Linear systems for constrained matching problems
Mathematics of Operations Research
A modified greedy heuristic for the set covering problem with improved worst case bound
Information Processing Letters
Approximation of k-set cover by semi-local optimization
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
A tight analysis of the greedy algorithm for set cover
Journal of Algorithms
A threshold of ln n for approximating set cover
Journal of the ACM (JACM)
Primal-Dual RNC Approximation Algorithms for Set Cover and Covering Integer Programs
SIAM Journal on Computing
Approximating discrete collections via local improvements
Proceedings of the sixth annual ACM-SIAM symposium on Discrete algorithms
Approximation algorithms
Approximating k-Set Cover and Complementary Graph Coloring
Proceedings of the 5th International IPCO Conference on Integer Programming and Combinatorial Optimization
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
Approximation algorithms for combinatorial problems
Journal of Computer and System Sciences
Covering analysis of the greedy algorithm for partial cover
Algorithms and Applications
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The set multicover (MC) problem is a natural extension of the set cover problem s.t. each element requires to be covered a prescribed number of times (instead of just once as in set cover). The k-set multicover (k-MC) problem is a variant in which every subset is of size at most k. Due to the multiple coverage requirement, two versions of MC have been studied; the one in which each subset can be chosen only once (constrained MC) and the other in which each subset can be chosen any number of times (unconstrained MC). For both versions the best approximation algorithm known so far is the classical greedy heuristic, whose performance ratio is H(k), where H(k)= ∑$_{i=1}^{k}$ (1/i). It is no hard, however, to come up with a natural modification of the greedy algorithm such that the resulting performance is never worse, but could also be strictly better. This paper will verify that this is indeed the case by showing that such a modification leads to an improved performance ratio of H(k)–1/6 for both versions of k-MC.