{"id":"https://openalex.org/W4293762729","doi":"https://doi.org/10.1145/3559764","title":"Approximating ( <i>k,\u2113</i> )-Median Clustering for Polygonal Curves","display_name":"Approximating ( <i>k,\u2113</i> )-Median Clustering for Polygonal Curves","publication_year":2022,"publication_date":"2022-08-31","ids":{"openalex":"https://openalex.org/W4293762729","doi":"https://doi.org/10.1145/3559764"},"language":"en","primary_location":{"id":"doi:10.1145/3559764","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3559764","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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":true,"oa_status":"hybrid","oa_url":"https://doi.org/10.1145/3559764","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5086805770","display_name":"Maike Buchin","orcid":"https://orcid.org/0000-0002-3446-4343"},"institutions":[{"id":"https://openalex.org/I904495901","display_name":"Ruhr University Bochum","ror":"https://ror.org/04tsk2644","country_code":"DE","type":"education","lineage":["https://openalex.org/I904495901"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Maike Buchin","raw_affiliation_strings":["Ruhr University Bochum"],"raw_orcid":"https://orcid.org/0000-0002-3446-4343","affiliations":[{"raw_affiliation_string":"Ruhr University Bochum","institution_ids":["https://openalex.org/I904495901"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5017692588","display_name":"Anne Driemel","orcid":"https://orcid.org/0000-0002-1943-2589"},"institutions":[{"id":"https://openalex.org/I135140700","display_name":"University of Bonn","ror":"https://ror.org/041nas322","country_code":"DE","type":"education","lineage":["https://openalex.org/I135140700"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Anne Driemel","raw_affiliation_strings":["University of Bonn"],"raw_orcid":"https://orcid.org/0000-0002-1943-2589","affiliations":[{"raw_affiliation_string":"University of Bonn","institution_ids":["https://openalex.org/I135140700"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5074984665","display_name":"Dennis Rohde","orcid":"https://orcid.org/0000-0001-8984-1962"},"institutions":[{"id":"https://openalex.org/I904495901","display_name":"Ruhr University Bochum","ror":"https://ror.org/04tsk2644","country_code":"DE","type":"education","lineage":["https://openalex.org/I904495901"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Dennis Rohde","raw_affiliation_strings":["Ruhr University Bochum"],"raw_orcid":"https://orcid.org/0000-0001-8984-1962","affiliations":[{"raw_affiliation_string":"Ruhr University Bochum","institution_ids":["https://openalex.org/I904495901"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5086805770"],"corresponding_institution_ids":["https://openalex.org/I904495901"],"apc_list":null,"apc_paid":null,"fwci":0.4464,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.58375719,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"19","issue":"1","first_page":"1","last_page":"32"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11106","display_name":"Data Management and Algorithms","score":0.9983000159263611,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/T11106","display_name":"Data Management and Algorithms","score":0.9983000159263611,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9979000091552734,"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/T12536","display_name":"Topological and Geometric Data Analysis","score":0.9947999715805054,"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/polygonal-chain","display_name":"Polygonal chain","score":0.810269832611084},{"id":"https://openalex.org/keywords/ackermann-function","display_name":"Ackermann function","score":0.8099771738052368},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7445888519287109},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6615817546844482},{"id":"https://openalex.org/keywords/cluster-analysis","display_name":"Cluster analysis","score":0.6312112212181091},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.5043801069259644},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.5033192038536072},{"id":"https://openalex.org/keywords/approximation-algorithm","display_name":"Approximation algorithm","score":0.4975440800189972},{"id":"https://openalex.org/keywords/lemma","display_name":"Lemma (botany)","score":0.49198076128959656},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.37181931734085083},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3584844470024109},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.12918338179588318},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.12652671337127686},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.12467187643051147}],"concepts":[{"id":"https://openalex.org/C182860218","wikidata":"https://www.wikidata.org/wiki/Q633674","display_name":"Polygonal chain","level":3,"score":0.810269832611084},{"id":"https://openalex.org/C33436860","wikidata":"https://www.wikidata.org/wiki/Q341835","display_name":"Ackermann function","level":3,"score":0.8099771738052368},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7445888519287109},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6615817546844482},{"id":"https://openalex.org/C73555534","wikidata":"https://www.wikidata.org/wiki/Q622825","display_name":"Cluster analysis","level":2,"score":0.6312112212181091},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.5043801069259644},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.5033192038536072},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.4975440800189972},{"id":"https://openalex.org/C2777759810","wikidata":"https://www.wikidata.org/wiki/Q149316","display_name":"Lemma (botany)","level":3,"score":0.49198076128959656},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.37181931734085083},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3584844470024109},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.12918338179588318},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.12652671337127686},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.12467187643051147},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.0},{"id":"https://openalex.org/C46757340","wikidata":"https://www.wikidata.org/wiki/Q43238","display_name":"Poaceae","level":2,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"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:10.1145/3559764","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3559764","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Algorithms","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1145/3559764","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3559764","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Algorithms","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":31,"referenced_works":["https://openalex.org/W143174683","https://openalex.org/W1561671573","https://openalex.org/W1568119442","https://openalex.org/W1943383135","https://openalex.org/W1965847996","https://openalex.org/W1984210972","https://openalex.org/W1998871699","https://openalex.org/W2068982516","https://openalex.org/W2083364906","https://openalex.org/W2084616221","https://openalex.org/W2096765209","https://openalex.org/W2108762162","https://openalex.org/W2110105238","https://openalex.org/W2122005371","https://openalex.org/W2124299914","https://openalex.org/W2128859735","https://openalex.org/W2150097763","https://openalex.org/W2572859058","https://openalex.org/W2595959570","https://openalex.org/W2620598837","https://openalex.org/W2810764694","https://openalex.org/W2914959486","https://openalex.org/W2988806372","https://openalex.org/W2990138404","https://openalex.org/W3015122244","https://openalex.org/W3107317566","https://openalex.org/W3107935356","https://openalex.org/W4225613585","https://openalex.org/W4250657332","https://openalex.org/W6640188369","https://openalex.org/W6674201379"],"related_works":["https://openalex.org/W4285827179","https://openalex.org/W4300427481","https://openalex.org/W2797361953","https://openalex.org/W2969539104","https://openalex.org/W2962917430","https://openalex.org/W2028468530","https://openalex.org/W2141882063","https://openalex.org/W4299801389","https://openalex.org/W2039745107","https://openalex.org/W2574604093"],"abstract_inverted_index":{"In":[0,74,198],"2015,":[1],"Driemel,":[2],"Krivo\u0161ija,":[3],"and":[4,91,126,133,173,203],"Sohler":[5],"introduced":[6],"the":[7,16,25,41,63,71,99,110,116,136,149,185,208],"k,\u2113":[8],"-median":[9],"clustering":[10,100,196],"problem":[11,26],"for":[12,85],"polygonal":[13,86,153],"curves":[14,32,49,65,87],"under":[15],"Fr\u00e9chet":[17,44],"distance.":[18],"Given":[19],"a":[20,79,144,152,205],"set":[21],"of":[22,33,43,58,112,119,151,163,167,207,217],"input":[23,48,64],"curves,":[24,113],"asks":[27],"to":[28,50,68,98,193],"find":[29],"k":[30],"median":[31,53,161],"at":[34,169],"most":[35,170],"\u2113":[36],"vertices":[37,120,175],"each":[38],"that":[39,62,83],"minimize":[40],"sum":[42],"distances":[45],"over":[46],"all":[47],"their":[51,59,124],"closest":[52],"curve.":[54],"A":[55],"major":[56],"shortcoming":[57],"algorithm":[60,82,103,209],"is":[61],"are":[66],"restricted":[67],"lie":[69],"on":[70],"real":[72],"line.":[73],"this":[75,141,182],"article,":[76],"we":[77,201],"present":[78],"randomized":[80],"bicriteria-approximation":[81],"works":[84],"in":[88,109,115,128],"\u211d":[89],"d":[90,129],"achieves":[92],"approximation":[93],"factor":[94],"(1+\u025b)":[95],"with":[96,155,184],"respect":[97],"costs.":[101],"The":[102],"has":[104],"worst-case":[105],"running":[106],"time":[107],"linear":[108],"number":[111,118],"polynomial":[114],"maximum":[117],"per":[121],"curve":[122,154,162],"(i.e.,":[123,135],"complexity),":[125],"exponential":[127],",":[130],"\u2113,":[131,165],"1/\u025b":[132],"1/\u03b4":[134],"failure":[137],"probability).":[138],"We":[139,180],"achieve":[140],"result":[142],"through":[143],"shortcutting":[145],"lemma,":[146],"which":[147,214],"guarantees":[148],"existence":[150],"similar":[156],"cost":[157],"as":[158],"an":[159],"optimal":[160],"complexity":[164,168],"but":[166],"2\u2113":[171],"-2,":[172],"whose":[174],"can":[176],"be":[177,216],"computed":[178],"efficiently.":[179],"combine":[181],"lemma":[183],"superset":[186],"sampling":[187],"technique":[188],"by":[189,210],"Kumar":[190],"et":[191,212],"al.":[192],"derive":[194],"our":[195],"result.":[197],"doing":[199],"so,":[200],"describe":[202],"analyze":[204],"generalization":[206],"Ackermann":[211],"al.,":[213],"may":[215],"independent":[218],"interest.":[219]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1}],"updated_date":"2026-04-28T14:05:53.105641","created_date":"2025-10-10T00:00:00"}