Computational investigations of maximum flow algorithms
Identifieur interne : 001632 ( Istex/Corpus ); précédent : 001631; suivant : 001633Computational investigations of maximum flow algorithms
Auteurs : Ravindra K. Ahuja ; Murali Kodialam ; Ajay K. Mishra ; James B. OrlinSource :
- European Journal of Operational Research [ 0377-2217 ] ; 1996.
Abstract
The maximum flow algorithm is distinguished by the long line of successive contributions researchers have made in obtaining algorithms with incrementally better worst-case complexity. Some, but not all, of these theoretical improvements have produced improvements in practice. The purpose of this paper is to test some of the major algorithmic ideas developed in the recent years and to assess their utility on the empirical front. However, our study differs from previous studies in several ways. Whereas previous studies focus primarily on CPU time analysis, our analysis goes further and provides detailed insight into algorithmic behavior. It not only observes how algorithms behave but also tries to explain why algorithms behave that way. We have limited our study to the best previous maximum flow algorithms and some of the recent algorithms that are likely to be efficient in practice. Our study encompasses ten maximum flow algorithms and five classes of networks. The augmenting path algorithms tested by us include Dinic's algorithm, the shortest augmenting path algorithm, and the capacity-scaling algorithm. The preflow-push algorithms tested by us include Karzanov's algorithm, three implementations of Goldberg-Tarjan's algorithm, and three versions of Ahuja-Orlin-Tarjan's excess-scaling algorithms. Among many findings, our study concludes that the preflow-push algorithms are substantially faster than other classes of algorithms, and the highest-label preflow-push algorithm is the fastest maximum flow algorithm for which the growth rate in the computational time is O(n1.5) on four out of five of our problem classes. Further, in contrast to the results of the worst-case analysis of maximum flow algorithms, our study finds that the time to perform relabel operations (or constructing the layered networks) takes at least as much computation time as that taken by augmentations and/or pushes.
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DOI: 10.1016/S0377-2217(96)00269-X
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Some, but not all, of these theoretical improvements have produced improvements in practice. The purpose of this paper is to test some of the major algorithmic ideas developed in the recent years and to assess their utility on the empirical front. However, our study differs from previous studies in several ways. Whereas previous studies focus primarily on CPU time analysis, our analysis goes further and provides detailed insight into algorithmic behavior. It not only observes how algorithms behave but also tries to explain why algorithms behave that way. We have limited our study to the best previous maximum flow algorithms and some of the recent algorithms that are likely to be efficient in practice. Our study encompasses ten maximum flow algorithms and five classes of networks. The augmenting path algorithms tested by us include Dinic's algorithm, the shortest augmenting path algorithm, and the capacity-scaling algorithm. The preflow-push algorithms tested by us include Karzanov's algorithm, three implementations of Goldberg-Tarjan's algorithm, and three versions of Ahuja-Orlin-Tarjan's excess-scaling algorithms. Among many findings, our study concludes that the preflow-push algorithms are substantially faster than other classes of algorithms, and the highest-label preflow-push algorithm is the fastest maximum flow algorithm for which the growth rate in the computational time is O(n1.5) on four out of five of our problem classes. Further, in contrast to the results of the worst-case analysis of maximum flow algorithms, our study finds that the time to perform relabel operations (or constructing the layered networks) takes at least as much computation time as that taken by augmentations and/or pushes.</div></front></TEI><istex><corpusName>elsevier</corpusName><author><json:item><name>Ravindra K. 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Orlin</name><affiliations><json:string>Corresponding author.</json:string><json:string>Sloan School of Management, Massachusetts Institute of Technology, Cambridge, MA 02139, USA</json:string></affiliations></json:item></author><language><json:string>eng</json:string></language><abstract>The maximum flow algorithm is distinguished by the long line of successive contributions researchers have made in obtaining algorithms with incrementally better worst-case complexity. Some, but not all, of these theoretical improvements have produced improvements in practice. The purpose of this paper is to test some of the major algorithmic ideas developed in the recent years and to assess their utility on the empirical front. However, our study differs from previous studies in several ways. Whereas previous studies focus primarily on CPU time analysis, our analysis goes further and provides detailed insight into algorithmic behavior. It not only observes how algorithms behave but also tries to explain why algorithms behave that way. We have limited our study to the best previous maximum flow algorithms and some of the recent algorithms that are likely to be efficient in practice. Our study encompasses ten maximum flow algorithms and five classes of networks. The augmenting path algorithms tested by us include Dinic's algorithm, the shortest augmenting path algorithm, and the capacity-scaling algorithm. The preflow-push algorithms tested by us include Karzanov's algorithm, three implementations of Goldberg-Tarjan's algorithm, and three versions of Ahuja-Orlin-Tarjan's excess-scaling algorithms. Among many findings, our study concludes that the preflow-push algorithms are substantially faster than other classes of algorithms, and the highest-label preflow-push algorithm is the fastest maximum flow algorithm for which the growth rate in the computational time is O(n1.5) on four out of five of our problem classes. 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Some, but not all, of these theoretical improvements have produced improvements in practice. The purpose of this paper is to test some of the major algorithmic ideas developed in the recent years and to assess their utility on the empirical front. However, our study differs from previous studies in several ways. Whereas previous studies focus primarily on CPU time analysis, our analysis goes further and provides detailed insight into algorithmic behavior. It not only observes how algorithms behave but also tries to explain why algorithms behave that way. We have limited our study to the best previous maximum flow algorithms and some of the recent algorithms that are likely to be efficient in practice. Our study encompasses ten maximum flow algorithms and five classes of networks. The augmenting path algorithms tested by us include Dinic's algorithm, the shortest augmenting path algorithm, and the capacity-scaling algorithm. The preflow-push algorithms tested by us include Karzanov's algorithm, three implementations of Goldberg-Tarjan's algorithm, and three versions of Ahuja-Orlin-Tarjan's excess-scaling algorithms. Among many findings, our study concludes that the preflow-push algorithms are substantially faster than other classes of algorithms, and the highest-label preflow-push algorithm is the fastest maximum flow algorithm for which the growth rate in the computational time is O(n1.5) on four out of five of our problem classes. Further, in contrast to the results of the worst-case analysis of maximum flow algorithms, our study finds that the time to perform relabel operations (or constructing the layered networks) takes at least as much computation time as that taken by augmentations and/or pushes.</p></abstract></profileDesc><revisionDesc><change when="1996-06-27">Registration</change><change when="1996">Published</change></revisionDesc></teiHeader></istex:fulltextTEI></fulltext><metadata><istex:metadataXml wicri:clean="Elsevier, elements deleted: tail"><istex:xmlDeclaration>version="1.0" encoding="utf-8"</istex:xmlDeclaration><istex:docType PUBLIC="-//ES//DTD journal article DTD version 4.5.2//EN//XML" URI="art452.dtd" name="istex:docType"></istex:docType><istex:document><converted-article version="4.5.2" docsubtype="fla"><item-info><jid>EOR</jid><aid>9600269X</aid><ce:pii>S0377-2217(96)00269-X</ce:pii><ce:doi>10.1016/S0377-2217(96)00269-X</ce:doi><ce:copyright type="unknown" year="1997"></ce:copyright></item-info><head><ce:dochead><ce:textfn>Theory and methodology</ce:textfn></ce:dochead><ce:title>Computational investigations of maximum flow algorithms</ce:title><ce:author-group><ce:author><ce:given-name>Ravindra K.</ce:given-name><ce:surname>Ahuja</ce:surname><ce:cross-ref refid="AFF1"><ce:sup>a</ce:sup></ce:cross-ref></ce:author><ce:author><ce:given-name>Murali</ce:given-name><ce:surname>Kodialam</ce:surname><ce:cross-ref refid="AFF2"><ce:sup>b</ce:sup></ce:cross-ref></ce:author><ce:author><ce:given-name>Ajay K.</ce:given-name><ce:surname>Mishra</ce:surname><ce:cross-ref refid="AFF3"><ce:sup>c</ce:sup></ce:cross-ref></ce:author><ce:author><ce:given-name>James B.</ce:given-name><ce:surname>Orlin</ce:surname><ce:cross-ref refid="COR1"><ce:sup>∗</ce:sup></ce:cross-ref><ce:cross-ref refid="AFF4"><ce:sup>d</ce:sup></ce:cross-ref></ce:author><ce:affiliation id="AFF1"><ce:label>a</ce:label><ce:textfn>Department of Industrial and Management Engineering, Indian Institute of Technology, Kanpur, 208 016, India</ce:textfn></ce:affiliation><ce:affiliation id="AFF2"><ce:label>b</ce:label><ce:textfn>AT&T Bell Laboratories, Holmdel, NJ 07733, USA</ce:textfn></ce:affiliation><ce:affiliation id="AFF3"><ce:label>c</ce:label><ce:textfn>KATZ Graduate School of Business, University of Pittsburgh, Pittsburgh, PA 15260, USA</ce:textfn></ce:affiliation><ce:affiliation id="AFF4"><ce:label>d</ce:label><ce:textfn>Sloan School of Management, Massachusetts Institute of Technology, Cambridge, MA 02139, USA</ce:textfn></ce:affiliation><ce:correspondence id="COR1"><ce:label>∗</ce:label><ce:text>Corresponding author.</ce:text></ce:correspondence></ce:author-group><ce:date-received day="30" month="8" year="1995"></ce:date-received><ce:date-accepted day="27" month="6" year="1996"></ce:date-accepted><ce:abstract><ce:section-title>Abstract</ce:section-title><ce:abstract-sec><ce:simple-para>The maximum flow algorithm is distinguished by the long line of successive contributions researchers have made in obtaining algorithms with incrementally better worst-case complexity. Some, but not all, of these theoretical improvements have produced improvements in practice. The purpose of this paper is to test some of the major algorithmic ideas developed in the recent years and to assess their utility on the empirical front. However, our study differs from previous studies in several ways. Whereas previous studies focus primarily on CPU time analysis, our analysis goes further and provides detailed insight into algorithmic behavior. It not only observes how algorithms behave but also tries to explain why algorithms behave that way. We have limited our study to the best previous maximum flow algorithms and some of the recent algorithms that are likely to be efficient in practice. Our study encompasses ten maximum flow algorithms and five classes of networks. The augmenting path algorithms tested by us include Dinic's algorithm, the shortest augmenting path algorithm, and the capacity-scaling algorithm. The preflow-push algorithms tested by us include Karzanov's algorithm, three implementations of Goldberg-Tarjan's algorithm, and three versions of Ahuja-Orlin-Tarjan's excess-scaling algorithms. Among many findings, our study concludes that the preflow-push algorithms are substantially faster than other classes of algorithms, and the highest-label preflow-push algorithm is the fastest maximum flow algorithm for which the growth rate in the computational time is <ce:italic>O</ce:italic>(<ce:italic>n</ce:italic><ce:sup>1.5</ce:sup>) on four out of five of our problem classes. Further, in contrast to the results of the worst-case analysis of maximum flow algorithms, our study finds that the time to perform relabel operations (or constructing the layered networks) takes at least as much computation time as that taken by augmentations and/or pushes.</ce:simple-para></ce:abstract-sec></ce:abstract></head></converted-article></istex:document></istex:metadataXml><mods version="3.6"><titleInfo><title>Computational investigations of maximum flow algorithms</title></titleInfo><titleInfo type="alternative" contentType="CDATA"><title>Computational investigations of maximum flow algorithms</title></titleInfo><name type="personal"><namePart type="given">Ravindra K.</namePart><namePart type="family">Ahuja</namePart><affiliation>Department of Industrial and Management Engineering, Indian Institute of Technology, Kanpur, 208 016, India</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">Murali</namePart><namePart type="family">Kodialam</namePart><affiliation>AT&T Bell Laboratories, Holmdel, NJ 07733, USA</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">Ajay K.</namePart><namePart type="family">Mishra</namePart><affiliation>KATZ Graduate School of Business, University of Pittsburgh, Pittsburgh, PA 15260, USA</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">James B.</namePart><namePart type="family">Orlin</namePart><affiliation>Corresponding author.</affiliation><affiliation>Sloan School of Management, Massachusetts Institute of Technology, Cambridge, MA 02139, USA</affiliation><role><roleTerm type="text">author</roleTerm></role></name><typeOfResource>text</typeOfResource><genre type="research-article" displayLabel="Full-length article"></genre><originInfo><publisher>ELSEVIER</publisher><dateIssued encoding="w3cdtf">1996</dateIssued><dateValid encoding="w3cdtf">1996-06-27</dateValid><copyrightDate encoding="w3cdtf">1997</copyrightDate></originInfo><language><languageTerm type="code" authority="iso639-2b">eng</languageTerm><languageTerm type="code" authority="rfc3066">en</languageTerm></language><physicalDescription><internetMediaType>text/html</internetMediaType></physicalDescription><abstract lang="en">The maximum flow algorithm is distinguished by the long line of successive contributions researchers have made in obtaining algorithms with incrementally better worst-case complexity. Some, but not all, of these theoretical improvements have produced improvements in practice. The purpose of this paper is to test some of the major algorithmic ideas developed in the recent years and to assess their utility on the empirical front. However, our study differs from previous studies in several ways. Whereas previous studies focus primarily on CPU time analysis, our analysis goes further and provides detailed insight into algorithmic behavior. It not only observes how algorithms behave but also tries to explain why algorithms behave that way. We have limited our study to the best previous maximum flow algorithms and some of the recent algorithms that are likely to be efficient in practice. Our study encompasses ten maximum flow algorithms and five classes of networks. The augmenting path algorithms tested by us include Dinic's algorithm, the shortest augmenting path algorithm, and the capacity-scaling algorithm. The preflow-push algorithms tested by us include Karzanov's algorithm, three implementations of Goldberg-Tarjan's algorithm, and three versions of Ahuja-Orlin-Tarjan's excess-scaling algorithms. Among many findings, our study concludes that the preflow-push algorithms are substantially faster than other classes of algorithms, and the highest-label preflow-push algorithm is the fastest maximum flow algorithm for which the growth rate in the computational time is O(n1.5) on four out of five of our problem classes. Further, in contrast to the results of the worst-case analysis of maximum flow algorithms, our study finds that the time to perform relabel operations (or constructing the layered networks) takes at least as much computation time as that taken by augmentations and/or pushes.</abstract><note type="content">Section title: Theory and methodology</note><relatedItem type="host"><titleInfo><title>European Journal of Operational Research</title></titleInfo><titleInfo type="abbreviated"><title>EOR</title></titleInfo><genre type="Journal">journal</genre><originInfo><dateIssued encoding="w3cdtf">19970316</dateIssued></originInfo><identifier type="ISSN">0377-2217</identifier><identifier type="PII">S0377-2217(00)X0051-3</identifier><part><date>19970316</date><detail type="volume"><number>97</number><caption>vol.</caption></detail><detail type="issue"><number>3</number><caption>no.</caption></detail><extent unit="issue pages"><start>409</start><end>613</end></extent><extent unit="pages"><start>509</start><end>542</end></extent></part></relatedItem><identifier type="istex">C70C8062F29D1B7A2EB5510574001C9AB0943E71</identifier><identifier type="DOI">10.1016/S0377-2217(96)00269-X</identifier><identifier type="PII">S0377-2217(96)00269-X</identifier><recordInfo><recordContentSource>ELSEVIER</recordContentSource></recordInfo></mods></metadata><enrichments><istex:catWosTEI uri="https://api.istex.fr/document/C70C8062F29D1B7A2EB5510574001C9AB0943E71/enrichments/catWos"><teiHeader><profileDesc><textClass><classCode scheme="WOS">OPERATIONS RESEARCH & MANAGEMENT SCIENCE</classCode><classCode scheme="WOS">MANAGEMENT</classCode></textClass></profileDesc></teiHeader></istex:catWosTEI></enrichments></istex></record>Pour manipuler ce document sous Unix (Dilib)
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