{"id":"https://openalex.org/W1999867351","doi":"https://doi.org/10.1145/1060590.1060618","title":"Multicommodity flow, well-linked terminals, and routing problems","display_name":"Multicommodity flow, well-linked terminals, and routing problems","publication_year":2005,"publication_date":"2005-05-22","ids":{"openalex":"https://openalex.org/W1999867351","doi":"https://doi.org/10.1145/1060590.1060618","mag":"1999867351"},"language":"en","primary_location":{"id":"doi:10.1145/1060590.1060618","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1060590.1060618","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the thirty-seventh annual ACM symposium on Theory of computing","raw_type":"proceedings-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5036503505","display_name":"Chandra Chekuri","orcid":"https://orcid.org/0000-0003-3035-1699"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Chandra Chekuri","raw_affiliation_strings":["Lucent Bell Labs, Murray Hill, NJ"],"affiliations":[{"raw_affiliation_string":"Lucent Bell Labs, Murray Hill, NJ","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5039619350","display_name":"Sanjeev Khanna","orcid":"https://orcid.org/0009-0000-2601-1689"},"institutions":[{"id":"https://openalex.org/I79576946","display_name":"University of Pennsylvania","ror":"https://ror.org/00b30xv10","country_code":"US","type":"education","lineage":["https://openalex.org/I79576946"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Sanjeev Khanna","raw_affiliation_strings":["University of Pennsylvania, Philadelphia, PA"],"affiliations":[{"raw_affiliation_string":"University of Pennsylvania, Philadelphia, PA","institution_ids":["https://openalex.org/I79576946"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5044801840","display_name":"F. Bruce Shepherd","orcid":"https://orcid.org/0000-0003-1972-1396"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"F. Bruce Shepherd","raw_affiliation_strings":["Lucent Bell Labs, Murray Hill, NJ"],"affiliations":[{"raw_affiliation_string":"Lucent Bell Labs, Murray Hill, NJ","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5036503505"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":6.3965,"has_fulltext":false,"cited_by_count":96,"citation_normalized_percentile":{"value":0.97307028,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":null,"issue":null,"first_page":"183","last_page":"192"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9993000030517578,"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":0.9993000030517578,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.998199999332428,"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/T10567","display_name":"Vehicle Routing Optimization Methods","score":0.9976999759674072,"subfield":{"id":"https://openalex.org/subfields/2209","display_name":"Industrial and Manufacturing Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6285988688468933},{"id":"https://openalex.org/keywords/multi-commodity-flow-problem","display_name":"Multi-commodity flow problem","score":0.6139971613883972},{"id":"https://openalex.org/keywords/node","display_name":"Node (physics)","score":0.5115712285041809},{"id":"https://openalex.org/keywords/routing","display_name":"Routing (electronic design automation)","score":0.4824712574481964},{"id":"https://openalex.org/keywords/logarithm","display_name":"Logarithm","score":0.4594595730304718},{"id":"https://openalex.org/keywords/disjoint-sets","display_name":"Disjoint sets","score":0.44188210368156433},{"id":"https://openalex.org/keywords/equal-cost-multi-path-routing","display_name":"Equal-cost multi-path routing","score":0.436275839805603},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4132331907749176},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4120931625366211},{"id":"https://openalex.org/keywords/flow-network","display_name":"Flow network","score":0.3606625497341156},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.349414587020874},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3411095142364502},{"id":"https://openalex.org/keywords/routing-table","display_name":"Routing table","score":0.3388546109199524},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.28888246417045593},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.2261611521244049},{"id":"https://openalex.org/keywords/computer-network","display_name":"Computer network","score":0.16473376750946045},{"id":"https://openalex.org/keywords/routing-protocol","display_name":"Routing protocol","score":0.16253456473350525}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6285988688468933},{"id":"https://openalex.org/C170334043","wikidata":"https://www.wikidata.org/wiki/Q6934437","display_name":"Multi-commodity flow problem","level":3,"score":0.6139971613883972},{"id":"https://openalex.org/C62611344","wikidata":"https://www.wikidata.org/wiki/Q1062658","display_name":"Node (physics)","level":2,"score":0.5115712285041809},{"id":"https://openalex.org/C74172769","wikidata":"https://www.wikidata.org/wiki/Q1446839","display_name":"Routing (electronic design automation)","level":2,"score":0.4824712574481964},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.4594595730304718},{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.44188210368156433},{"id":"https://openalex.org/C115443555","wikidata":"https://www.wikidata.org/wiki/Q5367790","display_name":"Equal-cost multi-path routing","level":5,"score":0.436275839805603},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4132331907749176},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4120931625366211},{"id":"https://openalex.org/C114809511","wikidata":"https://www.wikidata.org/wiki/Q1412924","display_name":"Flow network","level":2,"score":0.3606625497341156},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.349414587020874},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3411095142364502},{"id":"https://openalex.org/C184896649","wikidata":"https://www.wikidata.org/wiki/Q290066","display_name":"Routing table","level":4,"score":0.3388546109199524},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.28888246417045593},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2261611521244049},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.16473376750946045},{"id":"https://openalex.org/C104954878","wikidata":"https://www.wikidata.org/wiki/Q1648707","display_name":"Routing protocol","level":3,"score":0.16253456473350525},{"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/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/1060590.1060618","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1060590.1060618","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the thirty-seventh annual ACM symposium on Theory of computing","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":53,"referenced_works":["https://openalex.org/W1524585687","https://openalex.org/W1560551754","https://openalex.org/W1589172288","https://openalex.org/W1591562949","https://openalex.org/W1921591048","https://openalex.org/W1974115975","https://openalex.org/W1983058179","https://openalex.org/W1989234747","https://openalex.org/W1996073274","https://openalex.org/W2003160050","https://openalex.org/W2005509629","https://openalex.org/W2011039300","https://openalex.org/W2011764853","https://openalex.org/W2012687409","https://openalex.org/W2012969943","https://openalex.org/W2017713020","https://openalex.org/W2019062750","https://openalex.org/W2019137761","https://openalex.org/W2020066367","https://openalex.org/W2020632401","https://openalex.org/W2022191808","https://openalex.org/W2024654848","https://openalex.org/W2025470209","https://openalex.org/W2034269606","https://openalex.org/W2042276676","https://openalex.org/W2042899161","https://openalex.org/W2047099957","https://openalex.org/W2047871605","https://openalex.org/W2049609719","https://openalex.org/W2058821164","https://openalex.org/W2060632898","https://openalex.org/W2062948942","https://openalex.org/W2074762809","https://openalex.org/W2081008200","https://openalex.org/W2085348754","https://openalex.org/W2100699015","https://openalex.org/W2107881198","https://openalex.org/W2119862441","https://openalex.org/W2121839513","https://openalex.org/W2127114399","https://openalex.org/W2135424293","https://openalex.org/W2141793995","https://openalex.org/W2145818650","https://openalex.org/W2150148016","https://openalex.org/W2152195131","https://openalex.org/W2160167461","https://openalex.org/W2170344325","https://openalex.org/W2176446742","https://openalex.org/W2401610261","https://openalex.org/W2569646339","https://openalex.org/W2625029195","https://openalex.org/W2913492813","https://openalex.org/W2988480584"],"related_works":["https://openalex.org/W4231500168","https://openalex.org/W90079504","https://openalex.org/W2032436423","https://openalex.org/W3141113327","https://openalex.org/W3035974271","https://openalex.org/W1561045713","https://openalex.org/W2374451529","https://openalex.org/W2349715051","https://openalex.org/W2069541586","https://openalex.org/W1553098308"],"abstract_inverted_index":{"We":[0,223,284],"study":[1],"multicommodity":[2,293],"routing":[3,117,176,207,228,246],"problems":[4],"in":[5,96,122,135,149,167,195,271,278,295],"both":[6],"edge":[7,52,116,206],"and":[8,23,242,274],"node":[9,28,230,266,296],"capacitated":[10,20,267,297],"undirected":[11],"graphs.":[12],"The":[13,94],"input":[14],"to":[15,37,50,65,100,126,220],"each":[16],"problem":[17,270,277],"is":[18,36,63,72,87,125,147,189,215,236,300],"a":[19,24,39,60,68,131,143,150,183,196,261],"graph":[21,151,172],"G=(V,E)":[22],"set":[25,144],"\u03a4":[26,97],"of":[27,41,83,133,145,212],"pairs.":[29],"In":[30,178],"the":[31,34,51,57,73,84,90,106,109,137,202,213,239,244,256,265,288,304],"simplest":[32],"setting,":[33],"goal":[35],"route":[38],"unit":[40],"flow":[42,58,92,269],"for":[43,59,114,174,205,226,252,264,291],"as":[44,47,89,101],"many":[45],"pairs":[46],"possible":[48],"subject":[49],"(node)":[53],"capacity":[54],"constraints.":[55],"If":[56,78],"routed":[61],"pair":[62],"required":[64],"be":[66],"along":[67],"single":[69],"path,":[70],"it":[71,86,153,217],"well-studied":[74],"disjoint":[75],"paths":[76],"problem.":[77,93],"we":[79,181,259],"allow":[80],"fractional":[81],"routings":[82],"flow,":[85],"known":[88,237],"all-or-nothing":[91,268],"nodes":[95,146],"are":[98,139],"referred":[99],"terminals.In":[102],"recent":[103],"work":[104],"[8,9],":[105],"authors":[107],"obtained":[108],"first":[110],"poly-logarithmic":[111,250,262],"approximation":[112,263],"algorithms":[113,124],"some":[115],"problems.":[118,208,222],"A":[119,159],"key":[120],"idea":[121],"these":[123],"decompose":[127],"an":[128,232],"instance":[129],"into":[130,161],"collection":[132],"instances":[134,163],"which":[136],"terminals":[138],"well-linked.":[140],"Informally":[141],"speaking,":[142],"well-linked":[148,162,253],"if":[152],"does":[154],"not":[155],"have":[156],"small":[157],"separators.":[158],"decomposition":[160,173,186],"was":[164],"previously":[165],"achieved":[166],"[8]":[168],"via":[169],"racke's":[170],"hierarchical":[171],"oblivious":[175,227,245],"[32].":[177],"this":[179],"paper,":[180],"design":[182],"simple":[184],"new":[185,199,257],"algorithm":[187,200,214],"that":[188,216,225,287],"based":[190],"on":[191,238],"computing":[192],"sparse":[193],"cuts":[194],"graph.":[197],"Our":[198],"improves":[201],"earlier":[203],"results":[204],"Another":[209],"important":[210],"advantage":[211],"also":[218,285],"applies":[219],"node-capacitated":[221],"note":[224],"with":[229,281],"capacities,":[231],"\u03a9\u221an)":[233],"lower":[234],"bound":[235,307],"congestion":[240],"[18],":[241],"hence":[243],"approach":[247],"cannot":[248],"yield":[249],"bounds":[251],"decompositions.":[254],"Using":[255],"decomposition,":[258],"obtain":[260],"general":[272],"graphs":[273,280,299],"node-disjoint":[275],"path":[276],"planar":[279,298],"O(1)":[282],"congestion.":[283],"show":[286],"flow-cut":[289],"gap":[290],"product":[292],"flows":[294],"O(1),":[301],"improving":[302],"upon":[303],"O(log":[305],"n)":[306],"from":[308],"[28].":[309]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":6},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":8},{"year":2013,"cited_by_count":7},{"year":2012,"cited_by_count":6}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
