A 6/5-approximation algorithm for the maximum 3-cover problem

Authors:
Ioannis Caragiannis;Gianpiero Monaco
Affiliations:
Research Academic Computer Technology Institute & Department of Computer Engineering and Informatics, University of Patras, Rio, Greece 26500;Department of Computer Science, University of L'Aquila, L'Aquila, Italy 67100
Venue:
Journal of Combinatorial Optimization
Year:
2013

Citing 13
Cited 0

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
Maximum bounded 3-dimensional matching is MAX SNP-complete

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)
Approximating discrete collections via local improvements

Proceedings of the sixth 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 Some Tighter Inapproximability Results (Extended Abstract)

ICAL '99 Proceedings of the 26th International Colloquium on Automata, Languages and Programming
Approximation algorithms for partial covering problems

Journal of Algorithms
Complexity of approximating bounded variants of optimization problems

Theoretical Computer Science - Foundations of computation theory (FCT 2003)
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
Wavelength Management in WDM Rings to Maximize the Number of Connections

SIAM Journal on Discrete Mathematics

Quantified Score

Hi-index	0.00

Visualization

Abstract

In the maximum cover problem, we are given a collection of sets over a ground set of elements and a positive integer w, and we are asked to compute a collection of at most w sets whose union contains the maximum number of elements from the ground set. This is a fundamental combinatorial optimization problem with applications to resource allocation. We study the simplest APX-hard variant of the problem where all sets are of size at most 3 and we present a 6/5-approximation algorithm, improving the previously best known approximation guarantee. Our algorithm is based on the idea of first computing a large packing of disjoint sets of size 3 and then augmenting it by performing simple local improvements.