Commutativity in the algorithmic Lovasz local lemma Conference Paper


Author(s): Kolmogorov, Vladimir
Title: Commutativity in the algorithmic Lovasz local lemma
Affiliation IST Austria
Abstract: We consider the recent formulation of the Algorithmic Lovász Local Lemma [1], [2] for finding objects that avoid "bad features", or "flaws". It extends the Moser-Tardos resampling algorithm [3] to more general discrete spaces. At each step the method picks a flaw present in the current state and "resamples" it using a "resampling oracle" provided by the user. However, it is less flexible than the Moser-Tardos method since [1], [2] require a specific flaw selection rule, whereas [3] allows an arbitrary rule (and thus can potentially be implemented more efficiently). We formulate a new "commutativity" condition, and prove that it is sufficient for an arbitrary rule to work. It also enables an efficient parallelization under an additional assumption. We then show that existing resampling oracles for perfect matchings and permutations do satisfy this condition. Finally, we generalize the precondition in [2] (in the case of symmetric potential causality graphs). This unifies special cases that previously were treated separately.
Keywords: data structures; Computer science; Algorithm design and analysis; Probabilistic logic; Probability distribution; Indexes; Data models
Conference Title: FOCS: Foundations of Computer Science
Conference Dates: October 9 - October 11, 2016
Conference Location: New Brunswick, NJ, USA
Publisher: IEEE  
Date Published: 2016-12-15
Sponsor: European Unions Seventh Framework Programme (FP7/2007-2013)/ERC grant agreement no 616160
URL:
DOI: 10.1109/FOCS.2016.88
Open access: yes (repository)
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