The Moser--Tardos Framework with Partial Resampling
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The resampling algorithm of Moser and Tardos is a powerful approach to develop constructive versions of the Lovász Local Lemma, and this work generalizes this to partial resampled: When a bad event holds, an appropriately random subset of the variables that define this event rather than the entire set is resample.Abstract:
The resampling algorithm of Moser and Tardos is a powerful approach to develop constructive versions of the Lovasz Local Lemma. We generalize this to partial resampling: When a bad event holds, we resample an appropriately random subset of the variables that define this event rather than the entire set, as in Moser and Tardos. This is particularly useful when the bad events are determined by sums of random variables. This leads to several improved algorithmic applications in scheduling, graph transversals, packet routing, and so on. For instance, we settle a conjecture of Szabo and Tardos (2006) on graph transversals asymptotically and obtain improved approximation ratios for a packet routing problem of Leighton, Maggs, and Rao (1994).read more
Citations
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New bounds for the Moser‐Tardos distribution
TL;DR: In this article, the MT-distribution is shown to satisfy an approximate independence condition asymptotically stronger than the Lovasz Local Lemma (LLL) distribution.
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Deterministic algorithms for the Lovasz Local Lemma: simpler, more general, and more parallel.
TL;DR: This work provides a derandomized version of the MT-distribution, that is, the distribution of the variables at the termination of theMT algorithm, which gives deterministic algorithms which essentially match the best previous randomized sequential and parallel algorithms.
Journal ArticleDOI
Oblivious Resampling Oracles and Parallel Algorithms for the Lopsided Lovász Local Lemma
TL;DR: In this article, the Lovasz Local Lemma (LLL) was extended to a generalization of the LLL known as the Lipschitz LLL (LLL) and a new structural property called obliviousness was proposed.
Proceedings ArticleDOI
Sampling constraint satisfaction solutions in the local lemma regime
Weiming Feng,Kun He,Yitong Yin +2 more
TL;DR: In this paper, a Markov chain based algorithm for sampling almost uniform solutions of constraint satisfaction problems (CSPs) is presented. But the running time is a fixed polynomial whose dependency on n is close to linear, where n is the number of variables.
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Partial Resampling to Approximate Covering Integer Programs
TL;DR: For column-sparse covering integer programs, a generalization of set cover, a long line of research of (randomized) approximation algorithms has been carried out as discussed by the authors, which achieves an approximation ratio of O(log(1 + log(1+log(δ)-1+1) √ log(γ)-log (δ_1+δ-1)-norm of any column of the covering matrix (whose entries are scaled to lie in $[0, 1]$).
References
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A constructive proof of the general lovász local lemma
Robin A. Moser,Gábor Tardos +1 more
TL;DR: The Lovasz Local Lemma algorithm as mentioned in this paper is a powerful tool to nonconstructively prove the existence of combinatorial objects meeting a prescribed collection of criteria, and it has been used in many applications.
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