A (k+3)/2-approximation algorithm for monotone submodular k-set packing and general k-exchange systems

Justin Ward

We consider the monotone submodular k-set packing problem in the context of the more general problem of maximizing a monotone submodular function in a k-exchange system. These systems, introduced by Feldman et al. [Feldman,2011], generalize the matroid k-parity problem in a wide class of matroids and capture many other combinatorial optimization problems. We give a deterministic, non-oblivious local search algorithm that attains an approximation ratio of (k + 3)/2 + epsilon for the problem of maximizing a monotone submodular function in a k-exchange system, improving on the best known result of k+epsilon, and answering an open question posed by Feldman et al.

Mots clés: k-set packing; k-exchange systems; submodular maximization; local search; approximation algorithms

Domaines: Complexité [cs.CC]; Algorithme et structure de données [cs.DS]

Justin Ward. A (k+3)/2-approximation algorithm for monotone submodular k-set packing and general k-exchange systems. STACS'12 (29th Symposium on Theoretical Aspects of Computer Science), Feb 2012, Paris, France. pp.42-53. ⟨hal-00678202⟩