SIAM Journal on Discrete Mathematics
A modified greedy heuristic for the set covering problem with improved worst case bound
Information Processing Letters
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
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)
On Local Search for Weighted K-Set Packing
Mathematics of Operations Research
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
Journal of Algorithms
A d/2 approximation for maximum weight independent set in d-claw free graphs
Nordic Journal of Computing
Approximating k-Set Cover and Complementary Graph Coloring
Proceedings of the 5th International IPCO Conference on Integer Programming and Combinatorial Optimization
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The set cover problem is that of computing a minimum weight subfamily F' given a family F of weighted subsets of a base set U, 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 at most k. It has been long known that the problem can be approximated within a factor of H(k) = Σi=1k (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 3-set cover problem, as a first step towards better approximation of general k-set cover problem, where any two distinct subset costs differ by a multiplicative factor of at least 2. It will be shown, via LP duality, that an improved approximation bound of H(3) - 1/6 can be attained, when the greedy heuristic is suitably modified for this case. A key to our algorithm design and analysis is the Gallai-Edmonds structure theorem for maximum matchings.