SIAM Journal on Discrete Mathematics
Improved lower bounds on k-independence
Journal of Graph Theory
A threshold of ln n for approximating set cover
Journal of the ACM (JACM)
Approximating maximum independent set in bounded degree graphs
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
Improved approximation algorithms for the vertex cover problem in graphs and hypergraphs
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
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 coloring and maximum independent sets in 3-uniform hypergraphs
Journal of Algorithms
A note on greedy algorithms for the maximum weighted independent set problem
Discrete Applied Mathematics
Approximating Maximum Independent Sets in Uniform Hypergraphs
MFCS '98 Proceedings of the 23rd International Symposium on Mathematical Foundations of Computer Science
A d/2 Approximation for Maximum Weight Independent Set in d-Claw Free Graphs
SWAT '00 Proceedings of the 7th Scandinavian Workshop on Algorithm Theory
Approximations of Independent Sets in Graphs
APPROX '98 Proceedings of the International Workshop on Approximation Algorithms for Combinatorial Optimization
Approximating Min Sum Set Cover
Algorithmica
On the differential approximation of MIN SET COVER
Theoretical Computer Science
A lower bound on the independence number of arbitrary hypergraphs
Journal of Graph Theory
Approximation algorithms for combinatorial problems
Journal of Computer and System Sciences
Tight results on minimum entropy set cover
APPROX'06/RANDOM'06 Proceedings of the 9th international conference on Approximation Algorithms for Combinatorial Optimization Problems, and 10th international conference on Randomization and Computation
New differential approximation algorithm for k-customer vehicle routing problem
Information Processing Letters
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In this paper we analyze several approaches to the Maximum Independent Set problem in hypergraphs with degree bounded by Δ. We propose a general technique that reduces the worst case analysis of certain algorithms to their performance in the case of ordinary graphs. This technique allows us to show that the greedy algorithm that corresponds to the classical greedy set cover algorithm has a performance ratio of (Δ + 1)/2. It also allows us to apply results on local search algorithms of graphs to obtain a (Δ + 1)/2 approximation for a weighted case and (Δ + 3)/5 - ε approximation for an unweighted case. We improve the bound in the weighted case to [(Δ + 1)/3] using a simple partitioning algorithm. Finally, we show that another natural greedy algorihthm, that adds vertices of minimum degree, achieves only a ratio of Δ - 1, significantly worse than on ordinary graphs.