Improved Bounds and Algorithms for Hypergraph Two-Coloring

Authors:
Jaikumar Radhakrishnan;Aravind Srinivasan
Affiliations:
-;-
Venue:
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Year:
1998

Citing 0
Cited 5

A new algorithm approach to the general Lovász local lemma with applications to scheduling and satisfiability problems (extended abstract)

STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Coloring non-uniform hypergraphs: a new algorithmic approach to the general Lovász local lemma

SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Hardness results for approximate hypergraph coloring

STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Testing Hypergraph Coloring

ICALP '01 Proceedings of the 28th International Colloquium on Automata, Languages and Programming,
Testing hypergraph colorability

Theoretical Computer Science - Automata, languages and programming

Quantified Score

Hi-index	0.00

Visualization

Abstract

We show that for all large n, every n-uniform hypergraph with at most 0.7 sqrt{n/ln n} * 2^n edges can be two-colored. We, in fact, present fast algorithms that output a proper two-coloring with high probability for such hypergraphs. We also derandomize and parallelize these algorithms, to derive NC^1 versions of these results. This makes progress on a problem of Erdos (1963), improving the previous-best bound of n^{1/3-o(1)} * 2^n due to Beck (1978). We further generalize this to a ``local'' version, improving on one of the first applications of the Lovasz Local Lemma.