{"id":"https://openalex.org/W2568308068","doi":"https://doi.org/10.1137/130920526","title":"Computing the Discrete Fr\u00e9chet Distance in Subquadratic Time","display_name":"Computing the Discrete Fr\u00e9chet Distance in Subquadratic Time","publication_year":2014,"publication_date":"2014-01-01","ids":{"openalex":"https://openalex.org/W2568308068","doi":"https://doi.org/10.1137/130920526","mag":"2568308068"},"language":"en","primary_location":{"id":"doi:10.1137/130920526","is_oa":false,"landing_page_url":"https://doi.org/10.1137/130920526","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/A5043368187","display_name":"Pankaj Agarwal","orcid":"https://orcid.org/0000-0002-1027-2419"},"institutions":[{"id":"https://openalex.org/I170897317","display_name":"Duke University","ror":"https://ror.org/00py81415","country_code":"US","type":"education","lineage":["https://openalex.org/I170897317"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Pankaj K. Agarwal","raw_affiliation_strings":["Department of Computer Science, Box 90129, Duke University, Durham, NC 27708-0129, USA;"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Box 90129, Duke University, Durham, NC 27708-0129, USA;","institution_ids":["https://openalex.org/I170897317"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5054774963","display_name":"Rinat Ben Avraham","orcid":null},"institutions":[{"id":"https://openalex.org/I16391192","display_name":"Tel Aviv University","ror":"https://ror.org/04mhzgx49","country_code":"IL","type":"education","lineage":["https://openalex.org/I16391192"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Rinat Ben Avraham","raw_affiliation_strings":["School of Computer Science, Tel Aviv University, Tel Aviv 69978, Israel;"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Computer Science, Tel Aviv University, Tel Aviv 69978, Israel;","institution_ids":["https://openalex.org/I16391192"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5006699796","display_name":"Haim Kaplan","orcid":"https://orcid.org/0000-0001-9586-8002"},"institutions":[{"id":"https://openalex.org/I16391192","display_name":"Tel Aviv University","ror":"https://ror.org/04mhzgx49","country_code":"IL","type":"education","lineage":["https://openalex.org/I16391192"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Haim Kaplan","raw_affiliation_strings":["School of Computer Science, Tel Aviv University, Tel Aviv 69978, Israel;"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Computer Science, Tel Aviv University, Tel Aviv 69978, Israel;","institution_ids":["https://openalex.org/I16391192"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5055296785","display_name":"Micha Sharir","orcid":"https://orcid.org/0000-0002-2541-3763"},"institutions":[{"id":"https://openalex.org/I16391192","display_name":"Tel Aviv University","ror":"https://ror.org/04mhzgx49","country_code":"IL","type":"education","lineage":["https://openalex.org/I16391192"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Micha Sharir","raw_affiliation_strings":["School of Computer Science, Tel Aviv University, Tel Aviv 69978, Israel;"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Computer Science, Tel Aviv University, Tel Aviv 69978, Israel;","institution_ids":["https://openalex.org/I16391192"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5043368187"],"corresponding_institution_ids":["https://openalex.org/I170897317"],"apc_list":null,"apc_paid":null,"fwci":9.7273,"has_fulltext":false,"cited_by_count":91,"citation_normalized_percentile":{"value":0.98127691,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"43","issue":"2","first_page":"429","last_page":"449"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11269","display_name":"Algorithms and Data Compression","score":1.0,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T11269","display_name":"Algorithms and Data Compression","score":1.0,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T11567","display_name":"semigroups and automata theory","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/T12162","display_name":"Cellular Automata and Applications","score":0.9986000061035156,"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/mathematics","display_name":"Mathematics","score":0.6140590906143188},{"id":"https://openalex.org/keywords/edit-distance","display_name":"Edit distance","score":0.5882819890975952},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5850698947906494},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.5082525610923767},{"id":"https://openalex.org/keywords/backtracking","display_name":"Backtracking","score":0.4795515239238739},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.41966748237609863},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.40285545587539673}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6140590906143188},{"id":"https://openalex.org/C44359876","wikidata":"https://www.wikidata.org/wiki/Q5338467","display_name":"Edit distance","level":2,"score":0.5882819890975952},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5850698947906494},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.5082525610923767},{"id":"https://openalex.org/C156884757","wikidata":"https://www.wikidata.org/wiki/Q798554","display_name":"Backtracking","level":2,"score":0.4795515239238739},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.41966748237609863},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.40285545587539673},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/130920526","is_oa":false,"landing_page_url":"https://doi.org/10.1137/130920526","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/G1227625532","display_name":null,"funder_award_id":"CCF-08-30272","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G3236319302","display_name":null,"funder_award_id":"OEG-P200A070505","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"},{"id":"https://openalex.org/G3622582212","display_name":null,"funder_award_id":"W911NF-08-1","funder_id":"https://openalex.org/F4320338281","funder_display_name":"Army Research Office"},{"id":"https://openalex.org/G5040205760","display_name":null,"funder_award_id":"W911NF-07-1-0376","funder_id":"https://openalex.org/F4320338281","funder_display_name":"Army Research Office"},{"id":"https://openalex.org/G6127234021","display_name":null,"funder_award_id":"W911NF-08-1-0452","funder_id":"https://openalex.org/F4320338281","funder_display_name":"Army Research Office"},{"id":"https://openalex.org/G7452299184","display_name":null,"funder_award_id":"W911NF","funder_id":"https://openalex.org/F4320338281","funder_display_name":"Army Research Office"},{"id":"https://openalex.org/G8291921620","display_name":null,"funder_award_id":"338/09","funder_id":"https://openalex.org/F4320335016","funder_display_name":"Israeli Centers for Research Excellence"},{"id":"https://openalex.org/G8920401428","display_name":null,"funder_award_id":"1P50-GM-08183-01","funder_id":"https://openalex.org/F4320332161","funder_display_name":"National Institutes of Health"},{"id":"https://openalex.org/G8952211519","display_name":null,"funder_award_id":"CCF-09-40671","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320306084","display_name":"U.S. Department of Energy","ror":"https://ror.org/01bj3aw27"},{"id":"https://openalex.org/F4320322596","display_name":"Tel Aviv University","ror":"https://ror.org/04mhzgx49"},{"id":"https://openalex.org/F4320332161","display_name":"National Institutes of Health","ror":"https://ror.org/01cwqze88"},{"id":"https://openalex.org/F4320335016","display_name":"Israeli Centers for Research Excellence","ror":"https://ror.org/03w2v9593"},{"id":"https://openalex.org/F4320338281","display_name":"Army Research Office","ror":"https://ror.org/05epdh915"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W1679675208","https://openalex.org/W1972978715","https://openalex.org/W1974526404","https://openalex.org/W1985655539","https://openalex.org/W1998382219","https://openalex.org/W2008803097","https://openalex.org/W2012010763","https://openalex.org/W2015610842","https://openalex.org/W2016538969","https://openalex.org/W2049647076","https://openalex.org/W2059155916","https://openalex.org/W2083244827","https://openalex.org/W2089092392","https://openalex.org/W2097004206","https://openalex.org/W2124299914","https://openalex.org/W2157734830","https://openalex.org/W2554511021","https://openalex.org/W2570995828","https://openalex.org/W3022326557","https://openalex.org/W4213071546","https://openalex.org/W4301424533"],"related_works":["https://openalex.org/W2760348722","https://openalex.org/W2783885583","https://openalex.org/W2120095724","https://openalex.org/W2368326437","https://openalex.org/W1631221657","https://openalex.org/W2357479099","https://openalex.org/W2364309619","https://openalex.org/W1525406239","https://openalex.org/W2371864976","https://openalex.org/W4245746077"],"abstract_inverted_index":{"The":[0,62,88,153],"Fr\u00e9chet":[1,64,119,155,179],"distance":[2,65,120,156,180],"measures":[3],"similarity":[4],"between":[5,181],"two":[6,22,182],"curves":[7,55,101],"$f$":[8,102],"and":[9,41,69,83,103,116,132],"$g$":[10],"that":[11,77,128],"takes":[12],"into":[13],"account":[14],"the":[15,18,21,27,60,67,99,112,117,122,130,143,147,171,177,187,192,201,211,214,225],"ordering":[16],"of":[17,30,75,94,125,140,150,184,213,224,229],"points":[19,145,149,185],"along":[20,39,45,52],"curves:":[23],"Informally,":[24],"it":[25],"is":[26,121],"minimum":[28,123],"length":[29,124],"a":[31,36,73,126,138,164,217,230],"leash":[32],"required":[33],"to":[34,59,111,135,146,220],"connect":[35],"dog,":[37],"walking":[38,44],"$f$,":[40],"its":[42,70],"owner,":[43],"$g$,":[46],"as":[47,227],"they":[48],"walk":[49],"without":[50,114],"backtracking":[51],"their":[53,151],"respective":[54,100],"from":[56,98,108,142],"one":[57,109],"endpoint":[58],"other.":[61],"discrete":[63,118,154,178],"replaces":[66],"dog":[68],"owner":[71],"by":[72,163],"pair":[74],"frogs":[76,106,131,226],"can":[78,157],"only":[79],"reside":[80],"on":[81],"$m$":[82],"$n$":[84],"specific":[85],"stones,":[86],"respectively.":[87],"stones":[89],"are":[90],"in":[91,160,186,195,200,216],"fact":[92],"sequences":[93,183],"points,":[95],"typically":[96],"sampled":[97],"$g$.":[104],"These":[105],"hop":[107],"stone":[110],"next":[113],"backtracking,":[115],"\u201cleash\u201d":[127],"connects":[129],"allows":[133],"them":[134],"execute":[136],"such":[137],"sequence":[139],"hops":[141],"starting":[144],"terminal":[148],"sequences.":[152],"be":[158],"computed":[159],"$O(mn)$":[161],"time":[162],"straightforward":[165],"dynamic":[166],"programming":[167],"algorithm.":[168],"We":[169],"present":[170],"first":[172],"subquadratic":[173],"algorithm":[174,193],"for":[175],"computing":[176],"plane.":[188],"Assuming":[189],"$m\\le":[190],"n$,":[191],"runs":[194],"$O(\\frac{mn\\log\\log":[196],"n}{\\log":[197],"n})$":[198],"time,":[199],"word":[202],"RAM":[203],"model,":[204],"using":[205],"$O(n)$":[206],"storage.":[207],"Our":[208],"approach":[209],"uses":[210],"geometry":[212],"problem":[215],"subtle":[218],"way":[219],"encode":[221],"legal":[222],"positions":[223],"states":[228],"finite":[231],"automaton.":[232]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":9},{"year":2022,"cited_by_count":9},{"year":2021,"cited_by_count":10},{"year":2020,"cited_by_count":9},{"year":2019,"cited_by_count":11},{"year":2018,"cited_by_count":12},{"year":2017,"cited_by_count":6},{"year":2016,"cited_by_count":5},{"year":2015,"cited_by_count":8},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":2}],"updated_date":"2026-05-11T08:15:01.531666","created_date":"2025-10-10T00:00:00"}