Name
Abstract | ||
|---|---|---|
The Lovasz Local Lemma [2] 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 [3], 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)) [4]. Srinivasan presented in [9] a variant that achieves a bound of essentially O(2(k/4)). In [11], 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. |
Year | DOI | Venue |
|---|---|---|
2009 | 10.1145/1536414.1536462 | Clinical Orthopaedics and Related Research |
Keywords | DocType | Volume |
hypergraph colouring.,k-cnf formula,expected time polynomial,derandomization,deterministic variant,lovasz local lemma,hypergraph colouring,sz local lemma,randomized algorithm,breakthrough paper,constructive proof,present paper,. lovasz local lemma,satisfying assignment,bounded occurrence sat instances,local lemma,polynomial time algorithm,data structure,satisfiability | Conference | abs/0810.4812 |
ISSN | Citations | PageRank |
0737-8017 | 51 | 2.49 |
References | Authors | |
7 | 1 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Robin A. Moser | 1 | 240 | 12.51 |