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Circumspect descent prevails in solving random constraint satisfaction problems
KTH, School of Computer Science and Communication (CSC), Computational Biology, CB.
KTH, School of Computer Science and Communication (CSC), Computational Biology, CB.
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2008 (English)In: Proceedings of the National Academy of Sciences of the United States of America, ISSN 0027-8424, E-ISSN 1091-6490, Vol. 105, no 40, 15253-15257 p.Article in journal (Refereed) Published
Abstract [en]

We study the performance of stochastic local search algorithms for random instances of the K-satisfiability (K-SAT) problem. We present a stochastic local search algorithm, ChainSAT, which moves in the energy landscape of a problem instance by never going upwards in energy. ChainSAT is a focused algorithm in the sense that it focuses on variables occurring in unsatisfied clauses. We show by extensive numerical investigations that ChainSAT and other focused algorithms solve large K-SAT instances almost surely in linear time, up to high clause-to-variable ratios a; for example, for K = 4 we observe linear-time performance well beyond the recently postulated clustering and condensation transitions in the solution space. The performance of ChainSAT is a surprise given that by design the algorithm gets trapped into the first local energy minimum it encounters, yet no such minima are encountered. We also study the geometry of the solution space as accessed by stochastic local search algorithms.

Place, publisher, year, edition, pages
2008. Vol. 105, no 40, 15253-15257 p.
Keyword [en]
geometry of solutions local search, performance, random K-SAT
National Category
Other Biological Topics
Identifiers
URN: urn:nbn:se:kth:diva-8493DOI: 10.1073/pnas.0712263105ISI: 000260360500010Scopus ID: 2-s2.0-55749098814OAI: oai:DiVA.org:kth-8493DiVA: diva2:13832
Note
QC 20100903. Uppdaterad från Submitted till Published (20100903)Available from: 2008-05-19 Created: 2008-05-19 Last updated: 2017-12-14Bibliographically approved
In thesis
1. On state space structure and average case complexity in random K-SAT problems
Open this publication in new window or tab >>On state space structure and average case complexity in random K-SAT problems
2008 (English)Licentiate thesis, comprehensive summary (Other scientific)
Abstract [en]

This thesis gives an introduction to a currently active area in the cross-section between theoretical computer science and theoretical physics. In the last ten years it has been suggested that critical behaviour, usually seen in models from condensed matter physics, may be responsible for the intractability of NP complete computation problems. This would suggest a very deep connection between the two fields on the most fundamental level. How deep this connection really is is subject to ongoing research as well as the topic of this thesis. Some of the conjectrues from the physics community regarding computational hardness in certain problem classes has turned out to be wrong or misinterpreted but the gained interest in both fields has promising potiential in moving the research frontier forward.

The material presented in this thesis is the result of nearly two years work in trying to clearify how the results from physics can be interpreted in the language of actuall computation problems.

Abstract [sv]

Denna avhandling ger en introduktion till ett mycket aktivt forskningsområde i gränslandet mellan teortisk datalogi och teoretisk fysik. Under de senaste tio åren har det framkommit forskningsresultat som pekar på att kritiska fenomen, vanligen hemmahörande i modeller från teoretisk materialfysik, kan vara nyckeln till att förstå varför NP fullständiga problem är så svåra att lösa. Detta skulle innebära en mycket djup och fundamental koppling mellan de bägge områdena. Hur djup denna koppling verkligen är är temat i mycket av pågående forskning såväl som ämnet för denna avhandling. Vissa förutsägelser från den teoretiska fysiken har visat sig felaktiga eller feltolkade men det ökade intresset för dylika frågor inom bägge forskningområden ger hopp om att tillsammans kunna flytta from forskningsfronten.

Place, publisher, year, edition, pages
Stockholm: KTH, 2008. viii, 31 p.
Series
Trita-CSC-A, ISSN 1653-5723
National Category
Computer Science
Identifiers
urn:nbn:se:kth:diva-4765 (URN)978-91-7178-971-6 (ISBN)
Presentation
2008-05-14, FR42, NORDITA, Roslagstullsbacken 23, 13:00
Opponent
Supervisors
Note
QC 20101103Available from: 2008-05-19 Created: 2008-05-19 Last updated: 2010-11-03Bibliographically approved

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