The Phase Transition of the Linear Inequalities Problem
Identifieur interne : 003808 ( Istex/Corpus ); précédent : 003807; suivant : 003809The Phase Transition of the Linear Inequalities Problem
Auteurs : Alessandro Armando ; Felice Peccia ; Silvio RaniseSource :
- Lecture Notes in Computer Science [ 0302-9743 ]
Abstract
Abstract: One of the most important problems in the polynomial class is checking the satisfiabilityof systems of linear inequalities over the rationals. In this paper, we investigate the phase-transition behavior of this problem by adopting a methodology which has been proved very successful on NP-complete problems. The methodology is based on the concept of constrainedness, which characterizes an ensemble of randomly generated problems and allows to predict the location of the phase transition in solving such problems. Our work complements and confirms previous results obtained for other polynomial problems. The approach provides a new characterization of the performance of the Phase I of the Simplex algorithm and allows us to predict its behavior on very large instances by exploiting the technique of finite size scaling.
Url:
DOI: 10.1007/3-540-45578-7_29
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In this paper, we investigate the phase-transition behavior of this problem by adopting a methodology which has been proved very successful on NP-complete problems. The methodology is based on the concept of <Emphasis Type="Italic">constrainedness</Emphasis>, which characterizes an ensemble of randomly generated problems and allows to predict the location of the phase transition in solving such problems. Our work complements and confirms previous results obtained for other polynomial problems. The approach provides a new characterization of the performance of the Phase I of the Simplex algorithm and allows us to predict its behavior on very large instances by exploiting the technique of finite size scaling.</Para></Abstract></ChapterHeader><NoBody></NoBody></Chapter></Book></Series></Publisher></istex:document></istex:metadataXml><mods version="3.6"><titleInfo lang="en"><title>The Phase Transition of the Linear Inequalities Problem</title></titleInfo><titleInfo type="alternative" contentType="CDATA"><title>The Phase Transition of the Linear Inequalities Problem</title></titleInfo><name type="personal"><namePart type="given">Alessandro</namePart><namePart type="family">Armando</namePart><affiliation>DIST-Università degli Studi di Genova, via all’Opera Pia 13, 16145, Genova, Italy</affiliation><affiliation>E-mail: armando@dist.unige.it</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">Felice</namePart><namePart type="family">Peccia</namePart><affiliation>DIST-Università degli Studi di Genova, via all’Opera Pia 13, 16145, Genova, Italy</affiliation><affiliation>E-mail: peck@dist.unige.it</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">Silvio</namePart><namePart type="family">Ranise</namePart><affiliation>DIST-Università degli Studi di Genova, via all’Opera Pia 13, 16145, Genova, Italy</affiliation><affiliation>LORIA-INRIA-Lorraine, 615, rue du Jardin Botanique, BP 101, 54602, Villers les NancyCedex, France</affiliation><affiliation>E-mail: silvio@dist.unige.it</affiliation><role><roleTerm type="text">author</roleTerm></role></name><typeOfResource>text</typeOfResource><genre displayLabel="OriginalPaper" authority="ISTEX" authorityURI="https://content-type.data.istex.fr" type="conference" valueURI="https://content-type.data.istex.fr/ark:/67375/XTP-BFHXPBJJ-3">conference</genre><originInfo><publisher>Springer Berlin Heidelberg</publisher><place><placeTerm type="text">Berlin, Heidelberg</placeTerm></place><dateIssued encoding="w3cdtf">2001</dateIssued><copyrightDate encoding="w3cdtf">2001</copyrightDate></originInfo><language><languageTerm type="code" authority="rfc3066">en</languageTerm><languageTerm type="code" authority="iso639-2b">eng</languageTerm></language><abstract lang="en">Abstract: One of the most important problems in the polynomial class is checking the satisfiabilityof systems of linear inequalities over the rationals. In this paper, we investigate the phase-transition behavior of this problem by adopting a methodology which has been proved very successful on NP-complete problems. The methodology is based on the concept of constrainedness, which characterizes an ensemble of randomly generated problems and allows to predict the location of the phase transition in solving such problems. Our work complements and confirms previous results obtained for other polynomial problems. The approach provides a new characterization of the performance of the Phase I of the Simplex algorithm and allows us to predict its behavior on very large instances by exploiting the technique of finite size scaling.</abstract><relatedItem type="host"><titleInfo><title>Principles and Practice of Constraint Programming — CP 2001</title><subTitle>7th International Conference, CP 2001 Paphos, Cyprus, November 26 – December 1, 2001 Proceedings</subTitle></titleInfo><name type="personal"><namePart type="given">Toby</namePart><namePart type="family">Walsh</namePart><affiliation>Department of Computer Science, The University of York, YO10 5DD, Heslington, York, UK</affiliation><affiliation>E-mail: tw@cs.york.ac.uk</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><genre type="book-series" authority="ISTEX" authorityURI="https://publication-type.data.istex.fr" valueURI="https://publication-type.data.istex.fr/ark:/67375/JMC-0G6R5W5T-Z">book-series</genre><originInfo><publisher>Springer</publisher><copyrightDate encoding="w3cdtf">2001</copyrightDate><issuance>monographic</issuance></originInfo><subject><genre>Book-Subject-Collection</genre><topic authority="SpringerSubjectCodes" authorityURI="SUCO11645">Computer Science</topic></subject><subject><genre>Book-Subject-Group</genre><topic authority="SpringerSubjectCodes" authorityURI="I">Computer Science</topic><topic authority="SpringerSubjectCodes" authorityURI="I14010">Programming Techniques</topic><topic authority="SpringerSubjectCodes" authorityURI="I14037">Programming Languages, Compilers, Interpreters</topic><topic authority="SpringerSubjectCodes" authorityURI="I21017">Artificial Intelligence (incl. Robotics)</topic><topic authority="SpringerSubjectCodes" authorityURI="I1603X">Logics and Meanings of Programs</topic><topic authority="SpringerSubjectCodes" authorityURI="I16048">Mathematical Logic and Formal Languages</topic></subject><identifier type="DOI">10.1007/3-540-45578-7</identifier><identifier type="ISBN">978-3-540-42863-3</identifier><identifier type="eISBN">978-3-540-45578-3</identifier><identifier type="ISSN">0302-9743</identifier><identifier type="BookTitleID">71348</identifier><identifier type="BookID">3-540-45578-7</identifier><identifier type="BookChapterCount">84</identifier><identifier type="BookVolumeNumber">2239</identifier><identifier type="BookSequenceNumber">2239</identifier><part><date>2001</date><detail type="volume"><number>2239</number><caption>vol.</caption></detail><extent unit="pages"><start>422</start><end>432</end></extent></part><recordInfo><recordOrigin>Springer-Verlag Berlin Heidelberg, 2001</recordOrigin></recordInfo></relatedItem><relatedItem type="series"><titleInfo><title>Lecture Notes in Computer Science</title></titleInfo><name type="personal"><namePart type="given">Gerhard</namePart><namePart type="family">Goos</namePart><affiliation>Karlsruhe University, Germany</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Juris</namePart><namePart type="family">Hartmanis</namePart><affiliation>Cornell University, NY, USA</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Jan</namePart><namePart type="family">van Leeuwen</namePart><affiliation>Utrecht University, The Netherlands</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><originInfo><publisher>Springer</publisher><copyrightDate encoding="w3cdtf">2001</copyrightDate><issuance>serial</issuance></originInfo><identifier type="ISSN">0302-9743</identifier><identifier type="SeriesID">558</identifier><recordInfo><recordOrigin>Springer-Verlag Berlin Heidelberg, 2001</recordOrigin></recordInfo></relatedItem><identifier type="istex">EA3F15DC9EBE9D9E34EA036D275A6DE921BEAEC2</identifier><identifier type="ark">ark:/67375/HCB-6Z0KKTZR-1</identifier><identifier type="DOI">10.1007/3-540-45578-7_29</identifier><identifier type="ChapterID">29</identifier><identifier type="ChapterID">Chap29</identifier><accessCondition type="use and reproduction" contentType="copyright">Springer-Verlag Berlin Heidelberg, 2001</accessCondition><recordInfo><recordContentSource authority="ISTEX" authorityURI="https://loaded-corpus.data.istex.fr" valueURI="https://loaded-corpus.data.istex.fr/ark:/67375/XBH-RLRX46XW-4">springer</recordContentSource><recordOrigin>Springer-Verlag Berlin Heidelberg, 2001</recordOrigin></recordInfo></mods><json:item><extension>json</extension><original>false</original><mimetype>application/json</mimetype><uri>https://api.istex.fr/ark:/67375/HCB-6Z0KKTZR-1/record.json</uri></json:item></metadata></istex></record>Pour manipuler ce document sous Unix (Dilib)
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