{"id":"https://openalex.org/W2157346440","doi":"https://doi.org/10.1145/2591796.2591852","title":"Minimum bisection is fixed parameter tractable","display_name":"Minimum bisection is fixed parameter tractable","publication_year":2014,"publication_date":"2014-05-31","ids":{"openalex":"https://openalex.org/W2157346440","doi":"https://doi.org/10.1145/2591796.2591852","mag":"2157346440"},"language":"en","primary_location":{"id":"doi:10.1145/2591796.2591852","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2591796.2591852","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-sixth annual ACM symposium on Theory of computing","raw_type":"proceedings-article"},"type":"conference-paper","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/A5037989463","display_name":"Marek Cygan","orcid":"https://orcid.org/0000-0003-2472-2975"},"institutions":[{"id":"https://openalex.org/I4654613","display_name":"University of Warsaw","ror":"https://ror.org/039bjqg32","country_code":"PL","type":"education","lineage":["https://openalex.org/I4654613"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Marek Cygan","raw_affiliation_strings":["University of Warsaw, Poland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Warsaw, Poland","institution_ids":["https://openalex.org/I4654613"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5038531405","display_name":"Daniel Lokshtanov","orcid":"https://orcid.org/0000-0002-3166-9212"},"institutions":[{"id":"https://openalex.org/I4432739","display_name":"University of Bergen","ror":"https://ror.org/03zga2b32","country_code":"NO","type":"education","lineage":["https://openalex.org/I4432739"]}],"countries":["NO"],"is_corresponding":false,"raw_author_name":"Daniel Lokshtanov","raw_affiliation_strings":["University of Bergen, Norway"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Bergen, Norway","institution_ids":["https://openalex.org/I4432739"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5059330513","display_name":"Marcin Pilipczuk","orcid":"https://orcid.org/0000-0001-5680-7397"},"institutions":[{"id":"https://openalex.org/I4432739","display_name":"University of Bergen","ror":"https://ror.org/03zga2b32","country_code":"NO","type":"education","lineage":["https://openalex.org/I4432739"]}],"countries":["NO"],"is_corresponding":false,"raw_author_name":"Marcin Pilipczuk","raw_affiliation_strings":["University of Bergen, Norway"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Bergen, Norway","institution_ids":["https://openalex.org/I4432739"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5000479623","display_name":"Micha\u0142 Pilipczuk","orcid":"https://orcid.org/0000-0001-7891-1988"},"institutions":[{"id":"https://openalex.org/I4432739","display_name":"University of Bergen","ror":"https://ror.org/03zga2b32","country_code":"NO","type":"education","lineage":["https://openalex.org/I4432739"]}],"countries":["NO"],"is_corresponding":false,"raw_author_name":"Micha\u0142 Pilipczuk","raw_affiliation_strings":["University of Bergen, Norway"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Bergen, Norway","institution_ids":["https://openalex.org/I4432739"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5015806060","display_name":"Saket Saurabh","orcid":"https://orcid.org/0000-0001-7847-6402"},"institutions":[{"id":"https://openalex.org/I4432739","display_name":"University of Bergen","ror":"https://ror.org/03zga2b32","country_code":"NO","type":"education","lineage":["https://openalex.org/I4432739"]},{"id":"https://openalex.org/I59611059","display_name":"Institute of Mathematical Sciences","ror":"https://ror.org/05078rg59","country_code":"IN","type":"facility","lineage":["https://openalex.org/I59611059"]}],"countries":["IN","NO"],"is_corresponding":false,"raw_author_name":"Saket Saurabh","raw_affiliation_strings":["Institute of Mathematical Sciences, India and University of Bergen, Norway"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Mathematical Sciences, India and University of Bergen, Norway","institution_ids":["https://openalex.org/I59611059","https://openalex.org/I4432739"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":28,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"323","last_page":"332"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","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/T10374","display_name":"Advanced Graph Theory Research","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/T10829","display_name":"Interconnection Networks and Systems","score":0.9988999962806702,"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/T11797","display_name":"graph theory and CDMA systems","score":0.9977999925613403,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic 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/bisection-method","display_name":"Bisection method","score":0.6692151427268982},{"id":"https://openalex.org/keywords/partition","display_name":"Partition (number theory)","score":0.6512314081192017},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.6327031254768372},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6029541492462158},{"id":"https://openalex.org/keywords/bisection","display_name":"Bisection","score":0.6021952629089355},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5600613951683044},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5020573139190674},{"id":"https://openalex.org/keywords/graph-partition","display_name":"Graph partition","score":0.49079856276512146},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.47345229983329773},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.46872055530548096},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2958498001098633},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2778995633125305}],"concepts":[{"id":"https://openalex.org/C157544257","wikidata":"https://www.wikidata.org/wiki/Q866300","display_name":"Bisection method","level":2,"score":0.6692151427268982},{"id":"https://openalex.org/C42812","wikidata":"https://www.wikidata.org/wiki/Q1082910","display_name":"Partition (number theory)","level":2,"score":0.6512314081192017},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.6327031254768372},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6029541492462158},{"id":"https://openalex.org/C31599958","wikidata":"https://www.wikidata.org/wiki/Q3128632","display_name":"Bisection","level":2,"score":0.6021952629089355},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5600613951683044},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5020573139190674},{"id":"https://openalex.org/C48903430","wikidata":"https://www.wikidata.org/wiki/Q491370","display_name":"Graph partition","level":3,"score":0.49079856276512146},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.47345229983329773},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.46872055530548096},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2958498001098633},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2778995633125305},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/2591796.2591852","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2591796.2591852","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-sixth annual ACM symposium on Theory of computing","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G216536116","display_name":null,"funder_award_id":"UMO-2013/09/B/ST6/03136","funder_id":"https://openalex.org/F4320322511","funder_display_name":"Narodowe Centrum Nauki"},{"id":"https://openalex.org/G2761285720","display_name":null,"funder_award_id":"FP/2007-2013","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G5593277320","display_name":null,"funder_award_id":"2007-2013","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G8174586523","display_name":null,"funder_award_id":"267959","funder_id":"https://openalex.org/F4320334960","funder_display_name":"Seventh Framework Programme"},{"id":"https://openalex.org/G8391425800","display_name":null,"funder_award_id":"306992","funder_id":"https://openalex.org/F4320334960","funder_display_name":"Seventh Framework Programme"}],"funders":[{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320322511","display_name":"Narodowe Centrum Nauki","ror":"https://ror.org/03ha2q922"},{"id":"https://openalex.org/F4320323898","display_name":"Bergens Forskningsstiftelse","ror":"https://ror.org/04efaep75"},{"id":"https://openalex.org/F4320334960","display_name":"Seventh Framework Programme","ror":"https://ror.org/00k4n6c32"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":29,"referenced_works":["https://openalex.org/W119774723","https://openalex.org/W1562731796","https://openalex.org/W1571037334","https://openalex.org/W1965012931","https://openalex.org/W1965737603","https://openalex.org/W1981591809","https://openalex.org/W1991651214","https://openalex.org/W1996575062","https://openalex.org/W2003346537","https://openalex.org/W2005079828","https://openalex.org/W2005887911","https://openalex.org/W2031579107","https://openalex.org/W2069572927","https://openalex.org/W2086937160","https://openalex.org/W2088647669","https://openalex.org/W2091264711","https://openalex.org/W2106515361","https://openalex.org/W2106959995","https://openalex.org/W2121641644","https://openalex.org/W2126641717","https://openalex.org/W2129027842","https://openalex.org/W2129939288","https://openalex.org/W2136923206","https://openalex.org/W2157346440","https://openalex.org/W2169528477","https://openalex.org/W2296148711","https://openalex.org/W2798588639","https://openalex.org/W6633814237","https://openalex.org/W6750258011"],"related_works":["https://openalex.org/W2329494729","https://openalex.org/W41290553","https://openalex.org/W3112697985","https://openalex.org/W1986919722","https://openalex.org/W2585516632","https://openalex.org/W2093663313","https://openalex.org/W4296983618","https://openalex.org/W2158390333","https://openalex.org/W40332083","https://openalex.org/W3118962767"],"abstract_inverted_index":{"In":[0,61],"the":[1,57,80,90,121,141],"classic":[2],"Minimum":[3,69,87],"Bisection":[4,70],"problem":[5],"we":[6,64],"are":[7,46],"given":[8],"as":[9],"input":[10],"a":[11,26,96,132],"graph":[12,104],"G":[13,105],"and":[14,35,44,56],"an":[15,66],"integer":[16],"k.":[17],"The":[18],"task":[19],"is":[20,25,79,117],"to":[21],"determine":[22],"whether":[23],"there":[24,45],"partition":[27],"of":[28,92,126,135,140],"V":[29],"(G)":[30],"into":[31,112],"two":[32],"parts":[33,113],"A":[34,55],"B":[36],"such":[37],"that":[38,100,102],"||A|":[39],"--":[40],"|B||":[41],"\u2264":[42],"1":[43],"at":[47],"most":[48],"k":[49],"edges":[50],"with":[51,71],"one":[52],"endpoint":[53],"in":[54,59,120],"other":[58],"B.":[60],"this":[62],"paper":[63],"give":[65],"algorithm":[67,85,94],"for":[68,86],"running":[72],"time":[73],"O(2O(k3)":[74],"n3":[75],"log3":[76],"n).":[77],"This":[78],"first":[81],"fixed":[82],"parameter":[83],"tractable":[84],"Bisection.":[88],"At":[89],"core":[91],"our":[93],"lies":[95],"new":[97],"decomposition":[98],"theorem":[99],"states":[101],"every":[103],"can":[106,129],"be":[107],"decomposed":[108],"by":[109],"small":[110],"separators":[111],"where":[114],"each":[115,138],"part":[116,139],"\"highly":[118],"connected\"":[119],"following":[122],"sense:":[123],"any":[124],"cut":[125],"bounded":[127],"size":[128],"separate":[130],"only":[131],"limited":[133],"number":[134],"vertices":[136],"from":[137],"decomposition.":[142]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":7},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":7}],"updated_date":"2026-07-14T23:27:15.235271","created_date":"2025-10-10T00:00:00"}