{"id":"https://openalex.org/W6944602392","doi":"https://doi.org/10.20382/jocg.v12i2a6","title":"ETH-Tight Algorithms for Long Path and Cycle on Unit Disk Graphs","display_name":"ETH-Tight Algorithms for Long Path and Cycle on Unit Disk Graphs","publication_year":2022,"publication_date":"2022-01-11","ids":{"openalex":"https://openalex.org/W6944602392","doi":"https://doi.org/10.20382/jocg.v12i2a6"},"language":"en","primary_location":{"id":"pmh:oai:ojs.library.carleton.ca:article/3465","is_oa":false,"landing_page_url":"https://jocg.org/index.php/jocg/article/view/3465","pdf_url":null,"source":{"id":"https://openalex.org/S4306400962","display_name":"Journal of Computational Geometry (Carleton University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I67031392","host_organization_name":"Carleton University","host_organization_lineage":["https://openalex.org/I67031392"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Computational Geometry; Vol. 12 No. 2: Special Issue of Selected Papers from SoCG 2020; 126\u2013148","raw_type":"info:eu-repo/semantics/article"},"type":"article","indexed_in":["datacite","doaj"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doaj.org/article/465f74702bff436293bd9cbbe9798178","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Zehavi, Meirav","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zehavi, Meirav","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":null,"display_name":"Fomin, Fedor","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Fomin, Fedor","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":null,"display_name":"Lokshtanov, Daniel","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Lokshtanov, Daniel","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":null,"display_name":"Panolan, Fahad","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Panolan, Fahad","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":null,"display_name":"Saurabh, Saket","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Saurabh, Saket","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.7048,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.81144465,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":96},"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":true,"primary_topic":{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.4390000104904175,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.4390000104904175,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"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":0.27959999442100525,"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":0.06499999761581421,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/unit-disk","display_name":"Unit disk","score":0.49559998512268066},{"id":"https://openalex.org/keywords/tree","display_name":"Tree (set theory)","score":0.46799999475479126},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.44119998812675476},{"id":"https://openalex.org/keywords/tree-decomposition","display_name":"Tree decomposition","score":0.40689998865127563},{"id":"https://openalex.org/keywords/path","display_name":"Path (computing)","score":0.3970000147819519},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.3889000117778778},{"id":"https://openalex.org/keywords/dynamic-programming","display_name":"Dynamic programming","score":0.3840000033378601},{"id":"https://openalex.org/keywords/data-structure","display_name":"Data structure","score":0.36160001158714294},{"id":"https://openalex.org/keywords/kernel","display_name":"Kernel (algebra)","score":0.3310999870300293}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5943999886512756},{"id":"https://openalex.org/C47177299","wikidata":"https://www.wikidata.org/wiki/Q2390323","display_name":"Unit disk","level":2,"score":0.49559998512268066},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4941999912261963},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.46799999475479126},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.44119998812675476},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4392000138759613},{"id":"https://openalex.org/C70501317","wikidata":"https://www.wikidata.org/wiki/Q462095","display_name":"Tree decomposition","level":5,"score":0.40689998865127563},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.3970000147819519},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.3889000117778778},{"id":"https://openalex.org/C37404715","wikidata":"https://www.wikidata.org/wiki/Q380679","display_name":"Dynamic programming","level":2,"score":0.3840000033378601},{"id":"https://openalex.org/C162319229","wikidata":"https://www.wikidata.org/wiki/Q175263","display_name":"Data structure","level":2,"score":0.36160001158714294},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3571999967098236},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.3310999870300293},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.320499986410141},{"id":"https://openalex.org/C122637931","wikidata":"https://www.wikidata.org/wiki/Q118084","display_name":"Unit (ring theory)","level":2,"score":0.30379998683929443},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2985000014305115},{"id":"https://openalex.org/C7356347","wikidata":"https://www.wikidata.org/wiki/Q1307838","display_name":"Unit square","level":2,"score":0.2973000109195709},{"id":"https://openalex.org/C130184317","wikidata":"https://www.wikidata.org/wiki/Q3115549","display_name":"Unit disk graph","level":4,"score":0.29600000381469727},{"id":"https://openalex.org/C187407849","wikidata":"https://www.wikidata.org/wiki/Q6889712","display_name":"Modular decomposition","level":5,"score":0.28949999809265137},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.289000004529953},{"id":"https://openalex.org/C142417499","wikidata":"https://www.wikidata.org/wiki/Q331716","display_name":"Amortized analysis","level":3,"score":0.27390000224113464},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.2727999985218048},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.27160000801086426},{"id":"https://openalex.org/C98779529","wikidata":"https://www.wikidata.org/wiki/Q7650417","display_name":"Suurballe's algorithm","level":5,"score":0.2705000042915344},{"id":"https://openalex.org/C124681953","wikidata":"https://www.wikidata.org/wiki/Q339062","display_name":"Decomposition","level":2,"score":0.26820001006126404},{"id":"https://openalex.org/C1465435","wikidata":"https://www.wikidata.org/wiki/Q2916352","display_name":"Longest path problem","level":4,"score":0.2549000084400177}],"mesh":[],"locations_count":3,"locations":[{"id":"pmh:oai:ojs.library.carleton.ca:article/3465","is_oa":false,"landing_page_url":"https://jocg.org/index.php/jocg/article/view/3465","pdf_url":null,"source":{"id":"https://openalex.org/S4306400962","display_name":"Journal of Computational Geometry (Carleton University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I67031392","host_organization_name":"Carleton University","host_organization_lineage":["https://openalex.org/I67031392"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Computational Geometry; Vol. 12 No. 2: Special Issue of Selected Papers from SoCG 2020; 126\u2013148","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:doaj.org/article:465f74702bff436293bd9cbbe9798178","is_oa":true,"landing_page_url":"https://doaj.org/article/465f74702bff436293bd9cbbe9798178","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal of Computational Geometry, Vol 12, Iss 2 (2022)","raw_type":"article"},{"id":"doi:10.20382/jocg.v12i2a6","is_oa":true,"landing_page_url":"https://doi.org/10.20382/jocg.v12i2a6","pdf_url":null,"source":{"id":"https://openalex.org/S4306400962","display_name":"Journal of Computational Geometry (Carleton University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I67031392","host_organization_name":"Carleton University","host_organization_lineage":["https://openalex.org/I67031392"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"pmh:oai:doaj.org/article:465f74702bff436293bd9cbbe9798178","is_oa":true,"landing_page_url":"https://doaj.org/article/465f74702bff436293bd9cbbe9798178","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal of Computational Geometry, Vol 12, Iss 2 (2022)","raw_type":"article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"We":[0],"present":[1],"an":[2],"algorithm":[3,55,61,99,125,148],"for":[4,62,87],"the":[5,26,59,63,81,88,93,127,138,155,172],"extensively":[6],"studied":[7],"{\\sc":[8,12,30,34,67,103,107],"Long":[9,13,31,35,104,108],"Path}":[10,32,105],"and":[11,33,106],"Cycle}":[14,36,109],"problems":[15],"on":[16,37,100,110,180],"unit":[17,38,111],"disk":[18,39,112],"graphs":[19,40,113],"that":[20],"runs":[21],"in":[22,44,120],"time":[23,45,121],"$2^{O(\\sqrt{k})}(n+m)$.":[24],"Under":[25],"Exponential":[27],"Time":[28],"Hypothesis,":[29],"cannot":[41],"be":[42,118],"solved":[43],"$2^{o(\\sqrt{k})}(n+m)^{O(1)}$":[46],"[de":[47],"Berg":[48,73],"et":[49,74],"al.,":[50],"STOC":[51],"2018],":[52],"hence":[53],"our":[54],"is":[56,92,149],"optimal.":[57],"Besides":[58],"$2^{O(\\sqrt{k})}(n+m)^{O(1)}$-time":[60],"(arguably)":[64],"much":[65],"simpler":[66],"Vertex":[68],"Cover}":[69],"problem":[70,173],"by":[71],"de":[72],"al.~[STOC":[75],"2018]":[76],"(which":[77],"easily":[78],"follows":[79],"from":[80],"existence":[82],"of":[83,129,133,140,157,161,185],"a":[84,130,134,141,167,181],"$2k$-vertex":[85],"kernel":[86],"problem),":[89],"{\\em":[90],"this":[91,158],"only":[94,115],"known":[95,116],"ETH-optimal":[96],"fixed-parameter":[97],"tractable":[98],"UDGs}.":[101],"Previously,":[102],"were":[114],"to":[117,170,174],"solvable":[119],"$2^{O(\\sqrt{k}\\log":[122],"k)}(n+m)$.":[123],"This":[124],"involved":[126],"introduction":[128],"new":[131,159],"type":[132,160],"tree":[135,162,183],"decomposition,":[136],"entailing":[137],"design":[139],"very":[142],"tedious":[143],"dynamic":[144],"programming":[145],"procedure.":[146],"Our":[147],"substantially":[150],"simpler:":[151],"we":[152,165],"completely":[153],"avoid":[154],"use":[156,166],"decomposition.":[163],"Instead,":[164],"marking":[168],"procedure":[169],"reduce":[171],"(a":[175],"weighted":[176],"version":[177],"of)":[178],"itself":[179],"standard":[182],"decomposition":[184],"width":[186],"$O(\\sqrt{k})$.":[187]},"counts_by_year":[{"year":2024,"cited_by_count":2}],"updated_date":"2025-11-06T06:51:31.235846","created_date":"2025-10-10T00:00:00"}