{"id":"https://openalex.org/W2130307064","doi":"https://doi.org/10.1137/060654827","title":"New Approaches for Virtual Private Network Design","display_name":"New Approaches for Virtual Private Network Design","publication_year":2007,"publication_date":"2007-01-01","ids":{"openalex":"https://openalex.org/W2130307064","doi":"https://doi.org/10.1137/060654827","mag":"2130307064"},"language":"en","primary_location":{"id":"doi:10.1137/060654827","is_oa":false,"landing_page_url":"https://doi.org/10.1137/060654827","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://hdl.handle.net/2108/31163","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5000598657","display_name":"Friedrich Eisenbrand","orcid":"https://orcid.org/0000-0001-7928-1076"},"institutions":[{"id":"https://openalex.org/I200332995","display_name":"TU Dortmund University","ror":"https://ror.org/01k97gp34","country_code":"DE","type":"education","lineage":["https://openalex.org/I200332995"]},{"id":"https://openalex.org/I861853513","display_name":"Sapienza University of Rome","ror":"https://ror.org/02be6w209","country_code":"IT","type":"education","lineage":["https://openalex.org/I861853513"]}],"countries":["DE","IT"],"is_corresponding":false,"raw_author_name":"Friedrich Eisenbrand","raw_affiliation_strings":["Dipartimento di Informatica, Universit\u00e0 di Roma \"La Sapienza,\" Via Salaria 113, 00198 Roma, Italy","Fachbereich Informatik, Universit\u00e4t Dortmund, 44221 Dortmund, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dipartimento di Informatica, Universit\u00e0 di Roma \"La Sapienza,\" Via Salaria 113, 00198 Roma, Italy","institution_ids":["https://openalex.org/I861853513"]},{"raw_affiliation_string":"Fachbereich Informatik, Universit\u00e4t Dortmund, 44221 Dortmund, Germany","institution_ids":["https://openalex.org/I200332995"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5034276567","display_name":"Fabrizio Grandoni","orcid":"https://orcid.org/0000-0002-9676-4931"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Fabrizio Grandoni","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5009089187","display_name":"Gianpaolo Oriolo","orcid":"https://orcid.org/0000-0003-2028-7005"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Gianpaolo Oriolo","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5055693054","display_name":"Martin Skutella","orcid":"https://orcid.org/0000-0002-9814-1703"},"institutions":[{"id":"https://openalex.org/I116067653","display_name":"University of Rome Tor Vergata","ror":"https://ror.org/02p77k626","country_code":"IT","type":"education","lineage":["https://openalex.org/I116067653"]},{"id":"https://openalex.org/I200332995","display_name":"TU Dortmund University","ror":"https://ror.org/01k97gp34","country_code":"DE","type":"education","lineage":["https://openalex.org/I200332995"]}],"countries":["DE","IT"],"is_corresponding":false,"raw_author_name":"Martin Skutella","raw_affiliation_strings":["Dipartimento di Ingegneria dell'Impresa, Universit\u00e0 di Roma \"Tor Vergata,\" Via del Politecnico 1, 00165, Roma, Italy","Fachbereich Mathematik, Universit\u00e4t Dortmund, 44221 Dortmund, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dipartimento di Ingegneria dell'Impresa, Universit\u00e0 di Roma \"Tor Vergata,\" Via del Politecnico 1, 00165, Roma, Italy","institution_ids":["https://openalex.org/I116067653"]},{"raw_affiliation_string":"Fachbereich Mathematik, Universit\u00e4t Dortmund, 44221 Dortmund, Germany","institution_ids":["https://openalex.org/I200332995"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.9761,"has_fulltext":false,"cited_by_count":24,"citation_normalized_percentile":{"value":0.93718863,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"37","issue":"3","first_page":"706","last_page":"721"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12288","display_name":"Optimization and Search Problems","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9980999827384949,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.6494759321212769},{"id":"https://openalex.org/keywords/network-planning-and-design","display_name":"Network planning and design","score":0.6057958602905273},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6033253073692322},{"id":"https://openalex.org/keywords/approximation-algorithm","display_name":"Approximation algorithm","score":0.5649902820587158},{"id":"https://openalex.org/keywords/maximum-flow-problem","display_name":"Maximum flow problem","score":0.4811221659183502},{"id":"https://openalex.org/keywords/routing","display_name":"Routing (electronic design automation)","score":0.4576191008090973},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.4514840245246887},{"id":"https://openalex.org/keywords/node","display_name":"Node (physics)","score":0.4300227761268616},{"id":"https://openalex.org/keywords/network-topology","display_name":"Network topology","score":0.4181002676486969},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.41326162219047546},{"id":"https://openalex.org/keywords/flow-network","display_name":"Flow network","score":0.4104973375797272},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.3978146016597748},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.33591610193252563},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.32981106638908386},{"id":"https://openalex.org/keywords/computer-network","display_name":"Computer network","score":0.1449994444847107}],"concepts":[{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.6494759321212769},{"id":"https://openalex.org/C114563136","wikidata":"https://www.wikidata.org/wiki/Q19725982","display_name":"Network planning and design","level":2,"score":0.6057958602905273},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6033253073692322},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.5649902820587158},{"id":"https://openalex.org/C157469704","wikidata":"https://www.wikidata.org/wiki/Q2585642","display_name":"Maximum flow problem","level":2,"score":0.4811221659183502},{"id":"https://openalex.org/C74172769","wikidata":"https://www.wikidata.org/wiki/Q1446839","display_name":"Routing (electronic design automation)","level":2,"score":0.4576191008090973},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.4514840245246887},{"id":"https://openalex.org/C62611344","wikidata":"https://www.wikidata.org/wiki/Q1062658","display_name":"Node (physics)","level":2,"score":0.4300227761268616},{"id":"https://openalex.org/C199845137","wikidata":"https://www.wikidata.org/wiki/Q145490","display_name":"Network topology","level":2,"score":0.4181002676486969},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.41326162219047546},{"id":"https://openalex.org/C114809511","wikidata":"https://www.wikidata.org/wiki/Q1412924","display_name":"Flow network","level":2,"score":0.4104973375797272},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3978146016597748},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.33591610193252563},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.32981106638908386},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.1449994444847107},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C66938386","wikidata":"https://www.wikidata.org/wiki/Q633538","display_name":"Structural engineering","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/060654827","is_oa":false,"landing_page_url":"https://doi.org/10.1137/060654827","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Computing","raw_type":"journal-article"},{"id":"pmh:oai:art.torvergata.it:2108/31163","is_oa":true,"landing_page_url":"http://hdl.handle.net/2108/31163","pdf_url":null,"source":{"id":"https://openalex.org/S4306400993","display_name":"Cineca Institutional Research Information System (Tor Vergata University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I116067653","host_organization_name":"University of Rome Tor Vergata","host_organization_lineage":["https://openalex.org/I116067653"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:infoscience.epfl.ch:121643","is_oa":true,"landing_page_url":"http://infoscience.epfl.ch/record/121643","pdf_url":null,"source":{"id":"https://openalex.org/S4306400487","display_name":"Infoscience (Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"}],"best_oa_location":{"id":"pmh:oai:art.torvergata.it:2108/31163","is_oa":true,"landing_page_url":"http://hdl.handle.net/2108/31163","pdf_url":null,"source":{"id":"https://openalex.org/S4306400993","display_name":"Cineca Institutional Research Information System (Tor Vergata University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I116067653","host_organization_name":"University of Rome Tor Vergata","host_organization_lineage":["https://openalex.org/I116067653"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[{"display_name":"Industry, innovation and infrastructure","score":0.4399999976158142,"id":"https://metadata.un.org/sdg/9"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":6,"referenced_works":["https://openalex.org/W1967964204","https://openalex.org/W1975290397","https://openalex.org/W1980257116","https://openalex.org/W2003160050","https://openalex.org/W2068811470","https://openalex.org/W2150815458"],"related_works":["https://openalex.org/W2375873432","https://openalex.org/W4206915070","https://openalex.org/W2531764854","https://openalex.org/W3161514703","https://openalex.org/W2141299097","https://openalex.org/W1851375266","https://openalex.org/W2610002854","https://openalex.org/W3141113327","https://openalex.org/W4206407367","https://openalex.org/W3035974271"],"abstract_inverted_index":{"Virtual":[0],"private":[1,216],"network":[2,14,75,217,244],"design":[3,76],"is":[4,44,86,98,102,109,220,276,294,311,329],"the":[5,23,27,40,70,83,89,92,137,158,186,188,203,225,249,290,297,307,317,323,330],"following":[6],"NP-hard":[7],"problem.":[8],"We":[9,173],"are":[10,118],"given":[11],"a":[12,17,32,129,149,175,221,267,273,334],"communication":[13],"represented":[15],"as":[16,119,272],"weighted":[18],"graph":[19],"with":[20,202,302],"thresholds":[21],"on":[22,136,168,252],"nodes":[24,60],"which":[25,97,153],"represent":[26],"amount":[28,94],"of":[29,59,95,115,139,198,212,224,248,254,292,309,325],"flow":[30,96,125],"that":[31,62,91,278,333],"node":[33],"can":[34,66,283],"send":[35],"to":[36,45,52,182,320,342],"and":[37,51,107,131,162,235,239],"receive":[38],"from":[39,185,337],"network.":[41],"The":[42,112],"task":[43],"reserve":[46],"capacities":[47],"at":[48],"minimum":[49],"cost":[50,138],"specify":[53],"paths":[54],"between":[55,100],"every":[56],"ordered":[57],"pair":[58],"such":[61],"all":[63],"valid":[64],"traffic-matrices":[65],"be":[67,284],"routed":[68],"along":[69],"corresponding":[71],"paths.":[72],"Recently,":[73],"this":[74,116,144,328],"problem":[77],"has":[78,154],"received":[79],"considerable":[80,222],"attention":[81],"in":[82,105,157,246,286],"literature.":[84],"It":[85,275],"motivated":[87],"by":[88],"fact":[90],"exact":[93,304,338],"exchanged":[99],"terminals":[101,293,310],"not":[103,192],"known":[104,228,277],"advance":[106],"prediction":[108],"often":[110],"elusive.":[111],"main":[113],"contributions":[114],"paper":[117],"follows:":[120],"(1)":[121],"Using":[122],"Hu's":[123],"2-commodity":[124],"theorem,":[126],"we":[127,147,314],"provide":[128,163],"new":[130,176,200],"considerably":[132],"stronger":[133],"lower":[134,145],"bound":[135,146,167],"an":[140,164,208,279,303,343],"optimum":[141,280],"solution.":[142],"With":[143],"reanalyze":[148],"simple":[150,204],"routing":[151,205],"scheme":[152,206],"been":[155],"described":[156],"literature":[159],"many":[160],"times,":[161],"improved":[165,344],"upper":[166],"its":[169],"approximation":[170,178,241,270,318,346],"ratio.":[171],"(2)":[172],"present":[174],"randomized":[177],"algorithm.":[179,347],"In":[180],"contrast":[181],"earlier":[183],"approaches":[184],"literature,":[187],"resulting":[189],"solution":[190],"does":[191],"have":[193],"tree":[194,269,282,300],"structure.":[195],"A":[196],"combination":[197],"our":[199,326],"algorithm":[201,265,271],"yields":[207],"expected":[209],"performance":[210],"ratio":[211,319],"$3.79$":[213],"for":[214,243],"virtual":[215],"design.":[218],"This":[219],"improvement":[223],"previously":[226],"best":[227,324],"$5.55$-approximation":[229],"result":[230,336],"[A.":[231],"Gupta,":[232],"A.":[233],"Kumar,":[234],"T.":[236],"Roughgarden,":[237],"Simpler":[238],"better":[240],"algorithms":[242,340],"design,":[245],"Proceedings":[247],"ACM":[250],"Symposium":[251],"Theory":[253],"Computing,":[255],"ACM,":[256],"New":[257],"York,":[258],"2003,":[259],"pp.":[260],"365\u2013372].":[261],"(3)":[262],"Our":[263],"VPND":[264],"uses":[266],"Steiner":[268,281,299],"subroutine.":[274],"computed":[285],"polynomial":[287],"time":[288,332],"if":[289],"number":[291,308],"logarithmic.":[295],"Replacing":[296],"approximate":[298],"computation":[301],"one":[305],"whenever":[306],"sufficiently":[312],"small,":[313],"finally":[315],"reduce":[316],"$3.55$.":[321],"To":[322],"knowledge,":[327],"first":[331],"nontrivial":[335],"(exponential)":[339],"leads":[341],"polynomial-time":[345]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":2}],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2025-10-10T00:00:00"}
