SIAM Journal on Discrete Mathematics
A modified greedy heuristic for the set covering problem with improved worst case bound
Information Processing Letters
A threshold of ln n for approximating set cover (preliminary version)
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
A tight analysis of the greedy algorithm for set cover
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Nonoverlapping local alignments (weighted independent sets of axis-parallel rectangles)
Discrete Applied Mathematics - Special volume on computational molecular biology
Approximation of k-set cover by semi-local optimization
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Approximating discrete collections via local improvements
Proceedings of the sixth annual ACM-SIAM symposium on Discrete algorithms
Greedy local improvement and weighted set packing approximation
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Approximating k-Set Cover and Complementary Graph Coloring
Proceedings of the 5th International IPCO Conference on Integer Programming and Combinatorial Optimization
On Local Search for Weighted k-Set Packing
ESA '97 Proceedings of the 5th Annual European Symposium on Algorithms
An O(v|v| c |E|) algoithm for finding maximum matching in general graphs
SFCS '80 Proceedings of the 21st Annual Symposium on Foundations of Computer Science
Approximation algorithms for combinatorial problems
Journal of Computer and System Sciences
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The set cover problem is that of computing, given a family of weighted subsets of a base set U, a minimum weight subfamily F′ such that every element of U is covered by some subset in F′. The k-set cover problem is a variant in which every subset is of size bounded by k. It has been long known that the problem can be approximated within a factor of H(k) = Σki=1(1/i) by the greedy heuristic, but no better bound has been shown except for the case of unweighted subsets. In this paper we consider approximation of a restricted version of the weighted k-set cover problem, as a first step towards better approximation of general kset cover problem, where subset costs are limited to either 1 or 2. It will be shown, via LP duality, that improved approximation bounds of H(3)-1/6 for 3-set cover and H(k)-1/12 for k-set cover can be attained, when the greedy heuristic is suitably modified for this case.