Algorithmic Improvements of the Lovász Local Lemma via Cluster Expansion

Achlioptas, Dimitris; Gouleakis, Themis

doi:10.4230/LIPIcs.FSTTCS.2012.16

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Algorithmic Improvements of the Lovász Local Lemma via Cluster Expansion

Authors Dimitris Achlioptas, Themis Gouleakis

Part of: Volume: IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2012)
Part of: Series: Leibniz International Proceedings in Informatics (LIPIcs)
Part of: Conference: IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS)
License: Creative Commons Attribution 3.0 Unported license
Publication Date: 2012-12-14

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DOI: 10.4230/LIPIcs.FSTTCS.2012.16
URN: urn:nbn:de:0030-drops-38440

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Keywords

Probabilistic Method
Lovász Local Lemma
Algorithms

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Abstract

The Lovasz Local Lemma (LLL) is a powerful tool that can be used to prove that an object having none of a set of bad properties exists, using the probabilistic method. In many applications of the LLL it is also desirable to explicitly construct the combinatorial object. Recently it was shown that this is possible using a randomized algorithm in the full asymmetric LLL setting [R. Moser and G. Tardos, 2010]. A strengthening of the LLL for the case of dense local neighborhoods  proved in [R. Bissacot et al., 2010] was recently also made constructive in [W. Pegden, 2011]. In another recent work [B. Haupler, B. Saha, A. Srinivasan, 2010], it was proved that the algorithm of Moser and Tardos is still efficient even when the number of events is exponential. Here we prove that these last two contributions can be combined to yield a new version of the LLL.

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Dimitris Achlioptas and Themis Gouleakis. Algorithmic Improvements of the Lovász Local Lemma via Cluster Expansion. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2012). Leibniz International Proceedings in Informatics (LIPIcs), Volume 18, pp. 16-23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2012) https://doi.org/10.4230/LIPIcs.FSTTCS.2012.16

Author Details

Dimitris Achlioptas

Themis Gouleakis

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