SIAM Journal on Discrete Mathematics
A modified greedy heuristic for the set covering problem with improved worst case bound
Information Processing Letters
A survey of approximately optimal solutions to some covering and packing problems
ACM Computing Surveys (CSUR)
Approximation of k-set cover by semi-local optimization
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
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 Syntactic versus Computational Views of Approximability
SIAM Journal on Computing
Approximating k-Set Cover and Complementary Graph Coloring
Proceedings of the 5th International IPCO Conference on Integer Programming and Combinatorial Optimization
A Better-Than-Greedy Approximation Algorithm for the Minimum Set Cover Problem
SIAM Journal on Computing
A Modified Greedy Algorithm for the Set Cover Problem with Weights 1 and 2
ISAAC '01 Proceedings of the 12th International Symposium on Algorithms and Computation
Approximation algorithms for combinatorial problems
Journal of Computer and System Sciences
A 6/5-Approximation Algorithm for the Maximum 3-Cover Problem
MFCS '08 Proceedings of the 33rd international symposium on Mathematical Foundations of Computer Science
Note: Approximation of the k-batch consolidation problem
Theoretical Computer Science
Covering the edges of bipartite graphs using K2,2gaphs
WAOA'07 Proceedings of the 5th international conference on Approximation and online algorithms
Analysis of approximation algorithms for k-set cover using factor-revealing linear programs
FCT'07 Proceedings of the 16th international conference on Fundamentals of Computation Theory
Boolean functions with long prime implicants
Information Processing Letters
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In the unweighted set-cover problem we are given a set of elements E={ e1,e2, ...,en } and a collection $\cal F$ of subsets of E. The problem is to compute a sub-collection SOL⊆$\cal F$ such that $\bigcup_{S_j\in SOL}S_j=E$ and its size |SOL| is minimized. When |S|≤k for all $S\in\cal F$ we obtain the unweighted k-set cover problem. It is well known that the greedy algorithm is an Hk-approximation algorithm for the unweighted k-set cover, where $H_k=\sum_{i=1}^k {1 \over i}$ is the k-th harmonic number, and that this bound on the approximation ratio of the greedy algorithm, is tight for all constant values of k. Since the set cover problem is a fundamental problem, there is an ongoing research effort to improve this approximation ratio using modifications of the greedy algorithm. The previous best improvement of the greedy algorithm is an $\left( H_k-{1\over 2}\right)$-approximation algorithm. In this paper we present a new $\left( H_k-{196\over 390}\right)$-approximation algorithm for k ≥4 that improves the previous best approximation ratio for all values of k≥4 . Our algorithm is based on combining local search during various stages of the greedy algorithm.