{"id":"https://openalex.org/W1995031698","doi":"https://doi.org/10.1145/1255443.1255444","title":"(Almost) Tight bounds and existence theorems for single-commodity confluent flows","display_name":"(Almost) Tight bounds and existence theorems for single-commodity confluent flows","publication_year":2007,"publication_date":"2007-07-01","ids":{"openalex":"https://openalex.org/W1995031698","doi":"https://doi.org/10.1145/1255443.1255444","mag":"1995031698"},"language":"en","primary_location":{"id":"doi:10.1145/1255443.1255444","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1255443.1255444","pdf_url":null,"source":{"id":"https://openalex.org/S118992489","display_name":"Journal of the ACM","issn_l":"0004-5411","issn":["0004-5411","1557-735X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of the ACM","raw_type":"journal-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/A5065844089","display_name":"Jiangzhuo Chen","orcid":"https://orcid.org/0000-0002-2729-3881"},"institutions":[{"id":"https://openalex.org/I859038795","display_name":"Virginia Tech","ror":"https://ror.org/02smfhw86","country_code":"US","type":"education","lineage":["https://openalex.org/I859038795"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Jiangzhuo Chen","raw_affiliation_strings":["Virginia Tech, Blacksburg, Virginia"],"affiliations":[{"raw_affiliation_string":"Virginia Tech, Blacksburg, Virginia","institution_ids":["https://openalex.org/I859038795"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5040052580","display_name":"Robert Kleinberg","orcid":"https://orcid.org/0000-0002-8306-3407"},"institutions":[{"id":"https://openalex.org/I205783295","display_name":"Cornell University","ror":"https://ror.org/05bnh6r87","country_code":"US","type":"education","lineage":["https://openalex.org/I205783295"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Robert D. Kleinberg","raw_affiliation_strings":["Cornell University, Ithaca, New York","Cornell University Ithaca,, New York"],"affiliations":[{"raw_affiliation_string":"Cornell University, Ithaca, New York","institution_ids":["https://openalex.org/I205783295"]},{"raw_affiliation_string":"Cornell University Ithaca,, New York","institution_ids":["https://openalex.org/I205783295"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5067889485","display_name":"L\u00e1szl\u00f3 Lov\u00e1sz","orcid":"https://orcid.org/0000-0002-6242-5894"},"institutions":[{"id":"https://openalex.org/I106118109","display_name":"E\u00f6tv\u00f6s Lor\u00e1nd University","ror":"https://ror.org/01jsq2704","country_code":"HU","type":"education","lineage":["https://openalex.org/I106118109"]}],"countries":["HU"],"is_corresponding":false,"raw_author_name":"L\u00e1szl\u00f3 Lov\u00e1sz","raw_affiliation_strings":["E\u00f6tv\u00f6s Lor\u00e1nd University, Budapest, Hungary"],"affiliations":[{"raw_affiliation_string":"E\u00f6tv\u00f6s Lor\u00e1nd University, Budapest, Hungary","institution_ids":["https://openalex.org/I106118109"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5103525476","display_name":"Rajmohan Rajaraman","orcid":null},"institutions":[{"id":"https://openalex.org/I12912129","display_name":"Northeastern University","ror":"https://ror.org/04t5xt781","country_code":"US","type":"education","lineage":["https://openalex.org/I12912129"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Rajmohan Rajaraman","raw_affiliation_strings":["Northeastern University, Boston, Massachusetts"],"affiliations":[{"raw_affiliation_string":"Northeastern University, Boston, Massachusetts","institution_ids":["https://openalex.org/I12912129"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5103159653","display_name":"Ravi Sundaram","orcid":"https://orcid.org/0000-0001-5657-4298"},"institutions":[{"id":"https://openalex.org/I12912129","display_name":"Northeastern University","ror":"https://ror.org/04t5xt781","country_code":"US","type":"education","lineage":["https://openalex.org/I12912129"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Ravi Sundaram","raw_affiliation_strings":["Northeastern University, Boston, Massachusetts"],"affiliations":[{"raw_affiliation_string":"Northeastern University, Boston, Massachusetts","institution_ids":["https://openalex.org/I12912129"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5027727214","display_name":"Adrian Vetta","orcid":"https://orcid.org/0000-0002-2213-4937"},"institutions":[{"id":"https://openalex.org/I5023651","display_name":"McGill University","ror":"https://ror.org/01pxwe438","country_code":"CA","type":"education","lineage":["https://openalex.org/I5023651"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Adrian Vetta","raw_affiliation_strings":["McGill University, Montreal, Quebec, Canada"],"affiliations":[{"raw_affiliation_string":"McGill University, Montreal, Quebec, Canada","institution_ids":["https://openalex.org/I5023651"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5065844089"],"corresponding_institution_ids":["https://openalex.org/I859038795"],"apc_list":null,"apc_paid":null,"fwci":0.7487,"has_fulltext":false,"cited_by_count":27,"citation_normalized_percentile":{"value":0.7157937,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"54","issue":"4","first_page":"16","last_page":"16"},"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":0.9991999864578247,"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/mathematics","display_name":"Mathematics","score":0.5330905318260193},{"id":"https://openalex.org/keywords/flow","display_name":"Flow (mathematics)","score":0.5021743774414062},{"id":"https://openalex.org/keywords/maximum-flow-problem","display_name":"Maximum flow problem","score":0.4948510527610779},{"id":"https://openalex.org/keywords/flow-network","display_name":"Flow network","score":0.4890469014644623},{"id":"https://openalex.org/keywords/sink","display_name":"Sink (geography)","score":0.46862155199050903},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4137313663959503},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.38238850235939026},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.10376527905464172}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5330905318260193},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.5021743774414062},{"id":"https://openalex.org/C157469704","wikidata":"https://www.wikidata.org/wiki/Q2585642","display_name":"Maximum flow problem","level":2,"score":0.4948510527610779},{"id":"https://openalex.org/C114809511","wikidata":"https://www.wikidata.org/wiki/Q1412924","display_name":"Flow network","level":2,"score":0.4890469014644623},{"id":"https://openalex.org/C143050476","wikidata":"https://www.wikidata.org/wiki/Q194502","display_name":"Sink (geography)","level":2,"score":0.46862155199050903},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4137313663959503},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.38238850235939026},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.10376527905464172},{"id":"https://openalex.org/C205649164","wikidata":"https://www.wikidata.org/wiki/Q1071","display_name":"Geography","level":0,"score":0.0},{"id":"https://openalex.org/C58640448","wikidata":"https://www.wikidata.org/wiki/Q42515","display_name":"Cartography","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1145/1255443.1255444","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1255443.1255444","pdf_url":null,"source":{"id":"https://openalex.org/S118992489","display_name":"Journal of the ACM","issn_l":"0004-5411","issn":["0004-5411","1557-735X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of the ACM","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.123.835","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.123.835","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.cornell.edu/~rdk/papers/conflu.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.156.2508","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.156.2508","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.mcgill.ca/~vetta/Research.dir/confluent.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Clean water and sanitation","id":"https://metadata.un.org/sdg/6","score":0.5799999833106995}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W1589657219","https://openalex.org/W1964119857","https://openalex.org/W2002531683","https://openalex.org/W2013469283","https://openalex.org/W2034269606","https://openalex.org/W2070767236","https://openalex.org/W2083409154","https://openalex.org/W2094410510","https://openalex.org/W2098973560","https://openalex.org/W2100699015","https://openalex.org/W2102201348","https://openalex.org/W2109640907","https://openalex.org/W2111308047","https://openalex.org/W2113834527","https://openalex.org/W2143996311","https://openalex.org/W2569646339","https://openalex.org/W2599142459","https://openalex.org/W2798766386","https://openalex.org/W3014052784","https://openalex.org/W3040586665","https://openalex.org/W4213060883","https://openalex.org/W4242766606","https://openalex.org/W4301005547","https://openalex.org/W6674977452","https://openalex.org/W6750230808","https://openalex.org/W6780011183"],"related_works":["https://openalex.org/W2375873432","https://openalex.org/W4206915070","https://openalex.org/W2531764854","https://openalex.org/W2098682899","https://openalex.org/W3161514703","https://openalex.org/W2141299097","https://openalex.org/W4311255633","https://openalex.org/W2368007657","https://openalex.org/W2391191500","https://openalex.org/W2365398175"],"abstract_inverted_index":{"A":[0],"flow":[1,16,32,108,124,152,185,203,226,235,278,316,333],"of":[2,17,59,104,112,116,146,174,274,283,305,317,325,345,383,397,409,417],"a":[3,22,43,47,57,105,121,132,150,167,178,183,201,219,224,281,295,301,314,323,331],"commodity":[4,19],"is":[5,80,125,169,177,268,359,366,394,405,421],"said":[6],"to":[7,37,42,127,158,255,270,279,293],"be":[8],"confluent":[9,31,48,53,75,98,107,123,151,184,234,277,332,354,381],"if":[10,198,311,362],"at":[11,110,166,188,206,229,319,338],"any":[12,410],"node":[13,40,156,411],"all":[14,143],"the":[15,18,71,113,117,128,144,163,243,272,290,306,326,351,363,395,398,406],"leaves":[20],"along":[21],"single":[23,44],"edge.":[24],"In":[25,369],"this":[26,175,211,418],"article,":[27],"we":[28,35,217,264,371],"study":[29],"single-commodity":[30,97,106],"problems,":[33],"where":[34,392],"need":[36],"route":[38],"given":[39,131],"demands":[41,141],"destination":[45,81],"using":[46],"flow.":[49],"Single-":[50],"and":[51,90,139,252,356,402,423],"multi-commodity":[52],"flows":[54,69,76,355,358,382],"arise":[55],"in":[56,64,66,70,96,195,213,334,412],"variety":[58],"application":[60],"areas,":[61],"most":[62,68,189,207,230,320,339],"notably":[63],"networking;":[65],"fact,":[67],"Internet":[72,78],"are":[73],"(multi-commodity)":[74],"since":[77],"routing":[79],"based.":[82],"We":[83,209,298,308,348],"present":[84,218],"near-tight":[85],"approximation":[86],"algorithms,":[87],"hardness":[88],"results,":[89],"existence":[91,419],"theorems":[92],"for":[93,181],"minimizing":[94],"congestion":[95,103,165,187,205,228,237,273,318,327,337,384,396],"flows.":[99],"The":[100,171,415],"maximum":[101,164,407],"edge":[102],"occurs":[109],"one":[111],"incoming":[114],"edges":[115],"destination.":[118],"Therefore,":[119],"finding":[120],"minimum-congestion":[122],"equivalent":[126],"following":[129],"problem:":[130],"directed":[133],"graph":[134,220,365],"G":[135,147,196,199,221,312,335,413],"with":[136,186,204,227,236,336,377],"k":[137,193,241,244,286,367,374,378],"sinks":[138,379],"non-negative":[140],"on":[142,425],"nodes":[145],",":[148,197,242,391],"determine":[149],"that":[153,162,222,266,310,341,350,373],"routes":[154],"every":[155],"demand":[157,302,408],"some":[159],"sink":[160,168],"such":[161],"minimized.":[170],"main":[172],"result":[173,212],"article":[176],"polynomial-time":[179,291],"algorithm":[180,329],"determining":[182],"1":[190,340],"+":[191,388],"ln(":[192],")":[194],"admits":[200,223,313],"splittable":[202,225,315,357,400],"1.":[208,262],"complement":[210],"two":[214],"directions.":[215],"First,":[216],"1,":[231,321],"yet":[232],"no":[233],"smaller":[238],"than":[239,261,386],"H":[240],"th":[245],"harmonic":[246],"number,":[247],"thus":[248,288],"establishing":[249],"tight":[250],"upper":[251],"lower":[253],"bounds":[254],"within":[256,280,294],"an":[257,275],"additive":[258],"constant":[259],"less":[260,385],"Second,":[263],"show":[265,309,349],"it":[267],"NP-hard":[269],"approximate":[271],"optimal":[276],"factor":[282],"(log":[284],"2":[285],")/2,":[287],"resolving":[289],"approximability":[292],"multiplicative":[296],"constant.":[297],"also":[299],"consider":[300],"maximization":[303],"version":[304],"problem.":[307],"then":[322],"variant":[324],"minimization":[328],"yields":[330],"satisfies":[342],"1/3":[343],"fraction":[344],"total":[346],"demand.":[347],"gap":[352],"between":[353],"much":[360],"smaller,":[361],"underlying":[364],"-connected.":[368],"particular,":[370],"prove":[372],"-connected":[375],"graphs":[376],"admit":[380],"C":[387,393],"d":[389,403],"max":[390,404],"best":[399],"flow,":[401],".":[414],"proof":[416],"theorem":[420],"non-constructive":[422],"relies":[424],"topological":[426],"techniques":[427],"introduced":[428],"by":[429],"Lov\u00e1sz.":[430]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
