Packing-based approximation algorithm for the k-set cover problem

Authors:
Martin Fürer;Huiwen Yu
Affiliations:
Department of Computer Science and Engineering, The Pennsylvania State University, PA;Department of Computer Science and Engineering, The Pennsylvania State University, PA
Venue:
ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
Year:
2011

Citing 11
Cited 1

On the size of systems of sets every t of which have an SDR, with an application to the worst-case ratio of heuristics for packing problems

SIAM Journal on Discrete Mathematics
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 threshold of ln n for approximating set cover

Journal of the ACM (JACM)
Non-approximability results for optimization problems on bounded degree instances

STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Approximating k-Set Cover and Complementary Graph Coloring

Proceedings of the 5th International IPCO Conference on Integer Programming and Combinatorial Optimization
Greedy facility location algorithms analyzed using dual fitting with factor-revealing LP

Journal of the ACM (JACM)
On the complexity of approximating k-set packing

Computational Complexity
Analysis of Approximation Algorithms for k-Set Cover Using Factor-Revealing Linear Programs

Theory of Computing Systems
Approximating the Unweighted ${k}$-Set Cover Problem: Greedy Meets Local Search

SIAM Journal on Discrete Mathematics
Approximation algorithms for combinatorial problems

Journal of Computer and System Sciences

Tight approximation bounds for combinatorial frugal coverage algorithms

Journal of Combinatorial Optimization

Quantified Score

Hi-index	0.00

Visualization

Abstract

We present a packing-based approximation algorithm for the k-Set Cover problem. We introduce a new local search-based k-set packing heuristic, and call it Restricted k-Set Packing. We analyze its tight approximation ratio via a complicated combinatorial argument. Equipped with the Restricted k-Set Packing algorithm, our k-Set Cover algorithm is composed of the k-Set Packing heuristic [8] for k≥7, Restricted k-Set Packing for k=6,5,4 and the semi-local (2,1)-improvement [2] for 3-Set Cover. We show that our algorithm obtains a tight approximation ratio of $H_k-0.6402+\Theta(\frac{1}{k})$, where Hk is the k-th harmonic number. For small k, our results are 1.8667 for k=6, 1.7333 for k=5 and 1.5208 for k=4. Our algorithm improves the currently best approximation ratio for the k-Set Cover problem of any k≥4.