An Õ(n3/14)-coloring algorithm for 3-colorable graphs
Information Processing Letters
Hypergraph colouring and the Lovász local lemma
Discrete Mathematics
Some optimal inapproximability results
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Probabilistic checking of proofs: a new characterization of NP
Journal of the ACM (JACM)
Proof verification and the hardness of approximation problems
Journal of the ACM (JACM)
SIAM Journal on Computing
On the advantage over a random assignment
STOC '02 Proceedings of the thiry-fourth 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
Coloring 2-colorable hypergraphs with a sublinear number of colors
Nordic Journal of Computing
Improved Bounds and Algorithms for Hypergraph Two-Coloring
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Hardness of approximate hypergraph coloring
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Clique is hard to approximate within n1-
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Improved Inapproximability Results for MaxClique, Chromatic Number and Approximate Graph Coloring
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
On the advantage over a random assignment
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
Approximate coloring of uniform hypergraphs
Journal of Algorithms
On the advantage over a random assignment
Random Structures & Algorithms
The design space of probing algorithms for network-performance measurement
Proceedings of the ACM SIGMETRICS/international conference on Measurement and modeling of computer systems
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(MATH) Guruswami et al [6] show the hardness of coloring 2-colorable 4-uniform hypergraphs on n vertices with ω(log log n \over log log log n}) colors assuming NP $\not\subseteq$ DTIME(nO log log n)). We obtain a stronger hardness result for approximate coloring of p-colorable 4-uniform hypergraphs for any fixed integer p &rhoe; 7. We prove that there exists an absolute constant c ρ 0 such that for every fixed integer p &rhoe; 7, it is hard to color a p-colorable 4-uniform hypergraph with (log n)cp colors assuming NP $\not \subseteq$ DTIME(2(log n)O(1)).This work builds on the idea of "covering complexity" of probabilistically checkable proof systems (PCPs) developed in [6] and we introduce some new techniques as well. Firstly, we define a new code which we call the Split Code. This is a variation of the Long Code, but much shorter in length and it reduces the proof size significantly. Split Codes enable us to exploit the special structure of the "outer PCP verifier" constructed via Raz's Parallel Repetition Theorem [18]. Secondly, we make a novel use of the Split Codes over the domain GF(p) for a prime p. Working over non-boolean domain in fact makes our proof technically simpler than the proof of Guruswami at al [6].