Center problems with pos/neg weights on trees

Center problems with pos/neg weights on trees

In a network with positive and negative vertex weights the pos/neg 1-center problem asks to minimize a linear combination of the maximum weighted distances of the center to the vertices with positive weights and to the vertices with negative weights, respectively. We show that in a network with n ve...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:European journal of operational research 2003-03, Vol.145 (3), p.483-495
Hauptverfasser: Burkard, R.E., Dollani, Helidon
Format: Artikel
Sprache:eng
Schlagworte:
Center problem
Decision trees
Graphs
Linear programming
Location analysis
Location problem
Obnoxious facilities
Studies
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
container_end_page 495
container_issue 3
container_start_page 483
container_title European journal of operational research
container_volume 145
creator Burkard, R.E.
Dollani, Helidon
description In a network with positive and negative vertex weights the pos/neg 1-center problem asks to minimize a linear combination of the maximum weighted distances of the center to the vertices with positive weights and to the vertices with negative weights, respectively. We show that in a network with n vertices and m edges the pos/neg 1-center problem can be solved in O( mnlog n) time. In trees a better complexity can be achieved. In the case of a path or of a star graph this problem can be solved in linear time. Further this problem is studied for a cactus with vertex weights 1 and −1. Moreover, an algorithm for the discrete anti- p-center problem on a tree with the improved time complexity O( nlog 2 n) is given. Finally, the pos/neg discrete p-center on a tree is treated and solved by an algorithm of time complexity O( n 2log n).
doi_str_mv 10.1016/S0377-2217(02)00211-4
format Article
fullrecord <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_204196732</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><els_id>S0377221702002114</els_id><sourcerecordid>283883381</sourcerecordid><originalsourceid>FETCH-LOGICAL-c402t-7a2e8667cc5c110ee0c19af3d388ea0155866223cbab8fe0b079972cc1abf3a73</originalsourceid><addsrcrecordid>eNqFUMtOwzAQtBBIlMInIEWc4BC6tpM4OSFU8RKVOADnleNu2lRtEmy3Vf8et0G9Ymk8B8_Mroexaw73HHg2-gSpVCwEV7cg7gAE53FywgY8VyLO8gxO2eAoOWcXzi0AgKc8HbB4TI0nG3W2LZe0ctG29vOoa92ooVm0pXo29y5qm8hbInfJziq9dHT1x0P2_fz0NX6NJx8vb-PHSWwSED5WWlCeZcqY1HAORGB4oSs5lXlOOkxOw6sQ0pS6zCuCElRRKGEM12UltZJDdtPnhrV-1uQ8Ltq1bcJIFJDwIlNSBFHai4xtnbNUYWfrlbY75ID7YvBQDO5_jSDwUAwmwffe-yx1ZI4mCmfRWnK4Qal5koZ7FyAAZKA6YM9dQJJLTIoU534V0h76NAp9bGqy6ExNjaFpbcl4nLb1P_v8Ai9egjo</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>204196732</pqid></control><display><type>article</type><title>Center problems with pos/neg weights on trees</title><source>RePEc</source><source>ScienceDirect Journals (5 years ago - present)</source><creator>Burkard, R.E. ; Dollani, Helidon</creator><creatorcontrib>Burkard, R.E. ; Dollani, Helidon</creatorcontrib><description>In a network with positive and negative vertex weights the pos/neg 1-center problem asks to minimize a linear combination of the maximum weighted distances of the center to the vertices with positive weights and to the vertices with negative weights, respectively. We show that in a network with n vertices and m edges the pos/neg 1-center problem can be solved in O( mnlog n) time. In trees a better complexity can be achieved. In the case of a path or of a star graph this problem can be solved in linear time. Further this problem is studied for a cactus with vertex weights 1 and −1. Moreover, an algorithm for the discrete anti- p-center problem on a tree with the improved time complexity O( nlog 2 n) is given. Finally, the pos/neg discrete p-center on a tree is treated and solved by an algorithm of time complexity O( n 2log n).</description><identifier>ISSN: 0377-2217</identifier><identifier>EISSN: 1872-6860</identifier><identifier>DOI: 10.1016/S0377-2217(02)00211-4</identifier><identifier>CODEN: EJORDT</identifier><language>eng</language><publisher>Amsterdam: Elsevier B.V</publisher><subject>Center problem ; Decision trees ; Graphs ; Linear programming ; Location analysis ; Location problem ; Obnoxious facilities ; Studies</subject><ispartof>European journal of operational research, 2003-03, Vol.145 (3), p.483-495</ispartof><rights>2002</rights><rights>Copyright Elsevier Sequoia S.A. Mar 16, 2003</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c402t-7a2e8667cc5c110ee0c19af3d388ea0155866223cbab8fe0b079972cc1abf3a73</citedby><cites>FETCH-LOGICAL-c402t-7a2e8667cc5c110ee0c19af3d388ea0155866223cbab8fe0b079972cc1abf3a73</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://dx.doi.org/10.1016/S0377-2217(02)00211-4$$EHTML$$P50$$Gelsevier$$H</linktohtml><link.rule.ids>314,780,784,3549,4007,27923,27924,45994</link.rule.ids><backlink>$$Uhttp://econpapers.repec.org/article/eeeejores/v_3a145_3ay_3a2003_3ai_3a3_3ap_3a483-495.htm$$DView record in RePEc$$Hfree_for_read</backlink></links><search><creatorcontrib>Burkard, R.E.</creatorcontrib><creatorcontrib>Dollani, Helidon</creatorcontrib><title>Center problems with pos/neg weights on trees</title><title>European journal of operational research</title><description>In a network with positive and negative vertex weights the pos/neg 1-center problem asks to minimize a linear combination of the maximum weighted distances of the center to the vertices with positive weights and to the vertices with negative weights, respectively. We show that in a network with n vertices and m edges the pos/neg 1-center problem can be solved in O( mnlog n) time. In trees a better complexity can be achieved. In the case of a path or of a star graph this problem can be solved in linear time. Further this problem is studied for a cactus with vertex weights 1 and −1. Moreover, an algorithm for the discrete anti- p-center problem on a tree with the improved time complexity O( nlog 2 n) is given. Finally, the pos/neg discrete p-center on a tree is treated and solved by an algorithm of time complexity O( n 2log n).</description><subject>Center problem</subject><subject>Decision trees</subject><subject>Graphs</subject><subject>Linear programming</subject><subject>Location analysis</subject><subject>Location problem</subject><subject>Obnoxious facilities</subject><subject>Studies</subject><issn>0377-2217</issn><issn>1872-6860</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2003</creationdate><recordtype>article</recordtype><sourceid>X2L</sourceid><recordid>eNqFUMtOwzAQtBBIlMInIEWc4BC6tpM4OSFU8RKVOADnleNu2lRtEmy3Vf8et0G9Ymk8B8_Mroexaw73HHg2-gSpVCwEV7cg7gAE53FywgY8VyLO8gxO2eAoOWcXzi0AgKc8HbB4TI0nG3W2LZe0ctG29vOoa92ooVm0pXo29y5qm8hbInfJziq9dHT1x0P2_fz0NX6NJx8vb-PHSWwSED5WWlCeZcqY1HAORGB4oSs5lXlOOkxOw6sQ0pS6zCuCElRRKGEM12UltZJDdtPnhrV-1uQ8Ltq1bcJIFJDwIlNSBFHai4xtnbNUYWfrlbY75ID7YvBQDO5_jSDwUAwmwffe-yx1ZI4mCmfRWnK4Qal5koZ7FyAAZKA6YM9dQJJLTIoU534V0h76NAp9bGqy6ExNjaFpbcl4nLb1P_v8Ai9egjo</recordid><startdate>20030316</startdate><enddate>20030316</enddate><creator>Burkard, R.E.</creator><creator>Dollani, Helidon</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></search><sort><creationdate>20030316</creationdate><title>Center problems with pos/neg weights on trees</title><author>Burkard, R.E. ; Dollani, Helidon</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c402t-7a2e8667cc5c110ee0c19af3d388ea0155866223cbab8fe0b079972cc1abf3a73</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2003</creationdate><topic>Center problem</topic><topic>Decision trees</topic><topic>Graphs</topic><topic>Linear programming</topic><topic>Location analysis</topic><topic>Location problem</topic><topic>Obnoxious facilities</topic><topic>Studies</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Burkard, R.E.</creatorcontrib><creatorcontrib>Dollani, Helidon</creatorcontrib><collection>RePEc IDEAS</collection><collection>RePEc</collection><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical &amp; 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><jtitle>European journal of operational research</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Burkard, R.E.</au><au>Dollani, Helidon</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Center problems with pos/neg weights on trees</atitle><jtitle>European journal of operational research</jtitle><date>2003-03-16</date><risdate>2003</risdate><volume>145</volume><issue>3</issue><spage>483</spage><epage>495</epage><pages>483-495</pages><issn>0377-2217</issn><eissn>1872-6860</eissn><coden>EJORDT</coden><abstract>In a network with positive and negative vertex weights the pos/neg 1-center problem asks to minimize a linear combination of the maximum weighted distances of the center to the vertices with positive weights and to the vertices with negative weights, respectively. We show that in a network with n vertices and m edges the pos/neg 1-center problem can be solved in O( mnlog n) time. In trees a better complexity can be achieved. In the case of a path or of a star graph this problem can be solved in linear time. Further this problem is studied for a cactus with vertex weights 1 and −1. Moreover, an algorithm for the discrete anti- p-center problem on a tree with the improved time complexity O( nlog 2 n) is given. Finally, the pos/neg discrete p-center on a tree is treated and solved by an algorithm of time complexity O( n 2log n).</abstract><cop>Amsterdam</cop><pub>Elsevier B.V</pub><doi>10.1016/S0377-2217(02)00211-4</doi><tpages>13</tpages></addata></record>
fulltext fulltext
identifier ISSN: 0377-2217
ispartof European journal of operational research, 2003-03, Vol.145 (3), p.483-495
issn 0377-2217
1872-6860
language eng
recordid cdi_proquest_journals_204196732
source RePEc; ScienceDirect Journals (5 years ago - present)
subjects Center problem
Decision trees
Graphs
Linear programming
Location analysis
Location problem
Obnoxious facilities
Studies
title Center problems with pos/neg weights on trees
url https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-08T21%3A24%3A37IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Center%20problems%20with%20pos/neg%20weights%20on%20trees&rft.jtitle=European%20journal%20of%20operational%20research&rft.au=Burkard,%20R.E.&rft.date=2003-03-16&rft.volume=145&rft.issue=3&rft.spage=483&rft.epage=495&rft.pages=483-495&rft.issn=0377-2217&rft.eissn=1872-6860&rft.coden=EJORDT&rft_id=info:doi/10.1016/S0377-2217(02)00211-4&rft_dat=%3Cproquest_cross%3E283883381%3C/proquest_cross%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=204196732&rft_id=info:pmid/&rft_els_id=S0377221702002114&rfr_iscdi=true