{"id":"https://openalex.org/W6925633100","doi":"https://doi.org/10.17877/de290r-22055","title":"On clustering and related problems on curves under the Fr\u00e9chet distance","display_name":"On clustering and related problems on curves under the Fr\u00e9chet distance","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W6925633100","doi":"https://doi.org/10.17877/de290r-22055"},"language":"en","primary_location":{"id":"doi:10.17877/de290r-22055","is_oa":true,"landing_page_url":"https://doi.org/10.17877/de290r-22055","pdf_url":null,"source":{"id":"https://openalex.org/S4306400811","display_name":"Technische Universit\u00e4t Dortmund Eldorado (Technische Universit\u00e4t Dortmund)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210148506","host_organization_name":"Erich-Brost-Institut","host_organization_lineage":["https://openalex.org/I4210148506"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article-journal"},"type":"article","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.17877/de290r-22055","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Krivosija, Amer","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Krivosija, Amer","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.2049,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.66553447,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"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/T12232","display_name":"Yersinia bacterium, plague, ectoparasites research","score":0.2361000031232834,"subfield":{"id":"https://openalex.org/subfields/1311","display_name":"Genetics"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},"topics":[{"id":"https://openalex.org/T12232","display_name":"Yersinia bacterium, plague, ectoparasites research","score":0.2361000031232834,"subfield":{"id":"https://openalex.org/subfields/1311","display_name":"Genetics"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T11684","display_name":"Vibrio bacteria research studies","score":0.17239999771118164,"subfield":{"id":"https://openalex.org/subfields/1310","display_name":"Endocrinology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T12990","display_name":"Medical History and Innovations","score":0.16850000619888306,"subfield":{"id":"https://openalex.org/subfields/1202","display_name":"History"},"field":{"id":"https://openalex.org/fields/12","display_name":"Arts and Humanities"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/cluster-analysis","display_name":"Cluster analysis","score":0.6402999758720398},{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.5848000049591064},{"id":"https://openalex.org/keywords/computational-complexity-theory","display_name":"Computational complexity theory","score":0.48660001158714294},{"id":"https://openalex.org/keywords/cluster","display_name":"Cluster (spacecraft)","score":0.48190000653266907},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4616999924182892},{"id":"https://openalex.org/keywords/approximation-algorithm","display_name":"Approximation algorithm","score":0.4494999945163727},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.41100001335144043},{"id":"https://openalex.org/keywords/computational-geometry","display_name":"Computational geometry","score":0.3921999931335449}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7681000232696533},{"id":"https://openalex.org/C73555534","wikidata":"https://www.wikidata.org/wiki/Q622825","display_name":"Cluster analysis","level":2,"score":0.6402999758720398},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.5848000049591064},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.48660001158714294},{"id":"https://openalex.org/C164866538","wikidata":"https://www.wikidata.org/wiki/Q367351","display_name":"Cluster (spacecraft)","level":2,"score":0.48190000653266907},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4616999924182892},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.46149998903274536},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.4494999945163727},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.41100001335144043},{"id":"https://openalex.org/C29123130","wikidata":"https://www.wikidata.org/wiki/Q874709","display_name":"Computational geometry","level":2,"score":0.3921999931335449},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.39070001244544983},{"id":"https://openalex.org/C192209626","wikidata":"https://www.wikidata.org/wiki/Q190909","display_name":"Focus (optics)","level":2,"score":0.38999998569488525},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.38749998807907104},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3801000118255615},{"id":"https://openalex.org/C2779463800","wikidata":"https://www.wikidata.org/wiki/Q5062222","display_name":"Center (category theory)","level":2,"score":0.3452000021934509},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.313400000333786},{"id":"https://openalex.org/C2777894999","wikidata":"https://www.wikidata.org/wiki/Q4781758","display_name":"Approx","level":2,"score":0.3100999891757965},{"id":"https://openalex.org/C156778621","wikidata":"https://www.wikidata.org/wiki/Q1365748","display_name":"Spectrum (functional analysis)","level":2,"score":0.28929999470710754},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.287200003862381},{"id":"https://openalex.org/C63553672","wikidata":"https://www.wikidata.org/wiki/Q581168","display_name":"Binary logarithm","level":2,"score":0.26269999146461487},{"id":"https://openalex.org/C3017489831","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Running time","level":2,"score":0.2547000050544739},{"id":"https://openalex.org/C145242015","wikidata":"https://www.wikidata.org/wiki/Q774123","display_name":"Approximation theory","level":2,"score":0.25099998712539673}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.17877/de290r-22055","is_oa":true,"landing_page_url":"https://doi.org/10.17877/de290r-22055","pdf_url":null,"source":{"id":"https://openalex.org/S4306400811","display_name":"Technische Universit\u00e4t Dortmund Eldorado (Technische Universit\u00e4t Dortmund)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210148506","host_organization_name":"Erich-Brost-Institut","host_organization_lineage":["https://openalex.org/I4210148506"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"doi:10.17877/de290r-22055","is_oa":true,"landing_page_url":"https://doi.org/10.17877/de290r-22055","pdf_url":null,"source":{"id":"https://openalex.org/S4306400811","display_name":"Technische Universit\u00e4t Dortmund Eldorado (Technische Universit\u00e4t Dortmund)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210148506","host_organization_name":"Erich-Brost-Institut","host_organization_lineage":["https://openalex.org/I4210148506"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article-journal"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Sensor":[0,370],"measurements":[1,371],"can":[2,22,293,372],"be":[3,23],"represented":[4],"as":[5,25,407],"points":[6],"in":[7,29,73,83,97,103,124,139,233,314,333,346,385,401,487,500],"Rd.":[8,386],"Ordered":[9],"by":[10,342,425,514],"the":[11,30,37,43,62,90,95,100,105,109,158,162,178,182,200,208,211,234,250,254,260,266,271,300,305,315,322,352,368,388,397,408,417,422,431,437,446,449,460,481,492,516,526],"time-stamps":[12],"of":[13,36,42,92,94,108,121,127,165,168,184,199,207,302,304,330,382,391,468,503],"these":[14,185],"measurements,":[15],"they":[16],"yield":[17,245],"a":[18,26,67,118,277,343,357,375,383,454,465],"time":[19,231,486],"series,":[20],"that":[21,150,191,443],"interpreted":[24],"polygonal":[27,328],"curve":[28],"d-dimensional":[31],"ambient":[32,85],"space.":[33],"The":[34,286],"number":[35],"vertices":[38],"is":[39,66,117,134,175,187,205],"called":[40,146,284],"complexity":[41,128,153,331],"curve.":[44],"In":[45,157,177],"this":[46],"thesis":[47],"we":[48,215,275,292,435],"study":[49,89,299,396,436],"several":[50],"fundamental":[51],"computational":[52],"tasks":[53],"on":[54,81,281,367,430],"curves:":[55],"clustering,":[56],"sim-":[57],"pli\ufb01cation,":[58],"and":[59,76,112,149,225,241,291,318,364,448,471,489],"embedding,":[60],"under":[61,99,196,253,270,319],"Fr\u00b4echet":[63,101,201,213,256,273,306,324],"distance,":[64,102,202,214,274],"which":[65],"popular":[68],"distance":[69,164,307,325],"measure":[70],"for":[71,221,237,249,265,421,459,480],"curves,":[72],"its":[74,171,427],"continuous":[75,212,272],"discrete":[77,255,323,376],"version.":[78],"We":[79,88,189,297,311,361,395,452,509],"focus":[80],"curves":[82,96,123,138,329,353],"one-dimensional":[84,282],"space":[86,309,403],"R.":[87,156,242,310],"problem":[91,301,400,424,483],"clustering":[93,267],"R":[98],"particular,":[104],"following":[106],"variations":[107],"well-known":[110],"k-center":[111],"k-":[113],"median":[114,441,462],"problems.":[115,451],"Given":[116],"set":[119,440,461],"P":[120,144,169],"n":[122,392],"R,":[125,140],"each":[126,151],"at":[129,154],"most":[130,155],"m.":[131],"Our":[132,243,475],"goal":[133],"to":[135,170,433,496,525],"\ufb01nd":[136],"k":[137,204,240],"not":[141],"necessarily":[142],"from":[143],",":[145],"cluster":[147,173],"centers":[148],"has":[152],"(k,":[159,179,223,226],"R)-center":[160,224],"problem,":[161,181,228,442,463],"maximum":[163],"an":[166,511],"element":[167],"nearest":[172],"center":[174],"minimized.":[176,188],"R)-median":[180,227],"sum":[183],"distances":[186],"show":[190,312,362],"both":[192,197,222,445],"problems":[193,252,499],"are":[194,354],"NP-hard":[195],"versions":[198],"if":[203],"part":[206],"input.":[209],"Under":[210],"give":[216],"(1":[217,261,455,476],"+":[218,262,456,477],"\u03b5)-approximation":[219,263,457,478],"algorithms":[220,248,264],"with":[229,348],"running":[230],"near-linear":[232],"input":[235,389],"size":[236],"constant":[238,349],"\u03b5,":[239],"techniques":[244,470],"constant-factor":[246],"approximation":[247],"observed":[251],"distance.":[257],"To":[258,415],"obtain":[259],"prob-":[268],"lems":[269],"develop":[276],"new":[278],"simpli\ufb01cation":[279],"technique":[280],"curve,":[283],"\u03b4-signature.":[285],"signatures":[287],"al-":[288],"ways":[289],"exist,":[290],"compute":[294],"them":[295],"e\ufb03ciently.":[296],"also":[298,373,405],"embedding":[303],"into":[308],"that,":[313],"worst":[316],"case":[317],"reasonable":[320],"assumptions,":[321],"between":[326],"two":[327],"m":[332,347],"Rd,":[334,404],"where":[335],"2":[336],"\u2264":[337,339],"d":[338,488],"7,":[340],"degrades":[341],"factor":[344],"linear":[345,485],"probability,":[350],"when":[351],"projected":[355],"onto":[356],"randomly":[358],"chosen":[359],"line.":[360],"upper":[363],"lower":[365],"bounds":[366],"distortion.":[369],"de\ufb01ne":[374],"distribution":[377],"over":[378],"possi-":[379],"ble":[380],"locations":[381],"point":[384],"Then,":[387],"consists":[390],"probabilistic":[393,398,409,527],"points.":[394],"1-center":[399,447],"Euclidean":[402],"known":[406],"smallest":[410],"enclosing":[411],"ball":[412],"(pSEB)":[413],"problem.":[414],"improve":[416],"best":[418],"existing":[419],"algorithm":[420,458,479,494],"pSEB":[423,482,493],"reducing":[426],"exponential":[428],"dependence":[429],"dimension":[432,505],"linear,":[434],"determinis-":[438],"tic":[439],"generalizes":[444],"1-median":[450],"present":[453,510],"using":[464,506],"novel":[466],"combination":[467],"sampling":[469],"stochastic":[472],"subgradient":[473],"descent.":[474],"takes":[484],"n,":[490],"making":[491],"applicable":[495],"shape":[497,522],"\ufb01tting":[498,523],"Hilbert":[501],"spaces":[502],"unbounded":[504],"kernel":[507],"functions.":[508],"exemplary":[512],"application":[513],"extending":[515],"support":[517],"vector":[518],"data":[519],"description":[520],"(SVDD)":[521],"method":[524],"case.":[528]},"counts_by_year":[{"year":2022,"cited_by_count":1}],"updated_date":"2025-11-06T06:51:31.235846","created_date":"2025-10-10T00:00:00"}