{"id":"https://openalex.org/W4399521793","doi":"https://doi.org/10.1145/3618260.3649791","title":"Maximum Weight Independent Set in Graphs with no Long Claws in Quasi-Polynomial Time","display_name":"Maximum Weight Independent Set in Graphs with no Long Claws in Quasi-Polynomial Time","publication_year":2024,"publication_date":"2024-06-10","ids":{"openalex":"https://openalex.org/W4399521793","doi":"https://doi.org/10.1145/3618260.3649791"},"language":"en","primary_location":{"id":"doi:10.1145/3618260.3649791","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3618260.3649791","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/3618260.3649791","source":null,"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 56th Annual ACM Symposium on Theory of Computing","raw_type":"proceedings-article"},"type":"conference-paper","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://dl.acm.org/doi/pdf/10.1145/3618260.3649791","any_repository_has_fulltext":null},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5014907321","display_name":"Peter Gartland","orcid":"https://orcid.org/0000-0001-9249-4930"},"institutions":[{"id":"https://openalex.org/I154570441","display_name":"University of California, Santa Barbara","ror":"https://ror.org/02t274463","country_code":"US","type":"education","lineage":["https://openalex.org/I154570441"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Peter Gartland","raw_affiliation_strings":["University of California, Santa Barbara, USA"],"raw_orcid":"https://orcid.org/0000-0001-9249-4930","affiliations":[{"raw_affiliation_string":"University of California, Santa Barbara, USA","institution_ids":["https://openalex.org/I154570441"]}]},{"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/I154570441","display_name":"University of California, Santa Barbara","ror":"https://ror.org/02t274463","country_code":"US","type":"education","lineage":["https://openalex.org/I154570441"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Daniel Lokshtanov","raw_affiliation_strings":["University of California, Santa Barbara, USA"],"raw_orcid":"https://orcid.org/0000-0002-3166-9212","affiliations":[{"raw_affiliation_string":"University of California, Santa Barbara, USA","institution_ids":["https://openalex.org/I154570441"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5027217082","display_name":"Tom\u00e1\u0161 Masa\u0159\u00edk","orcid":"https://orcid.org/0000-0001-8524-4036"},"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":"Tom\u00e1\u0161 Masa\u0159\u00edk","raw_affiliation_strings":["University of Warsaw, Warsaw, Poland"],"raw_orcid":"https://orcid.org/0000-0001-8524-4036","affiliations":[{"raw_affiliation_string":"University of Warsaw, Warsaw, Poland","institution_ids":["https://openalex.org/I4654613"]}]},{"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/I4654613","display_name":"University of Warsaw","ror":"https://ror.org/039bjqg32","country_code":"PL","type":"education","lineage":["https://openalex.org/I4654613"]},{"id":"https://openalex.org/I83467386","display_name":"IT University of Copenhagen","ror":"https://ror.org/02309jg23","country_code":"DK","type":"education","lineage":["https://openalex.org/I83467386"]}],"countries":["DK","PL"],"is_corresponding":false,"raw_author_name":"Marcin Pilipczuk","raw_affiliation_strings":["University of Warsaw, Warsaw, Poland","University of Warsaw, Warsaw, Poland / IT\u00a0University, Copenhagen, Denmark"],"raw_orcid":"https://orcid.org/0000-0001-5680-7397","affiliations":[{"raw_affiliation_string":"University of Warsaw, Warsaw, Poland","institution_ids":["https://openalex.org/I4654613"]},{"raw_affiliation_string":"University of Warsaw, Warsaw, Poland / IT\u00a0University, Copenhagen, Denmark","institution_ids":["https://openalex.org/I83467386","https://openalex.org/I4654613"]}]},{"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/I4654613","display_name":"University of Warsaw","ror":"https://ror.org/039bjqg32","country_code":"PL","type":"education","lineage":["https://openalex.org/I4654613"]},{"id":"https://openalex.org/I83467386","display_name":"IT University of Copenhagen","ror":"https://ror.org/02309jg23","country_code":"DK","type":"education","lineage":["https://openalex.org/I83467386"]}],"countries":["DK","PL"],"is_corresponding":false,"raw_author_name":"Micha\u0142 Pilipczuk","raw_affiliation_strings":["University of Warsaw, Warsaw, Poland","University of Warsaw, Warsaw, Poland / IT\u00a0University, Copenhagen, Denmark"],"raw_orcid":"https://orcid.org/0000-0001-7891-1988","affiliations":[{"raw_affiliation_string":"University of Warsaw, Warsaw, Poland","institution_ids":["https://openalex.org/I4654613"]},{"raw_affiliation_string":"University of Warsaw, Warsaw, Poland / IT\u00a0University, Copenhagen, Denmark","institution_ids":["https://openalex.org/I83467386","https://openalex.org/I4654613"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5047941027","display_name":"Pawe\u0142 Rz\u0105\u017cewski","orcid":"https://orcid.org/0000-0001-7696-3848"},"institutions":[{"id":"https://openalex.org/I108403487","display_name":"Warsaw University of Technology","ror":"https://ror.org/00y0xnp53","country_code":"PL","type":"education","lineage":["https://openalex.org/I108403487"]},{"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":"Pawe\u0142 Rz\u0105\u017cewski","raw_affiliation_strings":["Warsaw University of Technology, Warsaw, Poland / University of Warsaw, Warsaw, Poland"],"raw_orcid":"https://orcid.org/0000-0001-7696-3848","affiliations":[{"raw_affiliation_string":"Warsaw University of Technology, Warsaw, Poland / University of Warsaw, Warsaw, Poland","institution_ids":["https://openalex.org/I108403487","https://openalex.org/I4654613"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"683","last_page":"691"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","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/T10374","display_name":"Advanced Graph Theory Research","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/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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9944999814033508,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8479855060577393},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6916952729225159},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.5446980595588684},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.5339357256889343},{"id":"https://openalex.org/keywords/induced-path","display_name":"Induced path","score":0.505624532699585},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.46026092767715454},{"id":"https://openalex.org/keywords/chordal-graph","display_name":"Chordal graph","score":0.45098528265953064},{"id":"https://openalex.org/keywords/treewidth","display_name":"Treewidth","score":0.4320811629295349},{"id":"https://openalex.org/keywords/minimum-weight","display_name":"Minimum weight","score":0.42537420988082886},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.4240760803222656},{"id":"https://openalex.org/keywords/pathwidth","display_name":"Pathwidth","score":0.39509475231170654},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.3738061785697937},{"id":"https://openalex.org/keywords/longest-path-problem","display_name":"Longest path problem","score":0.2665763199329376},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.14938586950302124}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8479855060577393},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6916952729225159},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.5446980595588684},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.5339357256889343},{"id":"https://openalex.org/C58228413","wikidata":"https://www.wikidata.org/wiki/Q15704639","display_name":"Induced path","level":5,"score":0.505624532699585},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.46026092767715454},{"id":"https://openalex.org/C160446614","wikidata":"https://www.wikidata.org/wiki/Q1322892","display_name":"Chordal graph","level":3,"score":0.45098528265953064},{"id":"https://openalex.org/C132569581","wikidata":"https://www.wikidata.org/wiki/Q5067368","display_name":"Treewidth","level":5,"score":0.4320811629295349},{"id":"https://openalex.org/C2778945305","wikidata":"https://www.wikidata.org/wiki/Q6865502","display_name":"Minimum weight","level":2,"score":0.42537420988082886},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.4240760803222656},{"id":"https://openalex.org/C43517604","wikidata":"https://www.wikidata.org/wiki/Q7144893","display_name":"Pathwidth","level":4,"score":0.39509475231170654},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.3738061785697937},{"id":"https://openalex.org/C1465435","wikidata":"https://www.wikidata.org/wiki/Q2916352","display_name":"Longest path problem","level":4,"score":0.2665763199329376},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.14938586950302124}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/3618260.3649791","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3618260.3649791","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/3618260.3649791","source":null,"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 56th Annual ACM Symposium on Theory of Computing","raw_type":"proceedings-article"}],"best_oa_location":{"id":"doi:10.1145/3618260.3649791","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3618260.3649791","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/3618260.3649791","source":null,"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 56th Annual ACM Symposium on Theory of Computing","raw_type":"proceedings-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4399521793.pdf"},"referenced_works_count":45,"referenced_works":["https://openalex.org/W116738217","https://openalex.org/W968859509","https://openalex.org/W1963707128","https://openalex.org/W1965412489","https://openalex.org/W1968402726","https://openalex.org/W1983504800","https://openalex.org/W1985733932","https://openalex.org/W1990092116","https://openalex.org/W2001258629","https://openalex.org/W2015311674","https://openalex.org/W2015564725","https://openalex.org/W2061513598","https://openalex.org/W2072480005","https://openalex.org/W2079563996","https://openalex.org/W2081254453","https://openalex.org/W2100432797","https://openalex.org/W2104062785","https://openalex.org/W2113688289","https://openalex.org/W2140079855","https://openalex.org/W2149269894","https://openalex.org/W2156760067","https://openalex.org/W2197961740","https://openalex.org/W2346400836","https://openalex.org/W2401610261","https://openalex.org/W2486237862","https://openalex.org/W2799127232","https://openalex.org/W2914414140","https://openalex.org/W2962704386","https://openalex.org/W2963740725","https://openalex.org/W2964197964","https://openalex.org/W3002749917","https://openalex.org/W3012065254","https://openalex.org/W3114951492","https://openalex.org/W3128980175","https://openalex.org/W3148781234","https://openalex.org/W3166205065","https://openalex.org/W3167580896","https://openalex.org/W3178722822","https://openalex.org/W4205377351","https://openalex.org/W4226048850","https://openalex.org/W4233756358","https://openalex.org/W4234503811","https://openalex.org/W4288701827","https://openalex.org/W4391169607","https://openalex.org/W4399521793"],"related_works":["https://openalex.org/W1511821218","https://openalex.org/W2175868772","https://openalex.org/W239742334","https://openalex.org/W1587078595","https://openalex.org/W2124176527","https://openalex.org/W1480846237","https://openalex.org/W1544821268","https://openalex.org/W1548014395","https://openalex.org/W3037533092","https://openalex.org/W4283803822"],"abstract_inverted_index":{"We":[0,134],"show":[1,135],"that":[2,83,245],"the":[3,53,56,81,84,114,194,228,236,248],"Maximum":[4],"Weight":[5],"Independent":[6],"Set":[7],"problem":[8],"(MWIS)":[9],"can":[10,142],"be":[11,89,113],"solved":[12],"in":[13,60,76,99,143,151,162],"quasi-polynomial":[14,77],"time":[15,145],"on":[16,120,215,247],"H-free":[17],"graphs":[18,62,69],"(graphs":[19],"excluding":[20],"a":[21,37,40,44,131,138,154,181,200,203],"fixed":[22],"graph":[23,115,139],"H":[24,31],"as":[25,103,174,180],"an":[26,106,148,165,222,241],"induced":[27,149],"subgraph)":[28],"for":[29,63,176,178],"every":[30,33],"whose":[32],"connected":[34,184],"component":[35],"is":[36,102,199],"path":[38,129],"or":[39,153,164],"subdivided":[41],"claw":[42],"(i.e.,":[43],"tree":[45],"with":[46,186],"at":[47],"most":[48],"three":[49,118],"leaves).":[50],"This":[51,198],"completes":[52],"dichotomy":[54],"of":[55,58,68,127,158,169,189,196,202,205,230],"complexity":[57],"MWIS":[59,179],"F-free":[61],"any":[64],"finite":[65],"set":[66],"F":[67],"into":[70,130,183],"NP-hard":[71,90],"cases":[72,74,85],"and":[73,79,212],"solvable":[75],"time,":[78],"corroborates":[80],"conjecture":[82],"not":[86],"known":[87],"to":[88],"are":[91],"actually":[92],"polynomial-time":[93],"solvable.":[94],"The":[95],"key":[96],"graph-theoretic":[97],"ingredient":[98],"our":[100],"result":[101,204],"follows.":[104],"Fix":[105],"integer":[107],"t":[108,121],"\u2265":[109],"1.":[110],"Let":[111],"St,t,t":[112,150],"created":[116],"from":[117],"paths":[119],"edges":[122],"by":[123],"identifying":[124],"one":[125,141],"endpoint":[126],"each":[128,187],"single":[132],"vertex.":[133],"that,":[136],"given":[137],"G,":[140,152,163],"polynomial":[144],"find":[146],"either":[147],"balanced":[155],"separator":[156],"consisting":[157],"O(log|V(G)|)":[159,231],"vertex":[160,232],"neighborhoods":[161],"extended":[166,223],"strip":[167,224],"decomposition":[168,172,225],"G":[170],"(a":[171],"almost":[173],"useful":[175],"recursion":[177],"partition":[182],"components)":[185],"particle":[188],"weight":[190,195],"multiplicatively":[191],"smaller":[192],"than":[193],"G.":[197],"strengthening":[201],"Majewski,":[206],"Masa\u0159\u00edk,":[207],"Novotn\u00e1,":[208],"Okrasa,":[209],"Pilipczuk,":[210],"Rz\u0105\u017cewski,":[211],"Soko\u0142owski":[213],"[Transactions":[214],"Computation":[216],"Theory":[217],"\u200d2024]":[218],"which":[219],"provided":[220],"such":[221],"only":[226],"after":[227],"deletion":[229],"neighborhoods.":[233],"To":[234],"reach":[235],"final":[237],"result,":[238],"we":[239],"employ":[240],"involved":[242],"branching":[243],"strategy":[244],"relies":[246],"structural":[249],"lemma":[250],"presented":[251],"above.":[252]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1}],"updated_date":"2026-07-14T23:27:15.235271","created_date":"2025-10-10T00:00:00"}
