Coloring nonuniform hypergraphs: A new algorithmic approach to the general lovász local lemma

Document Type

Article

Publication Date

1-1-2000

Abstract

The Lovász local lemma is a sieve method to prove the existence of certain structures with certain prescribed properties. In most of its applications the Lovász local lemma does not supply a polynomial-time algorithm for finding these structures. Beck was the first who gave a method of converting some of these existence proofs into efficient algorithmic procedures, at the cost of losing a little in the estimates. He applied his technique to the symmetric form of the Lovász local lemma and, in particular, to the problem of 2-coloring uniform hypergraphs. In this paper we investigate the general form of the Lovász local lemma. Our main result is a randomized algorithm for 2-coloring nonuniform hypergraphs that runs in expected linear time. Even for uniform hypergraphs no algorithm with such a runtime bound was previously known, and no polynomial-time algorithm was known at all for the class of nonuniform hypergraphs we will consider in this paper. Our algorithm and its analysis provide a novel approach to the general Lovász local lemma that may be of independent interest. We also show how to extend our result to the c-coloring problem. © 2000 John Wiley & Sons, Inc. Random Struct. Alg., 17, 213-237, 2000.

Identifier

0034361607 (Scopus)

Publication Title

Random Structures and Algorithms

External Full Text Location

https://doi.org/10.1002/1098-2418(200010/12)17:3/4<213::AID-RSA3>3.0.CO;2-Y

ISSN

10429832

First Page

213

Last Page

237

Issue

3-4

Volume

17

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