Exact Crossing Minimization
The crossing number of a graph is the minimum number of edge crossings in any drawing of the graph into the plane. This very basic property has been studied extensively in the literature from a theoretic point of view and many bounds exist for a variety of graph classes. In this paper, we present th...
Gespeichert in:
| Hauptverfasser: | , , , , , |
|---|---|
| Format: | Buchkapitel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 48 |
|---|---|
| container_issue | |
| container_start_page | 37 |
| container_title | |
| container_volume | |
| creator | Buchheim, Christoph Ebner, Dietmar Jünger, Michael Klau, Gunnar W. Mutzel, Petra Weiskircher, René |
| description | The crossing number of a graph is the minimum number of edge crossings in any drawing of the graph into the plane. This very basic property has been studied extensively in the literature from a theoretic point of view and many bounds exist for a variety of graph classes. In this paper, we present the first algorithm able to compute the crossing number of general sparse graphs of moderate size and present computational results on a popular benchmark set of graphs. The approach uses a new integer linear programming formulation of the problem combined with strong heuristics and problem reduction techniques. This enables us to compute the crossing number for 91 percent of all graphs on up to 40 nodes in the benchmark set within a time limit of five minutes per graph. |
| doi_str_mv | 10.1007/11618058_4 |
| format | Book Chapter |
| fullrecord | <record><control><sourceid>pascalfrancis_sprin</sourceid><recordid>TN_cdi_pascalfrancis_primary_19937711</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>19937711</sourcerecordid><originalsourceid>FETCH-LOGICAL-p254t-4016a11c1e2afc9ab225dfe78564ff35c36356b35df8901e2a1f8a83dbc3bbaa3</originalsourceid><addsrcrecordid>eNpFkLtOw0AQRZeXhAluaGnSINEYdjz7LJEVHlIQDdSr8cYbLSS25XUBfH0cBYnbjHTP0RSXsSvgd8C5vgdQYLg0ThyxC5SCIyil4ZhlE4ACUdgTllttDkyUUp-yjCMvC6sFnrM8pU8-BUFbbTN2vfgmP86roUsptuv5a2zjNv7SGLv2kp0F2qQm_7sz9vG4eK-ei-Xb00v1sCz6UoqxEBwUAXhoSgreUl2WchUabaQSIaD0qFCqGqfSWL63IBgyuKo91jURztjN4W9PydMmDNT6mFw_xC0NPw6sRa0BJu_24KUJtetmcHXXfSUH3O3Hcf_j4A5GTU-7</addsrcrecordid><sourcetype>Index Database</sourcetype><iscdi>true</iscdi><recordtype>book_chapter</recordtype></control><display><type>book_chapter</type><title>Exact Crossing Minimization</title><source>Springer Books</source><creator>Buchheim, Christoph ; Ebner, Dietmar ; Jünger, Michael ; Klau, Gunnar W. ; Mutzel, Petra ; Weiskircher, René</creator><contributor>Nikolov, Nikola S. ; Healy, Patrick</contributor><creatorcontrib>Buchheim, Christoph ; Ebner, Dietmar ; Jünger, Michael ; Klau, Gunnar W. ; Mutzel, Petra ; Weiskircher, René ; Nikolov, Nikola S. ; Healy, Patrick</creatorcontrib><description>The crossing number of a graph is the minimum number of edge crossings in any drawing of the graph into the plane. This very basic property has been studied extensively in the literature from a theoretic point of view and many bounds exist for a variety of graph classes. In this paper, we present the first algorithm able to compute the crossing number of general sparse graphs of moderate size and present computational results on a popular benchmark set of graphs. The approach uses a new integer linear programming formulation of the problem combined with strong heuristics and problem reduction techniques. This enables us to compute the crossing number for 91 percent of all graphs on up to 40 nodes in the benchmark set within a time limit of five minutes per graph.</description><identifier>ISSN: 0302-9743</identifier><identifier>ISBN: 9783540314257</identifier><identifier>ISBN: 3540314253</identifier><identifier>EISSN: 1611-3349</identifier><identifier>EISBN: 3540316671</identifier><identifier>EISBN: 9783540316671</identifier><identifier>DOI: 10.1007/11618058_4</identifier><language>eng</language><publisher>Berlin, Heidelberg: Springer Berlin Heidelberg</publisher><subject>Applied sciences ; Complete Bipartite Graph ; Computer science; control theory; systems ; Dummy Node ; Edge Crossing ; Exact sciences and technology ; Information retrieval. Graph ; Integer Linear Programming Formulation ; Layout Problem ; Theoretical computing</subject><ispartof>Graph Drawing, 2006, p.37-48</ispartof><rights>Springer-Verlag Berlin Heidelberg 2006</rights><rights>2008 INIST-CNRS</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><relation>Lecture Notes in Computer Science</relation></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/11618058_4$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/11618058_4$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>309,310,775,776,780,785,786,789,4035,4036,27904,38234,41421,42490</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=19937711$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><contributor>Nikolov, Nikola S.</contributor><contributor>Healy, Patrick</contributor><creatorcontrib>Buchheim, Christoph</creatorcontrib><creatorcontrib>Ebner, Dietmar</creatorcontrib><creatorcontrib>Jünger, Michael</creatorcontrib><creatorcontrib>Klau, Gunnar W.</creatorcontrib><creatorcontrib>Mutzel, Petra</creatorcontrib><creatorcontrib>Weiskircher, René</creatorcontrib><title>Exact Crossing Minimization</title><title>Graph Drawing</title><description>The crossing number of a graph is the minimum number of edge crossings in any drawing of the graph into the plane. This very basic property has been studied extensively in the literature from a theoretic point of view and many bounds exist for a variety of graph classes. In this paper, we present the first algorithm able to compute the crossing number of general sparse graphs of moderate size and present computational results on a popular benchmark set of graphs. The approach uses a new integer linear programming formulation of the problem combined with strong heuristics and problem reduction techniques. This enables us to compute the crossing number for 91 percent of all graphs on up to 40 nodes in the benchmark set within a time limit of five minutes per graph.</description><subject>Applied sciences</subject><subject>Complete Bipartite Graph</subject><subject>Computer science; control theory; systems</subject><subject>Dummy Node</subject><subject>Edge Crossing</subject><subject>Exact sciences and technology</subject><subject>Information retrieval. Graph</subject><subject>Integer Linear Programming Formulation</subject><subject>Layout Problem</subject><subject>Theoretical computing</subject><issn>0302-9743</issn><issn>1611-3349</issn><isbn>9783540314257</isbn><isbn>3540314253</isbn><isbn>3540316671</isbn><isbn>9783540316671</isbn><fulltext>true</fulltext><rsrctype>book_chapter</rsrctype><creationdate>2006</creationdate><recordtype>book_chapter</recordtype><recordid>eNpFkLtOw0AQRZeXhAluaGnSINEYdjz7LJEVHlIQDdSr8cYbLSS25XUBfH0cBYnbjHTP0RSXsSvgd8C5vgdQYLg0ThyxC5SCIyil4ZhlE4ACUdgTllttDkyUUp-yjCMvC6sFnrM8pU8-BUFbbTN2vfgmP86roUsptuv5a2zjNv7SGLv2kp0F2qQm_7sz9vG4eK-ei-Xb00v1sCz6UoqxEBwUAXhoSgreUl2WchUabaQSIaD0qFCqGqfSWL63IBgyuKo91jURztjN4W9PydMmDNT6mFw_xC0NPw6sRa0BJu_24KUJtetmcHXXfSUH3O3Hcf_j4A5GTU-7</recordid><startdate>2006</startdate><enddate>2006</enddate><creator>Buchheim, Christoph</creator><creator>Ebner, Dietmar</creator><creator>Jünger, Michael</creator><creator>Klau, Gunnar W.</creator><creator>Mutzel, Petra</creator><creator>Weiskircher, René</creator><general>Springer Berlin Heidelberg</general><general>Springer</general><scope>IQODW</scope></search><sort><creationdate>2006</creationdate><title>Exact Crossing Minimization</title><author>Buchheim, Christoph ; Ebner, Dietmar ; Jünger, Michael ; Klau, Gunnar W. ; Mutzel, Petra ; Weiskircher, René</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-p254t-4016a11c1e2afc9ab225dfe78564ff35c36356b35df8901e2a1f8a83dbc3bbaa3</frbrgroupid><rsrctype>book_chapters</rsrctype><prefilter>book_chapters</prefilter><language>eng</language><creationdate>2006</creationdate><topic>Applied sciences</topic><topic>Complete Bipartite Graph</topic><topic>Computer science; control theory; systems</topic><topic>Dummy Node</topic><topic>Edge Crossing</topic><topic>Exact sciences and technology</topic><topic>Information retrieval. Graph</topic><topic>Integer Linear Programming Formulation</topic><topic>Layout Problem</topic><topic>Theoretical computing</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Buchheim, Christoph</creatorcontrib><creatorcontrib>Ebner, Dietmar</creatorcontrib><creatorcontrib>Jünger, Michael</creatorcontrib><creatorcontrib>Klau, Gunnar W.</creatorcontrib><creatorcontrib>Mutzel, Petra</creatorcontrib><creatorcontrib>Weiskircher, René</creatorcontrib><collection>Pascal-Francis</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Buchheim, Christoph</au><au>Ebner, Dietmar</au><au>Jünger, Michael</au><au>Klau, Gunnar W.</au><au>Mutzel, Petra</au><au>Weiskircher, René</au><au>Nikolov, Nikola S.</au><au>Healy, Patrick</au><format>book</format><genre>bookitem</genre><ristype>CHAP</ristype><atitle>Exact Crossing Minimization</atitle><btitle>Graph Drawing</btitle><seriestitle>Lecture Notes in Computer Science</seriestitle><date>2006</date><risdate>2006</risdate><spage>37</spage><epage>48</epage><pages>37-48</pages><issn>0302-9743</issn><eissn>1611-3349</eissn><isbn>9783540314257</isbn><isbn>3540314253</isbn><eisbn>3540316671</eisbn><eisbn>9783540316671</eisbn><abstract>The crossing number of a graph is the minimum number of edge crossings in any drawing of the graph into the plane. This very basic property has been studied extensively in the literature from a theoretic point of view and many bounds exist for a variety of graph classes. In this paper, we present the first algorithm able to compute the crossing number of general sparse graphs of moderate size and present computational results on a popular benchmark set of graphs. The approach uses a new integer linear programming formulation of the problem combined with strong heuristics and problem reduction techniques. This enables us to compute the crossing number for 91 percent of all graphs on up to 40 nodes in the benchmark set within a time limit of five minutes per graph.</abstract><cop>Berlin, Heidelberg</cop><pub>Springer Berlin Heidelberg</pub><doi>10.1007/11618058_4</doi><tpages>12</tpages><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0302-9743 |
| ispartof | Graph Drawing, 2006, p.37-48 |
| issn | 0302-9743 1611-3349 |
| language | eng |
| recordid | cdi_pascalfrancis_primary_19937711 |
| source | Springer Books |
| subjects | Applied sciences Complete Bipartite Graph Computer science control theory systems Dummy Node Edge Crossing Exact sciences and technology Information retrieval. Graph Integer Linear Programming Formulation Layout Problem Theoretical computing |
| title | Exact Crossing Minimization |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-25T06%3A45%3A21IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-pascalfrancis_sprin&rft_val_fmt=info:ofi/fmt:kev:mtx:book&rft.genre=bookitem&rft.atitle=Exact%20Crossing%20Minimization&rft.btitle=Graph%20Drawing&rft.au=Buchheim,%20Christoph&rft.date=2006&rft.spage=37&rft.epage=48&rft.pages=37-48&rft.issn=0302-9743&rft.eissn=1611-3349&rft.isbn=9783540314257&rft.isbn_list=3540314253&rft_id=info:doi/10.1007/11618058_4&rft_dat=%3Cpascalfrancis_sprin%3E19937711%3C/pascalfrancis_sprin%3E%3Curl%3E%3C/url%3E&rft.eisbn=3540316671&rft.eisbn_list=9783540316671&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_id=info:pmid/&rfr_iscdi=true |