A constructive proof of the Lovasz Local Lemma
| dc.creator | Moser, Robin A. | |
| dc.date | 2008-10-27 | |
| dc.date | 2008-10-29 | |
| dc.date.accessioned | 2026-07-07T10:13:35Z | |
| dc.date.available | 2026-07-07T10:13:35Z | |
| dc.description | The Lovasz Local Lemma [EL75] is a powerful tool to prove the existence of combinatorial objects meeting a prescribed collection of criteria. The technique can directly be applied to the satisfiability problem, yielding that a k-CNF formula in which each clause has common variables with at most 2^(k-2) other clauses is always satisfiable. All hitherto known proofs of the Local Lemma are non-constructive and do thus not provide a recipe as to how a satisfying assignment to such a formula can be efficiently found. In his breakthrough paper [Bec91], Beck demonstrated that if the neighbourhood of each clause be restricted to O(2^(k/48)), a polynomial time algorithm for the search problem exists. Alon simplified and randomized his procedure and improved the bound to O(2^(k/8)) [Alo91]. Srinivasan presented in [Sri08] a variant that achieves a bound of essentially O(2^(k/4)). In [Mos08], we improved this to O(2^(k/2)). In the present paper, we give a randomized algorithm that finds a satisfying assignment to every k-CNF formula in which each clause has a neighbourhood of at most the asymptotic optimum of 2^(k-5)-1 other clauses and that runs in expected time polynomial in the size of the formula, irrespective of k. If k is considered a constant, we can also give a deterministic variant. In contrast to all previous approaches, our analysis does not anymore invoke the standard non-constructive versions of the Local Lemma and can therefore be considered an alternative, constructive proof of it. | |
| dc.description | 11 pages; minor corrections | |
| dc.identifier | https://arxiv.org/abs/0810.4812 | |
| dc.identifier | http://arxiv.org/abs/0810.4812 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/172584 | |
| dc.subject | Data Structures and Algorithms | |
| dc.subject | F.2; G.2 | |
| dc.title | A constructive proof of the Lovasz Local Lemma | |
| dc.type | text |