Heavy-tailed phenomena in satisfiability and constraint satisfaction problems
Autor(a) principal: | |
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Data de Publicação: | 2000 |
Outros Autores: | , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | http://hdl.handle.net/10400.5/27682 |
Resumo: | We study the runtime distributions of backtrack procedures for propositional satisfiability and constraint satisfaction. Such procedures often exhibit a large variability in performance. Our study reveals some intriguing properties of such distributions: They are often characterized by very long tails or “heavy tails”. We will show that these distributions are best characterized by a general class of distributions that can have infinite moments (i.e., an infinite mean, variance, etc.). Such nonstandard distributions have recently been observed in areas as diverse as economics, statistical physics, and geophysics. They are closely related to fractal phenomena, whose study was introduced by Mandelbrot. We also show how random restarts can effectively eliminate heavy-tailed behavior. Furthermore, for harder problem instances, we observe long tails on the left-hand side of the distribution, which is indicative of a non-negligible fraction of relatively short, successful runs. A rapid restart strategy eliminates heavy-tailed behavior and takes advantage of short runs, significantly reducing expected solution time. We demonstrate speedups of up to two orders of magnitude on SAT and CSP encodings of hard problems in planning, scheduling, and circuit synthesis. |
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Heavy-tailed phenomena in satisfiability and constraint satisfaction problemsSatisfiabilityConstraint SatisfactionHeavy TailsBacktrackingWe study the runtime distributions of backtrack procedures for propositional satisfiability and constraint satisfaction. Such procedures often exhibit a large variability in performance. Our study reveals some intriguing properties of such distributions: They are often characterized by very long tails or “heavy tails”. We will show that these distributions are best characterized by a general class of distributions that can have infinite moments (i.e., an infinite mean, variance, etc.). Such nonstandard distributions have recently been observed in areas as diverse as economics, statistical physics, and geophysics. They are closely related to fractal phenomena, whose study was introduced by Mandelbrot. We also show how random restarts can effectively eliminate heavy-tailed behavior. Furthermore, for harder problem instances, we observe long tails on the left-hand side of the distribution, which is indicative of a non-negligible fraction of relatively short, successful runs. A rapid restart strategy eliminates heavy-tailed behavior and takes advantage of short runs, significantly reducing expected solution time. We demonstrate speedups of up to two orders of magnitude on SAT and CSP encodings of hard problems in planning, scheduling, and circuit synthesis.Kluwer Academic PublisherRepositório da Universidade de LisboaGomes, Carla P.Selman, BartCrato, Nuno2023-05-02T09:05:27Z20002000-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.5/27682engGomes, Carla P. … [et al.]. (2000). "Heavy-tailed phenomena in satisfiability and constraint satisfaction problems". Journal of Automated Reasoning Vol. 24: pp. 67-100 .(Search PDF in 2023).info:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2023-05-07T01:30:53Zoai:www.repository.utl.pt:10400.5/27682Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T17:50:56.876579Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse |
dc.title.none.fl_str_mv |
Heavy-tailed phenomena in satisfiability and constraint satisfaction problems |
title |
Heavy-tailed phenomena in satisfiability and constraint satisfaction problems |
spellingShingle |
Heavy-tailed phenomena in satisfiability and constraint satisfaction problems Gomes, Carla P. Satisfiability Constraint Satisfaction Heavy Tails Backtracking |
title_short |
Heavy-tailed phenomena in satisfiability and constraint satisfaction problems |
title_full |
Heavy-tailed phenomena in satisfiability and constraint satisfaction problems |
title_fullStr |
Heavy-tailed phenomena in satisfiability and constraint satisfaction problems |
title_full_unstemmed |
Heavy-tailed phenomena in satisfiability and constraint satisfaction problems |
title_sort |
Heavy-tailed phenomena in satisfiability and constraint satisfaction problems |
author |
Gomes, Carla P. |
author_facet |
Gomes, Carla P. Selman, Bart Crato, Nuno |
author_role |
author |
author2 |
Selman, Bart Crato, Nuno |
author2_role |
author author |
dc.contributor.none.fl_str_mv |
Repositório da Universidade de Lisboa |
dc.contributor.author.fl_str_mv |
Gomes, Carla P. Selman, Bart Crato, Nuno |
dc.subject.por.fl_str_mv |
Satisfiability Constraint Satisfaction Heavy Tails Backtracking |
topic |
Satisfiability Constraint Satisfaction Heavy Tails Backtracking |
description |
We study the runtime distributions of backtrack procedures for propositional satisfiability and constraint satisfaction. Such procedures often exhibit a large variability in performance. Our study reveals some intriguing properties of such distributions: They are often characterized by very long tails or “heavy tails”. We will show that these distributions are best characterized by a general class of distributions that can have infinite moments (i.e., an infinite mean, variance, etc.). Such nonstandard distributions have recently been observed in areas as diverse as economics, statistical physics, and geophysics. They are closely related to fractal phenomena, whose study was introduced by Mandelbrot. We also show how random restarts can effectively eliminate heavy-tailed behavior. Furthermore, for harder problem instances, we observe long tails on the left-hand side of the distribution, which is indicative of a non-negligible fraction of relatively short, successful runs. A rapid restart strategy eliminates heavy-tailed behavior and takes advantage of short runs, significantly reducing expected solution time. We demonstrate speedups of up to two orders of magnitude on SAT and CSP encodings of hard problems in planning, scheduling, and circuit synthesis. |
publishDate |
2000 |
dc.date.none.fl_str_mv |
2000 2000-01-01T00:00:00Z 2023-05-02T09:05:27Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://hdl.handle.net/10400.5/27682 |
url |
http://hdl.handle.net/10400.5/27682 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Gomes, Carla P. … [et al.]. (2000). "Heavy-tailed phenomena in satisfiability and constraint satisfaction problems". Journal of Automated Reasoning Vol. 24: pp. 67-100 .(Search PDF in 2023). |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
application/pdf |
dc.publisher.none.fl_str_mv |
Kluwer Academic Publisher |
publisher.none.fl_str_mv |
Kluwer Academic Publisher |
dc.source.none.fl_str_mv |
reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação instacron:RCAAP |
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Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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RCAAP |
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RCAAP |
reponame_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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1799131588497244160 |