Deterministic algorithms for the Lovász Local Lemma
Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2010.
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| Format: | Thesis |
| Language: | eng |
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Massachusetts Institute of Technology
2010
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| Online Access: | http://hdl.handle.net/1721.1/60165 |
| _version_ | 1826211547871969280 |
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| author | Haeupler, Bernhard |
| author2 | David R. Karger. |
| author_facet | David R. Karger. Haeupler, Bernhard |
| author_sort | Haeupler, Bernhard |
| collection | MIT |
| description | Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2010. |
| first_indexed | 2024-09-23T15:07:31Z |
| format | Thesis |
| id | mit-1721.1/60165 |
| institution | Massachusetts Institute of Technology |
| language | eng |
| last_indexed | 2024-09-23T15:07:31Z |
| publishDate | 2010 |
| publisher | Massachusetts Institute of Technology |
| record_format | dspace |
| spelling | mit-1721.1/601652019-04-11T06:03:40Z Deterministic algorithms for the Lovász Local Lemma Haeupler, Bernhard David R. Karger. Massachusetts Institute of Technology. Dept. of Electrical Engineering and Computer Science. Massachusetts Institute of Technology. Dept. of Electrical Engineering and Computer Science. Electrical Engineering and Computer Science. Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2010. Includes bibliographical references (p. 34-36). The Lovász Local Lemma [6] (LLL) is a powerful result in probability theory that states that the probability that none of a set of bad events happens is nonzero if the probability of each event is small compared to the number of events that depend on it. It is often used in combination with the probabilistic method for non-constructive existence proofs. A prominent application is to k-CNF formulas, where LLL implies that, if every clause in the formula shares variables with at most d < 2k/e other clauses then such the formula has a satisfying assignment. Recently, a randomized algorithm to efficiently construct a satisfying assignment was given by Moser [17]. Subsequently Moser and Tardos [18] gave a randomized algorithm to construct the structures guaranteed by the LLL in a very general algorithmic framework. We address the main problem left open by Moser and Tardos of derandomizing these algorithms efficiently. Specifically, for a k-CNF formula with m clauses and d < 2k/(l+)/e for some c E (0, 1), we give an algorithm that finds a satisfying assignment in time O(m2(1+1/E)). This improves upon the deterministic algorithms of Moser and of Moser- Tardos with running times mn (k2) and mD(k 1/c) which are superpolynomial for k = w(1) and upon other previous algorithms which work only for d </= 2k/ 16 /e. Our algorithm works efficiently for the asymmetric version of LLL under the algorithmic framework of Moser and Tardos [18] and is also parallelizable, i.e., has polylogarithmic running time using polynomially many processors. by Bernhard Haeupler. S.M. 2010-12-06T17:32:14Z 2010-12-06T17:32:14Z 2010 2010 Thesis http://hdl.handle.net/1721.1/60165 681761564 eng M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission. http://dspace.mit.edu/handle/1721.1/7582 36 p. application/pdf Massachusetts Institute of Technology |
| spellingShingle | Electrical Engineering and Computer Science. Haeupler, Bernhard Deterministic algorithms for the Lovász Local Lemma |
| title | Deterministic algorithms for the Lovász Local Lemma |
| title_full | Deterministic algorithms for the Lovász Local Lemma |
| title_fullStr | Deterministic algorithms for the Lovász Local Lemma |
| title_full_unstemmed | Deterministic algorithms for the Lovász Local Lemma |
| title_short | Deterministic algorithms for the Lovász Local Lemma |
| title_sort | deterministic algorithms for the lovasz local lemma |
| topic | Electrical Engineering and Computer Science. |
| url | http://hdl.handle.net/1721.1/60165 |
| work_keys_str_mv | AT haeuplerbernhard deterministicalgorithmsforthelovaszlocallemma |