{"id":"https://openalex.org/W3149994998","doi":"https://doi.org/10.1137/20m1355902","title":"An Exponential Time Parameterized Algorithm for Planar Disjoint Paths","display_name":"An Exponential Time Parameterized Algorithm for Planar Disjoint Paths","publication_year":2025,"publication_date":"2025-03-14","ids":{"openalex":"https://openalex.org/W3149994998","doi":"https://doi.org/10.1137/20m1355902","mag":"3149994998"},"language":"en","primary_location":{"id":"doi:10.1137/20m1355902","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1355902","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Computing","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/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":true,"raw_author_name":"Daniel Lokshtanov","raw_affiliation_strings":["Department of Computer Science, University of California, Santa Barbara, CA 93106 USA"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of California, Santa Barbara, CA 93106 USA","institution_ids":["https://openalex.org/I154570441"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5045302816","display_name":"Pranabendu Misra","orcid":"https://orcid.org/0000-0002-7086-5590"},"institutions":[{"id":"https://openalex.org/I19149307","display_name":"Chennai Mathematical Institute","ror":"https://ror.org/04zp24820","country_code":"IN","type":"education","lineage":["https://openalex.org/I19149307"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Pranabendu Misra","raw_affiliation_strings":["Chennai Mathematical Institute, Siruseri, Tamil Nadu 603103, India"],"affiliations":[{"raw_affiliation_string":"Chennai Mathematical Institute, Siruseri, Tamil Nadu 603103, India","institution_ids":["https://openalex.org/I19149307"]}]},{"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":"Michal Pilipczuk","raw_affiliation_strings":["Institute of Informatics, University of Warsaw, Warsaw 02-097, Poland"],"affiliations":[{"raw_affiliation_string":"Institute of Informatics, University of Warsaw, Warsaw 02-097, Poland","institution_ids":["https://openalex.org/I4654613"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5015806060","display_name":"Saket Saurabh","orcid":"https://orcid.org/0000-0001-7847-6402"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Saket Saurabh","raw_affiliation_strings":["The Institute of Mathematical Sciences, HBNI, Chennai, Tamil Nadu 600113, India; University of Bergen, 5007 Bergen, Norway; and IRL 2000 ReLaX, Chennai Mathematical Institute, Siruseri, Tamil Nadu 603103, India"],"affiliations":[{"raw_affiliation_string":"The Institute of Mathematical Sciences, HBNI, Chennai, Tamil Nadu 600113, India; University of Bergen, 5007 Bergen, Norway; and IRL 2000 ReLaX, Chennai Mathematical Institute, Siruseri, Tamil Nadu 603103, India","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5082025487","display_name":"Meirav Zehavi","orcid":"https://orcid.org/0000-0002-3636-5322"},"institutions":[{"id":"https://openalex.org/I124227911","display_name":"Ben-Gurion University of the Negev","ror":"https://ror.org/05tkyf982","country_code":"IL","type":"education","lineage":["https://openalex.org/I124227911"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Meirav Zehavi","raw_affiliation_strings":["Ben-Gurion University, Beersheba, Israel"],"affiliations":[{"raw_affiliation_string":"Ben-Gurion University, Beersheba, Israel","institution_ids":["https://openalex.org/I124227911"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5038531405"],"corresponding_institution_ids":["https://openalex.org/I154570441"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.00143419,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"54","issue":"2","first_page":"321","last_page":"418"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9997000098228455,"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":0.9997000098228455,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9994999766349792,"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":0.9968000054359436,"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":0.744028627872467},{"id":"https://openalex.org/keywords/disjoint-sets","display_name":"Disjoint sets","score":0.6505340337753296},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5355539321899414},{"id":"https://openalex.org/keywords/parameterized-complexity","display_name":"Parameterized complexity","score":0.5301450490951538},{"id":"https://openalex.org/keywords/planar-graph","display_name":"Planar graph","score":0.5198022127151489},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5125748515129089},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.4697364270687103},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.46569952368736267},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.426460862159729},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.363603413105011}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.744028627872467},{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.6505340337753296},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5355539321899414},{"id":"https://openalex.org/C165464430","wikidata":"https://www.wikidata.org/wiki/Q1570441","display_name":"Parameterized complexity","level":2,"score":0.5301450490951538},{"id":"https://openalex.org/C101837359","wikidata":"https://www.wikidata.org/wiki/Q547823","display_name":"Planar graph","level":3,"score":0.5198022127151489},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5125748515129089},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.4697364270687103},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.46569952368736267},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.426460862159729},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.363603413105011}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/20m1355902","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1355902","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Computing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G5082504313","display_name":null,"funder_award_id":"101039913","funder_id":"https://openalex.org/F4320335787","funder_display_name":"Fundamental Research Funds for the Central Universities"},{"id":"https://openalex.org/G5730270640","display_name":null,"funder_award_id":"2018302","funder_id":"https://openalex.org/F4320320950","funder_display_name":"United States-Israel Binational Science Foundation"},{"id":"https://openalex.org/G6623332439","display_name":null,"funder_award_id":"948057","funder_id":"https://openalex.org/F4320335787","funder_display_name":"Fundamental Research Funds for the Central Universities"},{"id":"https://openalex.org/G7225649516","display_name":null,"funder_award_id":"819416","funder_id":"https://openalex.org/F4320335787","funder_display_name":"Fundamental Research Funds for the Central Universities"},{"id":"https://openalex.org/G7702557058","display_name":null,"funder_award_id":"1176/18","funder_id":"https://openalex.org/F4320322252","funder_display_name":"Israel Science Foundation"},{"id":"https://openalex.org/G7996078985","display_name":null,"funder_award_id":"677651","funder_id":"https://openalex.org/F4320335787","funder_display_name":"Fundamental Research Funds for the Central Universities"},{"id":"https://openalex.org/G8190667764","display_name":null,"funder_award_id":"715744","funder_id":"https://openalex.org/F4320335787","funder_display_name":"Fundamental Research Funds for the Central Universities"}],"funders":[{"id":"https://openalex.org/F4320320950","display_name":"United States-Israel Binational Science Foundation","ror":"https://ror.org/00j8z2m73"},{"id":"https://openalex.org/F4320322252","display_name":"Israel Science Foundation","ror":"https://ror.org/04sazxf24"},{"id":"https://openalex.org/F4320335787","display_name":"Fundamental Research Funds for the Central Universities","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":37,"referenced_works":["https://openalex.org/W100926944","https://openalex.org/W594463866","https://openalex.org/W1550254812","https://openalex.org/W1964849735","https://openalex.org/W1967565181","https://openalex.org/W1976463682","https://openalex.org/W2002055996","https://openalex.org/W2005079828","https://openalex.org/W2035409201","https://openalex.org/W2046069847","https://openalex.org/W2050579693","https://openalex.org/W2060632898","https://openalex.org/W2085348754","https://openalex.org/W2112406764","https://openalex.org/W2115589427","https://openalex.org/W2115607023","https://openalex.org/W2158584754","https://openalex.org/W2183582012","https://openalex.org/W2202596972","https://openalex.org/W2253740506","https://openalex.org/W2278828694","https://openalex.org/W2295563127","https://openalex.org/W2297903070","https://openalex.org/W2398655357","https://openalex.org/W2550041253","https://openalex.org/W2563156040","https://openalex.org/W2563767922","https://openalex.org/W2569646339","https://openalex.org/W2785736399","https://openalex.org/W2803460775","https://openalex.org/W2890355536","https://openalex.org/W2962856411","https://openalex.org/W2963908100","https://openalex.org/W2988480584","https://openalex.org/W3149604617","https://openalex.org/W4298227433","https://openalex.org/W4319589071"],"related_works":["https://openalex.org/W2051058708","https://openalex.org/W1494268238","https://openalex.org/W154868527","https://openalex.org/W1983207144","https://openalex.org/W2490706771","https://openalex.org/W2480116122","https://openalex.org/W4255576661","https://openalex.org/W1516574938","https://openalex.org/W2625725254","https://openalex.org/W2040444410"],"abstract_inverted_index":{"In":[0,50,255],"the":[1,5,24,65,73,76,86,105,156,172,178,229,242,247,260],"Disjoint":[2,56,144,200,212,232,244,274,283],"Paths":[3,57,145,201,213,233,245,275],"problem,":[4,246],"input":[6],"is":[7,26,58,72,107,124,138,148,154,209],"an":[8,43,141,191],"undirected":[9,94],"graph":[10,78,136],"$G$":[11,96,111],"on":[12,99,167,206,218,224],"$n$":[13,100],"vertices":[14],"and":[15,23,48,81,97,101,122,164,169,202,221],"a":[16,82,115,131,194,239,268,278],"set":[17],"of":[18,67,75,155,162],"$k$":[19,29,102],"vertex":[20,68],"pairs,":[21],"$\\{s_i,t_i\\}_{i=1}^k$,":[22],"task":[25],"to":[27,35,41,108,139,174,184,189,210,231,236],"find":[28],"pairwise":[30],"vertex-disjoint":[31],"paths":[32],"connecting":[33],"$s_i$":[34],"$t_i$.":[36],"The":[37,160],"problem":[38,134,173],"was":[39],"shown":[40],"have":[42],"$f(k)n^3$":[44],"algorithm":[45,71,88,142,161,192,250,272,280],"by":[46,64,276],"Robertson":[47,163],"Seymour.":[49],"modern":[51],"terminology,":[52],"this":[53,256],"means":[54],"that":[55,125,182],"fixed":[59],"parameter":[60],"tractable":[61],"(FPT),":[62],"parameterized":[63],"number":[66],"pairs.":[69],"This":[70],"cornerstone":[74],"entire":[77],"minor":[79],"theory,":[80],"vital":[83],"ingredient":[84],"in":[85,135,187,214,222],"$g(k)n^3$":[87],"for":[89,143,199,266,273,281],"Minor":[90,204],"Testing":[91],"(given":[92],"two":[93],"graphs,":[95,238],"$H$":[98,113],"vertices,":[103],"respectively,":[104],"objective":[106],"check":[109],"whether":[110],"contains":[112],"as":[114],"minor).":[116],"All":[117],"we":[118,258],"know":[119],"about":[120],"$f$":[121,147,153],"$g$":[123],"these":[126],"are":[127,234],"computable":[128],"functions.":[129],"Thus,":[130,177],"challenging":[132],"open":[133],"algorithms":[137],"devise":[140],"where":[146],"single":[149,195,215,269],"exponential.":[150],"That":[151],"is,":[152],"form":[157],"$2^{{\\sf":[158],"poly}(k)}$.":[159],"Seymour":[165],"relies":[166],"topology":[168],"essentially":[170],"reduces":[171],"surface-embedded":[175,219],"graphs.":[176,226],"first":[179,261],"major":[180],"obstacle":[181],"has":[183,251],"be":[185],"overcome":[186],"order":[188],"get":[190],"with":[193],"exponential":[196,216,270],"running":[197,252],"time":[198,217,253,271],"{\\sf":[203],"Testing}":[205],"general":[207],"graphs":[208,220],"solve":[211],"particular":[223],"planar":[225,237],"Even":[227],"when":[228],"inputs":[230],"restricted":[235],"case":[240],"called":[241],"Planar":[243,282],"best":[248],"known":[249],"$2^{2^{O(k)}}n^2$.":[254],"paper,":[257],"make":[259],"step":[262],"towards":[263],"our":[264],"quest":[265],"designing":[267],"giving":[277],"$2^{O(k^2)}n^{O(1)}$-time":[279],"Paths.":[284]},"counts_by_year":[],"updated_date":"2025-12-28T23:10:05.387466","created_date":"2025-10-10T00:00:00"}