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Temperature dependent sampling in hard satisfiability problems
SICS.
2008 (English)Article in journal (Other academic) Submitted
Abstract [en]

The solution sets of constraint satisfaction problems (CSPs)have been conjectured to to split up into clusters (connectedcomponents) when they are close to critically constrained,and this has been assumed to be related to computationalhardness. Simple stochastic local search (SLS) heuristics hashowever shown to be very efficient for many of these problems,and it has been unclear if this is related to clustering.In this work an SLS is used to sample the space of solutionsand the results are compared to the actual solution space generatedwith a complete solver. We show that different heuristicsfind different types of clusters. An increased greedinessresults in a sampling more uniform over the set of clusters,rather than over the set of solutions and the fastest solver visitsthe smaller cluster much more frequently than its solutionsdensity would imply. We also show that the level of randomness(temperature) is related in a non-trivial way to the abilityto escape from local minimas. This approach confirms thatclusters are important in understanding computational hardnessand may begin to explain the efficiency of SLSs in fragmentedsolution spaces.

Place, publisher, year, edition, pages
2008.
National Category
Computer Science
Identifiers
URN: urn:nbn:se:kth:diva-8494OAI: oai:DiVA.org:kth-8494DiVA: diva2:13833
Note
QS 20120314Available from: 2008-05-19 Created: 2008-05-19 Last updated: 2012-03-14Bibliographically 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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Citation style
  • apa
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Output format
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