{"id":"https://openalex.org/W2059742977","doi":"https://doi.org/10.1002/net.3230210602","title":"The cut cone, <i>L</i><sup>1</sup> embeddability, complexity, and multicommodity flows","display_name":"The cut cone, <i>L</i><sup>1</sup> embeddability, complexity, and multicommodity flows","publication_year":1991,"publication_date":"1991-10-01","ids":{"openalex":"https://openalex.org/W2059742977","doi":"https://doi.org/10.1002/net.3230210602","mag":"2059742977"},"language":"en","primary_location":{"id":"doi:10.1002/net.3230210602","is_oa":false,"landing_page_url":"https://doi.org/10.1002/net.3230210602","pdf_url":null,"source":{"id":"https://openalex.org/S191798613","display_name":"Networks","issn_l":"0028-3045","issn":["0028-3045","1097-0037"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Networks","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/A5020530779","display_name":"David Avis","orcid":null},"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":true,"raw_author_name":"David Avis","raw_affiliation_strings":["School of Computer Science, McGill University, 3480 University, Montreal, Canada, H3A 2A7"],"affiliations":[{"raw_affiliation_string":"School of Computer Science, McGill University, 3480 University, Montreal, Canada, H3A 2A7","institution_ids":["https://openalex.org/I5023651"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5113871341","display_name":"Michel Deza","orcid":null},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"funder","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I204730241","display_name":"Universit\u00e9 Paris Cit\u00e9","ror":"https://ror.org/05f82e368","country_code":"FR","type":"education","lineage":["https://openalex.org/I204730241"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Michel Deza","raw_affiliation_strings":["CNRS, UA 212, Universite de Paris VII, 17, Passage de l'industrie, 750010 Paris, France"],"affiliations":[{"raw_affiliation_string":"CNRS, UA 212, Universite de Paris VII, 17, Passage de l'industrie, 750010 Paris, France","institution_ids":["https://openalex.org/I204730241","https://openalex.org/I1294671590"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5020530779"],"corresponding_institution_ids":["https://openalex.org/I5023651"],"apc_list":{"value":3400,"currency":"USD","value_usd":3400},"apc_paid":null,"fwci":4.47,"has_fulltext":false,"cited_by_count":43,"citation_normalized_percentile":{"value":0.95559947,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"21","issue":"6","first_page":"595","last_page":"617"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9962999820709229,"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":0.9962999820709229,"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":0.9962000250816345,"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9871000051498413,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"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":0.8213551044464111},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7536073923110962},{"id":"https://openalex.org/keywords/cone","display_name":"Cone (formal languages)","score":0.624172031879425},{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.5024802684783936},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.42381757497787476},{"id":"https://openalex.org/keywords/metric-space","display_name":"Metric space","score":0.41878557205200195},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3895263671875},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.21904942393302917},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.0703057050704956}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8213551044464111},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7536073923110962},{"id":"https://openalex.org/C30014739","wikidata":"https://www.wikidata.org/wiki/Q5159445","display_name":"Cone (formal languages)","level":2,"score":0.624172031879425},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.5024802684783936},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.42381757497787476},{"id":"https://openalex.org/C198043062","wikidata":"https://www.wikidata.org/wiki/Q180953","display_name":"Metric space","level":2,"score":0.41878557205200195},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3895263671875},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.21904942393302917},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.0703057050704956},{"id":"https://openalex.org/C21547014","wikidata":"https://www.wikidata.org/wiki/Q1423657","display_name":"Operations management","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1002/net.3230210602","is_oa":false,"landing_page_url":"https://doi.org/10.1002/net.3230210602","pdf_url":null,"source":{"id":"https://openalex.org/S191798613","display_name":"Networks","issn_l":"0028-3045","issn":["0028-3045","1097-0037"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Networks","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":37,"referenced_works":["https://openalex.org/W1472219562","https://openalex.org/W1534735876","https://openalex.org/W1963625837","https://openalex.org/W1964119857","https://openalex.org/W1971387646","https://openalex.org/W2011376360","https://openalex.org/W2012292283","https://openalex.org/W2012605254","https://openalex.org/W2013294386","https://openalex.org/W2016986275","https://openalex.org/W2018214829","https://openalex.org/W2026936769","https://openalex.org/W2028218873","https://openalex.org/W2040506679","https://openalex.org/W2050062492","https://openalex.org/W2059936808","https://openalex.org/W2060660073","https://openalex.org/W2068221647","https://openalex.org/W2084236013","https://openalex.org/W2085035171","https://openalex.org/W2086049536","https://openalex.org/W2097956810","https://openalex.org/W2100440346","https://openalex.org/W2113227678","https://openalex.org/W2148016452","https://openalex.org/W2150815458","https://openalex.org/W2159739530","https://openalex.org/W2164209543","https://openalex.org/W2207839030","https://openalex.org/W2323216128","https://openalex.org/W2402407411","https://openalex.org/W3084987570","https://openalex.org/W4244424643","https://openalex.org/W4246971533","https://openalex.org/W4253982521","https://openalex.org/W4291439952","https://openalex.org/W6618140832"],"related_works":["https://openalex.org/W2371409811","https://openalex.org/W2956921597","https://openalex.org/W2070412032","https://openalex.org/W4249185839","https://openalex.org/W2116371063","https://openalex.org/W2888047994","https://openalex.org/W2383812375","https://openalex.org/W2320435126","https://openalex.org/W2349669595","https://openalex.org/W4297851895"],"abstract_inverted_index":{"Abstract":[0],"A":[1,93,141,308],"finite":[2],"metric":[3,94,143,146,193],"(or":[4,44],"more":[5,309],"properly":[6],"semimetric)":[7],"on":[8,166,238,388],"n":[9,26,111,139,167,173],"points":[10],"is":[11,71,96,144,174,188,194,203,350],"a":[12,145,160,192,215,220,256,289,318,324,344],"nonnegative":[13,182],"vector":[14,158],"d":[15,32,35,38,95,121],"=":[16,58,64,80,123],"(d":[17],"ij":[18,33,122],")":[19,46,61,67],"1":[20,43,53,79,98,105,131,133,196,227,253,271,396],"\u2a7d":[21,25,34,84,134,138],"i":[22,60,66,83,88,91,126,135],"&lt;":[23,136],"j":[24,129,137],"that":[27,120,191,299,332,352,374,391],"satisfies":[28],"the":[29,156,163,175,206,230,239,243,247,251,260,264,267,274,286,314,321,353,356,365,375,389],"triangle":[30],"inequality":[31,298,331],"ik":[36],"+":[37],"jk":[39],".":[40,140,307,339],"The":[41,169,280],"L":[42,97,195,226,252,270,395],"Manhattan":[45],"distance":[47],"\u2016":[48,52,74,78,124,130],"x":[49,57,75,87],"\u2212":[50,76,89,127],"y":[51,63,77,90],"between":[54],"two":[55],"vectors":[56,103],"(x":[59],"and":[62,153,199,229,235,246,282,372],"(y":[65],"in":[68,112,162,205,273],"R":[69,113],"m":[70,85,114,117],"given":[72],"by":[73,179,336],"\u2211":[81],"1\u2a7d":[82],"|":[86],"|.":[92],"\u2010embeddable":[99,197],"if":[100,198,201],"there":[101],"exist":[102],"z":[104,107,110,125,128],",":[106,118],"2":[108],",\u2026,":[109],"for":[115,132,218,277,285,303,320,381],"some":[116],"such":[119,378],"cut":[142,161,170,185,207,231,244,305],"with":[147,362,383],"all":[148,181,304,337],"distances":[149],"zero":[150],"or":[151],"one":[152,363],"corresponds":[154],"to":[155,225],"incidence":[157],"of":[159,184,222,242,249,255,259,263,269,288,323,347,355,364,377],"complete":[164],"graph":[165],"vertices.":[168],"cone":[171,177,245],"H":[172],"convex":[176],"formed":[178],"taking":[180],"combinations":[183],"metrics.":[186],"It":[187],"easily":[189],"shown":[190],"only":[200],"it":[202,349],"contained":[204],"cone.":[208,232],"In":[209],"this":[210],"expository":[211],"paper,":[212],"we":[213],"provide":[214],"unified":[216],"setting":[217],"describing":[219],"number":[221,346],"results":[223,237,371],"related":[224],"\u2010embeddability":[228,254,272],"We":[233,368],"collect":[234],"describe":[236],"facial":[240],"structure":[241],"complexity":[248],"testing":[250],"metric.":[257],"One":[258],"main":[261],"sections":[262],"paper":[265],"describes":[266],"role":[268],"feasibility":[275],"problem":[276],"multi\u2010commodity":[278],"flows.":[279],"Ford":[281],"Fulkerson":[283],"theorem":[284,328,358],"existence":[287,322,376],"single":[290],"commodity":[291],"flow":[292],"can":[293,359],"be":[294,301,334,360],"restated":[295],"as":[296,313],"an":[297,330],"must":[300,333],"valid":[302],"metrics":[306,338,393],"general":[310],"result,":[311],"known":[312,351],"Japanese":[315,357],"theorem,":[316],"gives":[317,329],"condition":[319,354],"multicommodity":[325,341],"flow.":[326],"This":[327],"satisfied":[335],"For":[340],"flows":[342,382],"involving":[343],"small":[345],"terminals,":[348],"replaced":[361],"Ford\u2013Fulkerson":[366],"type.":[367],"review":[369],"these":[370],"show":[373],"Ford\u2013Fulkerson\u2010type":[379],"conditions":[380],"few":[384],"terminals":[385],"depends":[386],"critically":[387],"fact":[390],"certain":[392],"are":[394],"\u2010embeddable.":[397]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
