{"id":"https://openalex.org/W2115448953","doi":"https://doi.org/10.1145/2213977.2214039","title":"On vertex sparsifiers with Steiner nodes","display_name":"On vertex sparsifiers with Steiner nodes","publication_year":2012,"publication_date":"2012-05-19","ids":{"openalex":"https://openalex.org/W2115448953","doi":"https://doi.org/10.1145/2213977.2214039","mag":"2115448953"},"language":"en","primary_location":{"id":"doi:10.1145/2213977.2214039","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2213977.2214039","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the forty-fourth 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/A5056023203","display_name":"Julia Chuzhoy","orcid":"https://orcid.org/0000-0001-7839-751X"},"institutions":[{"id":"https://openalex.org/I160992636","display_name":"Toyota Technological Institute at Chicago","ror":"https://ror.org/02sn5gb64","country_code":"US","type":"education","lineage":["https://openalex.org/I160992636"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Julia Chuzhoy","raw_affiliation_strings":["Toyota Technological Institute, Chicago, IL, USA"],"affiliations":[{"raw_affiliation_string":"Toyota Technological Institute, Chicago, IL, USA","institution_ids":["https://openalex.org/I160992636"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5056023203"],"corresponding_institution_ids":["https://openalex.org/I160992636"],"apc_list":null,"apc_paid":null,"fwci":3.8009,"has_fulltext":false,"cited_by_count":26,"citation_normalized_percentile":{"value":0.93621562,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":null,"issue":null,"first_page":"673","last_page":"688"},"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":0.9948999881744385,"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/T12072","display_name":"Machine Learning and Algorithms","score":0.991599977016449,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/steiner-tree-problem","display_name":"Steiner tree problem","score":0.6315714120864868},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.6222233176231384},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5956774353981018},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.42752954363822937},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3999212682247162},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3839988112449646},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3670713007450104},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.14195963740348816}],"concepts":[{"id":"https://openalex.org/C76220878","wikidata":"https://www.wikidata.org/wiki/Q1764144","display_name":"Steiner tree problem","level":2,"score":0.6315714120864868},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.6222233176231384},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5956774353981018},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.42752954363822937},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3999212682247162},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3839988112449646},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3670713007450104},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.14195963740348816}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/2213977.2214039","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2213977.2214039","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the forty-fourth annual ACM symposium on Theory of computing","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W406039428","https://openalex.org/W1999867351","https://openalex.org/W2011334641","https://openalex.org/W2012776084","https://openalex.org/W2019041817","https://openalex.org/W2036669621","https://openalex.org/W2044343300","https://openalex.org/W2057931683","https://openalex.org/W2066398433","https://openalex.org/W2088844265","https://openalex.org/W2107881198","https://openalex.org/W2119862441","https://openalex.org/W2141793995","https://openalex.org/W2145818650","https://openalex.org/W2150148016","https://openalex.org/W2150187954"],"related_works":["https://openalex.org/W3047993683","https://openalex.org/W2135965211","https://openalex.org/W2086305925","https://openalex.org/W2619106660","https://openalex.org/W3194189065","https://openalex.org/W1972602069","https://openalex.org/W2949165555","https://openalex.org/W2973952324","https://openalex.org/W2776184136","https://openalex.org/W3094179009"],"abstract_inverted_index":{"Given":[0],"an":[1],"undirected":[2],"graph":[3,26],"G=(V,E)":[4],"with":[5],"edge":[6,97],"capacities":[7],"ce\u2265":[8],"1":[9],"for":[10,33,39,77,83,153],"e\u2208":[11],"E":[12],"and":[13,38,53,58,82,110,160],"a":[14,25,29,62,73,114,128,167],"subset":[15],"T":[16],"of":[17,43,47,87,94,170,176],"k":[18],"vertices":[19],"called":[20],"terminals,":[21,91],"we":[22],"say":[23,69],"that":[24,70,143],"H":[27,59,71,111,134],"is":[28,72,135,144],"quality-q":[30,74],"cut":[31,159,180],"sparsifier":[32,76,133],"G":[34,57,78,109],"iff":[35,79],"T\u2286":[36,80],"V(H),":[37,81],"any":[40,84,140,177],"partition":[41],"(A,B)":[42],"T,":[44],"the":[45,48,90,92,95,103,132,174],"values":[46,93],"minimum":[49,96],"cuts":[50],"separating":[51],"A":[52],"B":[54],"in":[55,105,107,127],"graphs":[56,108],"are":[60,112,151],"within":[61,113],"factor":[63,115],"q":[64,116],"from":[65,117],"each":[66,118],"other.":[67,119],"We":[68],"flow":[75,161,178],"set":[85],"D":[86,106],"demands":[88,104],"over":[89],"congestion":[98],"incurred":[99],"by":[100],"fractionally":[101],"routing":[102],"So":[120],"far":[121],"vertex":[122,162],"sparsifiers":[123],"have":[124],"been":[125],"studied":[126],"restricted":[129],"setting":[130],"where":[131],"not":[136],"allowed":[137],"to":[138],"contain":[139],"non-terminal":[141],"vertices,":[142],"V(H)=T.":[145],"For":[146],"this":[147],"setting,":[148],"efficient":[149],"algorithms":[150],"known":[152],"constructing":[154],"quality-O(log":[155],"k/log":[156],"log":[157],"k)":[158,172],"sparsifiers,":[163],"as":[164,166],"well":[165],"lower":[168],"bound":[169],"\u03a9(\u221alog":[171],"on":[173],"quality":[175],"or":[179],"sparsifier.":[181]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":6},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":5},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":2}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
