333 for k = 5 and 1.5208 for k = 4. Our algorithm improves the currently best approximation ratio for the k-Set Cover problem of any k ≥ 4.