Approximate set covering in uniform hypergraphs
Journal of Algorithms
Improved non-approximability results for minimum vertex cover with density constraints
Theoretical Computer Science
Non-approximability results for optimization problems on bounded degree instances
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Vertex cover on 4-regular hyper-graphs is hard to approximate within 2 - &egr;
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
On the power of unique 2-prover 1-round games
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Improved Approximation Algorithms for the Vertex Cover Problem in Graphs and Hypergraphs
SIAM Journal on Computing
Improved Inapproximability Results for Vertex Cover on k -Uniform Hypergraphs
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
Approximating the dense set-cover problem
Journal of Computer and System Sciences
A New Multilayered PCP and the Hardness of Hypergraph Vertex Cover
SIAM Journal on Computing
Approximating vertex cover on dense graphs
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Vertex cover might be hard to approximate to within 2-ε
Journal of Computer and System Sciences
A better approximation ratio for the vertex cover problem
ACM Transactions on Algorithms (TALG)
The Complexity of Perfect Matching Problems on Dense Hypergraphs
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Inapproximability of hypergraph vertex cover and applications to scheduling problems
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
On the inapproximability of vertex cover on k-partite k-uniform hypergraphs
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
On approximation of the vertex cover problem in hypergraphs
Discrete Optimization
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We consider the Minimum Vertex Cover problem in hypergraphs in which every hyperedge has size k (also known as Minimum Hitting Set problem, or minimum set cover with element frequency k). Simple algorithms exist that provide k-approximations, and this is believed to be the best approximation achievable in polynomial time. We show how to exploit density and regularity properties of the input hypergraph to break this barrier. In particular, we provide a randomized polynomial-time algorithm with approximation factor k/(1+(k-1)d@?k@D), where d@? and @D are the average and maximum degree, and @D must be @W(n^k^-^1/logn). The proposed algorithm generalizes the recursive sampling technique of Imamura and Iwama (SODA@?05) for vertex cover in dense graphs. As a corollary, we obtain an approximation factor arbitrarily close to k/(2-1/k) for subdense regular hypergraphs, which is shown to be the best possible under the Unique Games conjecture.