{"id":"https://openalex.org/W4284681932","doi":"https://doi.org/10.48550/arxiv.2207.02136","title":"Width Helps and Hinders Splitting Flows","display_name":"Width Helps and Hinders Splitting Flows","publication_year":2022,"publication_date":"2022-01-01","ids":{"openalex":"https://openalex.org/W4284681932","doi":"https://doi.org/10.48550/arxiv.2207.02136"},"language":"en","primary_location":{"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2207.02136","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":["Cornell University"],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false},"type":"preprint","type_crossref":"posted-content","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/abs/2207.02136","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5064412838","display_name":"Manuel C\u00e1ceres","orcid":"https://orcid.org/0000-0003-0235-6951"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"C\u00e1ceres, Manuel","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5007584366","display_name":"Massimo Cairo","orcid":"https://orcid.org/0000-0001-7247-756X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Cairo, Massimo","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5009794956","display_name":"Andreas Grigorjew","orcid":"https://orcid.org/0000-0003-0989-2415"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Grigorjew, Andreas","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5014870050","display_name":"Shahbaz Khan","orcid":"https://orcid.org/0000-0001-9352-0088"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Khan, Shahbaz","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5084888509","display_name":"Brendan Mumey","orcid":"https://orcid.org/0000-0001-7151-2124"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Mumey, Brendan","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5061874157","display_name":"Rom\u00e9o Rizzi","orcid":"https://orcid.org/0000-0002-2387-0952"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Rizzi, Romeo","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5063897224","display_name":"Alexandru I. Tomescu","orcid":"https://orcid.org/0000-0002-5747-8350"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Tomescu, Alexandru I.","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5023404314","display_name":"Lucia Williams","orcid":"https://orcid.org/0000-0003-3785-0247"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Williams, Lucia","raw_affiliation_strings":[],"affiliations":[]}],"institution_assertions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":0,"max":60},"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"primary_topic":{"id":"https://openalex.org/T10661","display_name":"biodegradable polymer synthesis and properties","score":0.9075,"subfield":{"id":"https://openalex.org/subfields/2502","display_name":"Biomaterials"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10661","display_name":"biodegradable polymer synthesis and properties","score":0.9075,"subfield":{"id":"https://openalex.org/subfields/2502","display_name":"Biomaterials"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/independence-number","display_name":"Independence number","score":0.5659117},{"id":"https://openalex.org/keywords/maximum-flow-problem","display_name":"Maximum flow problem","score":0.4784515},{"id":"https://openalex.org/keywords/minimum-cut","display_name":"Minimum cut","score":0.41041678}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.72218925},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.69066215},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.5879034},{"id":"https://openalex.org/C2984853995","wikidata":"https://www.wikidata.org/wiki/Q1060343","display_name":"Independence number","level":3,"score":0.5659117},{"id":"https://openalex.org/C2779557605","wikidata":"https://www.wikidata.org/wiki/Q9890","display_name":"Omega","level":2,"score":0.49127358},{"id":"https://openalex.org/C157469704","wikidata":"https://www.wikidata.org/wiki/Q2585642","display_name":"Maximum flow problem","level":2,"score":0.4784515},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.42552784},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.4131992},{"id":"https://openalex.org/C185690422","wikidata":"https://www.wikidata.org/wiki/Q6865438","display_name":"Minimum cut","level":2,"score":0.41041678},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3935309},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.3660144},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.13651145},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2207.02136","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":["Cornell University"],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false},{"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2207.02136","pdf_url":"http://arxiv.org/pdf/2207.02136","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":["Cornell University"],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false},{"is_oa":false,"landing_page_url":"https://api.datacite.org/dois/10.48550/arxiv.2207.02136","pdf_url":null,"source":{"id":"https://openalex.org/S4393179698","display_name":"DataCite API","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210145204","host_organization_name":"DataCite","host_organization_lineage":["https://openalex.org/I4210145204"],"host_organization_lineage_names":["DataCite"],"type":"metadata"},"license":null,"license_id":null,"version":null}],"best_oa_location":{"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2207.02136","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":["Cornell University"],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false},"sustainable_development_goals":[],"grants":[],"datasets":[],"versions":[],"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W3155269421","https://openalex.org/W3141688457","https://openalex.org/W2188409860","https://openalex.org/W2186707160","https://openalex.org/W2141353198","https://openalex.org/W2121204510","https://openalex.org/W2095284441","https://openalex.org/W2078695342","https://openalex.org/W2039086323","https://openalex.org/W1974018476"],"abstract_inverted_index":{"Minimum":[0,135],"flow":[1,96,221],"decomposition":[2,12,191],"(MFD)":[3],"is":[4,89,117],"the":[5,38,41,64,67,94,118,123,151,171,215,252],"NP-hard":[6],"problem":[7,68,130],"of":[8,13,40,46,52,60,66,81,97,120,175,192,204,218,238,244],"finding":[9],"a":[10,14,19,78,86,90,128,147,159,181,190,201,212,241,248],"smallest":[11],"network":[15],"flow/circulation":[16],"$X$":[17,176],"on":[18,131,177],"directed":[20],"graph":[21,42],"$G$":[22],"into":[23],"weighted":[24],"source-to-sink":[25],"paths":[26,47,245],"whose":[27],"superposition":[28],"equals":[29],"$X$.":[30],"We":[31,125],"show":[32,141,231],"that,":[33],"for":[34,84,112,206,251],"acyclic":[35],"graphs,":[36,83,114],"considering":[37],"\\emph{width}":[39],"(the":[43],"minimum":[44,219],"number":[45,119],"needed":[48],"to":[49,107,240,246],"cover":[50],"all":[51],"its":[53,61,101,233],"edges)":[54],"yields":[55],"advances":[56],"in":[57,122],"our":[58],"understanding":[59],"approximability.":[62],"For":[63,150],"version":[65,152],"that":[69,142,232],"uses":[70],"only":[71],"non-negative":[72],"weights,":[73,156],"we":[74,157,210],"identify":[75],"and":[76,99,140,189],"characterise":[77],"new":[79,129],"class":[80],"\\emph{width-stable}":[82],"which":[85],"popular":[87],"heuristic":[88],"\\gwsimple-approximation":[91],"($|X|$":[92],"being":[93,170],"total":[95],"$X$),":[98],"strengthen":[100],"worst-case":[102],"approximation":[103],"ratio":[104],"from":[105],"$\\Omega(\\sqrt{m})$":[106],"$\\Omega(m":[108],"/":[109],"\\log":[110,161],"m)$":[111],"sparse":[113],"where":[115],"$m$":[116],"edges":[121],"graph.":[124],"also":[126,154],"study":[127],"graphs":[132],"with":[133,185],"cycles,":[134],"Cost":[136],"Circulation":[137],"Decomposition":[138],"(MCCD),":[139],"it":[143],"generalises":[144],"MFD":[145],"through":[146],"simple":[148],"reduction.":[149],"allowing":[153],"negative":[155,253],"give":[158],"$(\\lceil":[160],"\\Vert":[162,164,197],"X":[163,168,196],"\\rceil":[165],"+1)$-approximation":[166],"($\\Vert":[167,195],"\\Vert$":[169],"maximum":[172],"absolute":[173],"value":[174],"any":[178],"edge)":[179],"using":[180,200],"power-of-two":[182],"approach,":[183],"combined":[184],"parity":[186],"fixing":[187],"arguments":[188],"unitary":[193],"circulations":[194],"\\leq":[198],"1$),":[199],"generalised":[202],"notion":[203],"width":[205],"this":[207],"problem.":[208],"Finally,":[209],"disprove":[211],"conjecture":[213],"about":[214],"linear":[216],"independence":[217],"(non-negative)":[220],"decompositions":[222],"posed":[223],"by":[224],"Kloster":[225],"et":[226],"al.":[227],"[ALENEX":[228],"2018],":[229],"but":[230],"useful":[234],"implication":[235],"(polynomial-time":[236],"assignments":[237],"weights":[239],"given":[242],"set":[243],"decompose":[247],"flow)":[249],"holds":[250],"version.":[254]},"cited_by_api_url":"https://api.openalex.org/works?filter=cites:W4284681932","counts_by_year":[],"updated_date":"2024-12-15T18:08:34.178035","created_date":"2022-07-08"}