A new multilayered PCP and the hardness of hypergraph vertex cover
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Approximate coloring of uniform hypergraphs
Journal of Algorithms
Asymmetric k-center is log* n-hard to approximate
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Guest column: inapproximability results via Long Code based PCPs
ACM SIGACT News
Asymmetric k-center is log* n-hard to approximate
Journal of the ACM (JACM)
Parallel computations and committee constructions
Automation and Remote Control
The complexity of properly learning simple concept classes
Journal of Computer and System Sciences
Path coupling using stopping times and counting independent sets and colorings in hypergraphs
Random Structures & Algorithms
On the complexity of SNP block partitioning under the perfect phylogeny model
WABI'06 Proceedings of the 6th international conference on Algorithms in Bioinformatics
Path coupling using stopping times
FCT'05 Proceedings of the 15th international conference on Fundamentals of Computation Theory
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We prove that coloring a 3-uniform 2-colorable hypergraph with any constant number of colors is NP-hard. The best known algorithm [20] colors such a graph using O(n1/5) colors. Our result immediately implies that for any constants k 2 and c2 c1 1, coloring a k-uniform c1-colorable hypergraph with c2 colors is NP-hard; leaving completely open only the k = 2 graph case.We are the first to obtain a hardness result for approximately-coloring a 3-uniform hypergraph that is colorable with a constant number of colors. For k 驴 4 such a result has been shown by [14], who also discussed the inherent difference between the k = 3 case and k 驴 4.Our proof presents a new connection between the Long-Code and the Kneser graph, and relies on the high chromatic numbers of the Kneser graph [19, 22] and the Schrijver graph [26]. We prove a certain maximization variant of the Kneser conjecture, namely that any coloring of the Kneser graph by fewer colors than its chromatic number, has many' non-monochromatic edges.