{"id":"https://openalex.org/W2950987206","doi":"https://doi.org/10.1145/3506707","title":"Solving Connectivity Problems Parameterized by Treewidth in Single Exponential Time","display_name":"Solving Connectivity Problems Parameterized by Treewidth in Single Exponential Time","publication_year":2022,"publication_date":"2022-03-04","ids":{"openalex":"https://openalex.org/W2950987206","doi":"https://doi.org/10.1145/3506707","mag":"2950987206"},"language":"en","primary_location":{"id":"doi:10.1145/3506707","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3506707","pdf_url":null,"source":{"id":"https://openalex.org/S137348503","display_name":"ACM Transactions on Algorithms","issn_l":"1549-6325","issn":["1549-6325","1549-6333"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Algorithms","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/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":true,"raw_author_name":"Marek Cygan","raw_affiliation_strings":["University of Warsaw, Warsaw, Poland"],"raw_orcid":"https://orcid.org/0000-0003-2472-2975","affiliations":[{"raw_affiliation_string":"University of Warsaw, Warsaw, Poland","institution_ids":["https://openalex.org/I4654613"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5068357631","display_name":"Jesper Nederlof","orcid":"https://orcid.org/0000-0003-1848-0076"},"institutions":[{"id":"https://openalex.org/I193662353","display_name":"Utrecht University","ror":"https://ror.org/04pp8hn57","country_code":"NL","type":"education","lineage":["https://openalex.org/I193662353"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Jesper Nederlof","raw_affiliation_strings":["Utrecht University, Utrecht, The Netherlands"],"raw_orcid":"https://orcid.org/0000-0003-1848-0076","affiliations":[{"raw_affiliation_string":"Utrecht University, Utrecht, The Netherlands","institution_ids":["https://openalex.org/I193662353"]}]},{"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"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Marcin Pilipczuk","raw_affiliation_strings":["University of Warsaw, Warsaw, Poland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Warsaw, Warsaw, Poland","institution_ids":["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"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Micha\u0142 Pilipczuk","raw_affiliation_strings":["University of Warsaw, Warsaw, Poland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Warsaw, Warsaw, Poland","institution_ids":["https://openalex.org/I4654613"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5055143803","display_name":"Johan M. M. van Rooij","orcid":"https://orcid.org/0000-0001-9149-4162"},"institutions":[{"id":"https://openalex.org/I193662353","display_name":"Utrecht University","ror":"https://ror.org/04pp8hn57","country_code":"NL","type":"education","lineage":["https://openalex.org/I193662353"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Johan M. M. Van Rooij","raw_affiliation_strings":["Utrecht University, Utrecht, The Netherlands"],"raw_orcid":"https://orcid.org/0000-0001-9149-4162","affiliations":[{"raw_affiliation_string":"Utrecht University, Utrecht, The Netherlands","institution_ids":["https://openalex.org/I193662353"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5083165224","display_name":"Jakub Onufry Wojtaszczyk","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jakub Onufry Wojtaszczyk","raw_affiliation_strings":["Google Inc., Warsaw, Poland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Google Inc., Warsaw, Poland","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5037989463"],"corresponding_institution_ids":["https://openalex.org/I4654613"],"apc_list":null,"apc_paid":null,"fwci":3.1678,"has_fulltext":false,"cited_by_count":67,"citation_normalized_percentile":{"value":0.92546268,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"18","issue":"2","first_page":"1","last_page":"31"},"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":0.9993000030517578,"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/T12288","display_name":"Optimization and Search Problems","score":0.9983000159263611,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/treewidth","display_name":"Treewidth","score":0.8751479387283325},{"id":"https://openalex.org/keywords/parameterized-complexity","display_name":"Parameterized complexity","score":0.6525867581367493},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6501046419143677},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5508496761322021},{"id":"https://openalex.org/keywords/exponential-time-hypothesis","display_name":"Exponential time hypothesis","score":0.5475883483886719},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5098230242729187},{"id":"https://openalex.org/keywords/reachability","display_name":"Reachability","score":0.46765202283859253},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.44934260845184326},{"id":"https://openalex.org/keywords/tree-decomposition","display_name":"Tree decomposition","score":0.44640350341796875},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.4318860173225403},{"id":"https://openalex.org/keywords/steiner-tree-problem","display_name":"Steiner tree problem","score":0.4315423369407654},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.4158402681350708},{"id":"https://openalex.org/keywords/pathwidth","display_name":"Pathwidth","score":0.3610815405845642},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.2836666703224182},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.09090402722358704}],"concepts":[{"id":"https://openalex.org/C132569581","wikidata":"https://www.wikidata.org/wiki/Q5067368","display_name":"Treewidth","level":5,"score":0.8751479387283325},{"id":"https://openalex.org/C165464430","wikidata":"https://www.wikidata.org/wiki/Q1570441","display_name":"Parameterized complexity","level":2,"score":0.6525867581367493},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6501046419143677},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5508496761322021},{"id":"https://openalex.org/C71017364","wikidata":"https://www.wikidata.org/wiki/Q5421532","display_name":"Exponential time hypothesis","level":3,"score":0.5475883483886719},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5098230242729187},{"id":"https://openalex.org/C136643341","wikidata":"https://www.wikidata.org/wiki/Q1361526","display_name":"Reachability","level":2,"score":0.46765202283859253},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.44934260845184326},{"id":"https://openalex.org/C70501317","wikidata":"https://www.wikidata.org/wiki/Q462095","display_name":"Tree decomposition","level":5,"score":0.44640350341796875},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.4318860173225403},{"id":"https://openalex.org/C76220878","wikidata":"https://www.wikidata.org/wiki/Q1764144","display_name":"Steiner tree problem","level":2,"score":0.4315423369407654},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.4158402681350708},{"id":"https://openalex.org/C43517604","wikidata":"https://www.wikidata.org/wiki/Q7144893","display_name":"Pathwidth","level":4,"score":0.3610815405845642},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.2836666703224182},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.09090402722358704},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/3506707","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3506707","pdf_url":null,"source":{"id":"https://openalex.org/S137348503","display_name":"ACM Transactions on Algorithms","issn_l":"1549-6325","issn":["1549-6325","1549-6333"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Algorithms","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":85,"referenced_works":["https://openalex.org/W66071877","https://openalex.org/W89448923","https://openalex.org/W143512583","https://openalex.org/W200045149","https://openalex.org/W1493574560","https://openalex.org/W1515822898","https://openalex.org/W1517036688","https://openalex.org/W1517074594","https://openalex.org/W1532197868","https://openalex.org/W1539375795","https://openalex.org/W1542928981","https://openalex.org/W1564399013","https://openalex.org/W1575411448","https://openalex.org/W1579510955","https://openalex.org/W1599026900","https://openalex.org/W1600783214","https://openalex.org/W1787126581","https://openalex.org/W1850475437","https://openalex.org/W1852383912","https://openalex.org/W1968245619","https://openalex.org/W1968952709","https://openalex.org/W1971393213","https://openalex.org/W1976584101","https://openalex.org/W1979312598","https://openalex.org/W1981234161","https://openalex.org/W1983156760","https://openalex.org/W1985061810","https://openalex.org/W1985572324","https://openalex.org/W2002722727","https://openalex.org/W2007985221","https://openalex.org/W2008391796","https://openalex.org/W2009803313","https://openalex.org/W2012438638","https://openalex.org/W2015321560","https://openalex.org/W2021180976","https://openalex.org/W2026036943","https://openalex.org/W2044104853","https://openalex.org/W2045326192","https://openalex.org/W2045749371","https://openalex.org/W2051856222","https://openalex.org/W2058748455","https://openalex.org/W2059273723","https://openalex.org/W2067016370","https://openalex.org/W2067264828","https://openalex.org/W2067431706","https://openalex.org/W2070432726","https://openalex.org/W2076449283","https://openalex.org/W2076461672","https://openalex.org/W2076595213","https://openalex.org/W2080132708","https://openalex.org/W2081414924","https://openalex.org/W2084595628","https://openalex.org/W2087638517","https://openalex.org/W2091977535","https://openalex.org/W2119044694","https://openalex.org/W2120141762","https://openalex.org/W2125350407","https://openalex.org/W2127485201","https://openalex.org/W2130481157","https://openalex.org/W2136595209","https://openalex.org/W2139087151","https://openalex.org/W2151732151","https://openalex.org/W2154399201","https://openalex.org/W2157295389","https://openalex.org/W2163751818","https://openalex.org/W2165094933","https://openalex.org/W2166658560","https://openalex.org/W2184232537","https://openalex.org/W2296469570","https://openalex.org/W2401610261","https://openalex.org/W2508797883","https://openalex.org/W2568031003","https://openalex.org/W2570206580","https://openalex.org/W2596605817","https://openalex.org/W2610479830","https://openalex.org/W2612171860","https://openalex.org/W2913372010","https://openalex.org/W2951007762","https://openalex.org/W2989722117","https://openalex.org/W3002754118","https://openalex.org/W3101258912","https://openalex.org/W4214889528","https://openalex.org/W4238913085","https://openalex.org/W4285719527","https://openalex.org/W4292230561"],"related_works":["https://openalex.org/W2985636744","https://openalex.org/W1587078595","https://openalex.org/W2125058377","https://openalex.org/W1511821218","https://openalex.org/W2027388354","https://openalex.org/W1973972417","https://openalex.org/W1586184743","https://openalex.org/W1485639265","https://openalex.org/W2059372025","https://openalex.org/W2060933875"],"abstract_inverted_index":{"For":[0],"the":[1,26,47,50,64,75,188,204,222,267,272,289,293,306],"vast":[2],"majority":[3],"of":[4,9,28,49,159,240,274,308],"local":[5,14],"problems":[6,68,268,301],"on":[7,148,157],"graphs":[8,153,158],"small":[10],"treewidth":[11,48],"(where,":[12],"by":[13,23,94,258],"we":[15,98,177,199,278,285],"mean":[16],"that":[17,101,182,225,277,302],"a":[18,61,70,96,213],"solution":[19],"can":[20],"be":[21,297],"verified":[22],"checking":[24],"separately":[25],"neighbourhood":[27],"each":[29],"vertex),":[30],"standard":[31],"dynamic":[32,80],"programming":[33,81],"techniques":[34],"give":[35],"c":[36,59,105,164],"tw":[37,45,87,88,106,243,244],"|":[38,40,107,109],"V":[39,108],"O(1)":[41,110],"time":[42,111],"algorithms,":[43],"where":[44],"is":[46,60,168],"input":[51],"graph":[52],"G":[53],"=":[54],"(":[55],"V,E":[56],")":[57],"and":[58,128,145,150,154,173,261],"constant.":[62],"On":[63],"other":[65],"hand,":[66],"for":[67,114,207,247,299],"with":[69,230],"global":[71,235],"requirement":[72],"(usually":[73],"connectivity)":[74],"best\u2013known":[76],"algorithms":[77,113,147,156,167],"were":[78],"naive":[79],"schemes":[82],"running":[83],"in":[84,138,165,169,174],"at":[85,241,270],"least":[86,242],"time.":[89],"We":[90],"bridge":[91],"this":[92],"gap":[93,295],"introducing":[95],"technique":[97],"named":[99],"Cut&amp;Count":[100,281],"allows":[102],"to":[103,180,193,202,232,234,238,266,304],"produce":[104],"Monte-Carlo":[112],"most":[115],"connectivity-type":[116],"problems,":[117],"including":[118],"Hamiltonian":[119],"Path":[120],",":[121,124],"Steiner":[122],"Tree":[123],"Feedback":[125],"Vertex":[126],"Set":[127,131],"Connected":[129],"Dominating":[130],".":[132,314],"These":[133],"results":[134,206,218,252],"have":[135],"numerous":[136],"consequences":[137],"various":[139],"fields,":[140],"like":[141,311],"parameterized":[142],"complexity,":[143],"exact":[144,155],"approximate":[146],"planar":[149],"H":[151],"-minor-free":[152],"bounded":[160],"degree.":[161],"The":[162],"constant":[163],"our":[166,217],"all":[170,196,227,248],"cases":[171,176],"small,":[172],"several":[175],"are":[178,200,219],"able":[179,201],"show":[181,286],"improving":[183],"those":[184],"constants":[185],"would":[186],"cause":[187],"Strong":[189],"Exponential":[190,290],"Time":[191,291],"Hypothesis":[192],"fail.":[194],"In":[195,264],"these":[197,249],"fields":[198],"improve":[203],"best-known":[205],"some":[208,300],"problems.":[209,250],"Also,":[210],"looking":[211],"from":[212],"more":[214],"theoretical":[215],"perspective,":[216],"surprising":[220],"since":[221],"equivalence":[223,245],"relation":[224],"partitions":[226],"partial":[228],"solutions":[229,236],"respect":[231],"extendability":[233],"seems":[237],"consist":[239],"classes":[246],"Our":[251],"answer":[253],"an":[254],"open":[255],"problem":[256],"raised":[257],"Lokshtanov,":[259],"Marx":[260],"Saurabh":[262],"[SODA\u201911].":[263],"contrast":[265],"aimed":[269],"minimizing":[271],"number":[273,307],"connected":[275,309],"components":[276,310],"solve":[279],"using":[280],"as":[282],"mentioned":[283],"above,":[284],"that,":[287],"assuming":[288],"Hypothesis,":[292],"aforementioned":[294],"cannot":[296],"bridged":[298],"aim":[303],"maximize":[305],"Cycle":[312],"Packing":[313]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":7},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":9},{"year":2022,"cited_by_count":3},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":7},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":9},{"year":2016,"cited_by_count":6},{"year":2015,"cited_by_count":6},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":5},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
