Minimal multicut and maximal integer multiflow: A survey
We present a survey about the maximum integral multiflow and minimum multicut problems and their subproblems, such as the multiterminal cut and the unsplittable flow problems. We consider neither continuous multiflow nor minimum cost multiflow. Most of the results are very recent and some are new. W...
Gespeichert in:
| Veröffentlicht in: | European journal of operational research 2005-04, Vol.162 (1), p.55-69 |
|---|---|
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 69 |
|---|---|
| container_issue | 1 |
| container_start_page | 55 |
| container_title | European journal of operational research |
| container_volume | 162 |
| creator | Costa, Marie-Christine Létocart, Lucas Roupin, Frédéric |
| description | We present a survey about the maximum integral multiflow and minimum multicut problems and their subproblems, such as the multiterminal cut and the unsplittable flow problems. We consider neither continuous multiflow nor minimum cost multiflow. Most of the results are very recent and some are new. We recall the dual relationship between both problems, give complexity results and algorithms, firstly in unrestricted graphs and secondly in several special graphs: trees, bipartite or planar graphs. A table summarizes the most important results. |
| doi_str_mv | 10.1016/j.ejor.2003.10.037 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_hal_p</sourceid><recordid>TN_cdi_hal_primary_oai_HAL_hal_00003243v2</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><els_id>S0377221703008348</els_id><sourcerecordid>730586411</sourcerecordid><originalsourceid>FETCH-LOGICAL-c479t-b37d759775c44fff7aa3ac782cac4e610be69a835ca3fa4f23a523952ec18d943</originalsourceid><addsrcrecordid>eNp9UE1LxDAUDKLguvoHPBVvHlrz0TSteFkWv2DFi55DTF81pduuSbu6_95XK3s0MHkwmRlehpBzRhNGWXZVJ1B3PuGUCiQSKtQBmbFc8TjLM3pIZsiomHOmjslJCDWllEkmZyR_cq1bmyZaD03v7NBHpi2jtfn-JV3bwzv46bFquq_raBGFwW9hd0qOKtMEOPubc_J6d_uyfIhXz_ePy8Uqtqkq-vhNqFLJQilp07SqKmWMMFbl3BqbQsboG2SFyYW0RlQmrbgwkotCcrAsL4tUzMnllPthGr3xuJbf6c44_bBY6ZHDr1DBU7HlqL2YtBvffQ4Qel13g29xPc1pyoQomEQRn0TWdyF4qPapjOqxTF3rsUw9ljlyWB2aHieThw3YvQPwoBSC3mphWMbx3iHQKnG4kURsEFLqrNAf_RqzbqYswNq2DrwO1kFroXQebK_Lzv23yg_fapTi</addsrcrecordid><sourcetype>Open Access Repository</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>204133915</pqid></control><display><type>article</type><title>Minimal multicut and maximal integer multiflow: A survey</title><source>RePEc</source><source>Elsevier ScienceDirect Journals</source><creator>Costa, Marie-Christine ; Létocart, Lucas ; Roupin, Frédéric</creator><creatorcontrib>Costa, Marie-Christine ; Létocart, Lucas ; Roupin, Frédéric</creatorcontrib><description>We present a survey about the maximum integral multiflow and minimum multicut problems and their subproblems, such as the multiterminal cut and the unsplittable flow problems. We consider neither continuous multiflow nor minimum cost multiflow. Most of the results are very recent and some are new. We recall the dual relationship between both problems, give complexity results and algorithms, firstly in unrestricted graphs and secondly in several special graphs: trees, bipartite or planar graphs. A table summarizes the most important results.</description><identifier>ISSN: 0377-2217</identifier><identifier>EISSN: 1872-6860</identifier><identifier>DOI: 10.1016/j.ejor.2003.10.037</identifier><identifier>CODEN: EJORDT</identifier><language>eng</language><publisher>Amsterdam: Elsevier B.V</publisher><subject>Algorithms ; Approximation ; Complexity ; Computer Science ; Discrete Mathematics ; Integer multicommodity flows ; Integer programming ; Minimum multicut ; Multiway cut ; Studies</subject><ispartof>European journal of operational research, 2005-04, Vol.162 (1), p.55-69</ispartof><rights>2003 Elsevier B.V.</rights><rights>Copyright Elsevier Sequoia S.A. Apr 1, 2005</rights><rights>Distributed under a Creative Commons Attribution 4.0 International License</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c479t-b37d759775c44fff7aa3ac782cac4e610be69a835ca3fa4f23a523952ec18d943</citedby><cites>FETCH-LOGICAL-c479t-b37d759775c44fff7aa3ac782cac4e610be69a835ca3fa4f23a523952ec18d943</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://www.sciencedirect.com/science/article/pii/S0377221703008348$$EHTML$$P50$$Gelsevier$$H</linktohtml><link.rule.ids>230,314,776,780,881,3537,3994,27901,27902,65306</link.rule.ids><backlink>$$Uhttp://econpapers.repec.org/article/eeeejores/v_3a162_3ay_3a2005_3ai_3a1_3ap_3a55-69.htm$$DView record in RePEc$$Hfree_for_read</backlink><backlink>$$Uhttps://hal.science/hal-00003243$$DView record in HAL$$Hfree_for_read</backlink></links><search><creatorcontrib>Costa, Marie-Christine</creatorcontrib><creatorcontrib>Létocart, Lucas</creatorcontrib><creatorcontrib>Roupin, Frédéric</creatorcontrib><title>Minimal multicut and maximal integer multiflow: A survey</title><title>European journal of operational research</title><description>We present a survey about the maximum integral multiflow and minimum multicut problems and their subproblems, such as the multiterminal cut and the unsplittable flow problems. We consider neither continuous multiflow nor minimum cost multiflow. Most of the results are very recent and some are new. We recall the dual relationship between both problems, give complexity results and algorithms, firstly in unrestricted graphs and secondly in several special graphs: trees, bipartite or planar graphs. A table summarizes the most important results.</description><subject>Algorithms</subject><subject>Approximation</subject><subject>Complexity</subject><subject>Computer Science</subject><subject>Discrete Mathematics</subject><subject>Integer multicommodity flows</subject><subject>Integer programming</subject><subject>Minimum multicut</subject><subject>Multiway cut</subject><subject>Studies</subject><issn>0377-2217</issn><issn>1872-6860</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2005</creationdate><recordtype>article</recordtype><sourceid>X2L</sourceid><recordid>eNp9UE1LxDAUDKLguvoHPBVvHlrz0TSteFkWv2DFi55DTF81pduuSbu6_95XK3s0MHkwmRlehpBzRhNGWXZVJ1B3PuGUCiQSKtQBmbFc8TjLM3pIZsiomHOmjslJCDWllEkmZyR_cq1bmyZaD03v7NBHpi2jtfn-JV3bwzv46bFquq_raBGFwW9hd0qOKtMEOPubc_J6d_uyfIhXz_ePy8Uqtqkq-vhNqFLJQilp07SqKmWMMFbl3BqbQsboG2SFyYW0RlQmrbgwkotCcrAsL4tUzMnllPthGr3xuJbf6c44_bBY6ZHDr1DBU7HlqL2YtBvffQ4Qel13g29xPc1pyoQomEQRn0TWdyF4qPapjOqxTF3rsUw9ljlyWB2aHieThw3YvQPwoBSC3mphWMbx3iHQKnG4kURsEFLqrNAf_RqzbqYswNq2DrwO1kFroXQebK_Lzv23yg_fapTi</recordid><startdate>20050401</startdate><enddate>20050401</enddate><creator>Costa, Marie-Christine</creator><creator>Létocart, Lucas</creator><creator>Roupin, Frédéric</creator><general>Elsevier B.V</general><general>Elsevier</general><general>Elsevier Sequoia S.A</general><scope>DKI</scope><scope>X2L</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>JQ2</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><scope>1XC</scope><scope>VOOES</scope></search><sort><creationdate>20050401</creationdate><title>Minimal multicut and maximal integer multiflow: A survey</title><author>Costa, Marie-Christine ; Létocart, Lucas ; Roupin, Frédéric</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c479t-b37d759775c44fff7aa3ac782cac4e610be69a835ca3fa4f23a523952ec18d943</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2005</creationdate><topic>Algorithms</topic><topic>Approximation</topic><topic>Complexity</topic><topic>Computer Science</topic><topic>Discrete Mathematics</topic><topic>Integer multicommodity flows</topic><topic>Integer programming</topic><topic>Minimum multicut</topic><topic>Multiway cut</topic><topic>Studies</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Costa, Marie-Christine</creatorcontrib><creatorcontrib>Létocart, Lucas</creatorcontrib><creatorcontrib>Roupin, Frédéric</creatorcontrib><collection>RePEc IDEAS</collection><collection>RePEc</collection><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><collection>Hyper Article en Ligne (HAL)</collection><collection>Hyper Article en Ligne (HAL) (Open Access)</collection><jtitle>European journal of operational research</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Costa, Marie-Christine</au><au>Létocart, Lucas</au><au>Roupin, Frédéric</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Minimal multicut and maximal integer multiflow: A survey</atitle><jtitle>European journal of operational research</jtitle><date>2005-04-01</date><risdate>2005</risdate><volume>162</volume><issue>1</issue><spage>55</spage><epage>69</epage><pages>55-69</pages><issn>0377-2217</issn><eissn>1872-6860</eissn><coden>EJORDT</coden><abstract>We present a survey about the maximum integral multiflow and minimum multicut problems and their subproblems, such as the multiterminal cut and the unsplittable flow problems. We consider neither continuous multiflow nor minimum cost multiflow. Most of the results are very recent and some are new. We recall the dual relationship between both problems, give complexity results and algorithms, firstly in unrestricted graphs and secondly in several special graphs: trees, bipartite or planar graphs. A table summarizes the most important results.</abstract><cop>Amsterdam</cop><pub>Elsevier B.V</pub><doi>10.1016/j.ejor.2003.10.037</doi><tpages>15</tpages><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0377-2217 |
| ispartof | European journal of operational research, 2005-04, Vol.162 (1), p.55-69 |
| issn | 0377-2217 1872-6860 |
| language | eng |
| recordid | cdi_hal_primary_oai_HAL_hal_00003243v2 |
| source | RePEc; Elsevier ScienceDirect Journals |
| subjects | Algorithms Approximation Complexity Computer Science Discrete Mathematics Integer multicommodity flows Integer programming Minimum multicut Multiway cut Studies |
| title | Minimal multicut and maximal integer multiflow: A survey |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-02-08T02%3A47%3A31IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_hal_p&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Minimal%20multicut%20and%20maximal%20integer%20multiflow:%20A%20survey&rft.jtitle=European%20journal%20of%20operational%20research&rft.au=Costa,%20Marie-Christine&rft.date=2005-04-01&rft.volume=162&rft.issue=1&rft.spage=55&rft.epage=69&rft.pages=55-69&rft.issn=0377-2217&rft.eissn=1872-6860&rft.coden=EJORDT&rft_id=info:doi/10.1016/j.ejor.2003.10.037&rft_dat=%3Cproquest_hal_p%3E730586411%3C/proquest_hal_p%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=204133915&rft_id=info:pmid/&rft_els_id=S0377221703008348&rfr_iscdi=true |