{"id":"https://openalex.org/W1982197402","doi":"https://doi.org/10.1145/1064092.1064122","title":"Kinetic sorting and kinetic convex hulls","display_name":"Kinetic sorting and kinetic convex hulls","publication_year":2005,"publication_date":"2005-06-06","ids":{"openalex":"https://openalex.org/W1982197402","doi":"https://doi.org/10.1145/1064092.1064122","mag":"1982197402"},"language":"en","primary_location":{"id":"doi:10.1145/1064092.1064122","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1064092.1064122","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the twenty-first annual symposium on Computational geometry","raw_type":"proceedings-article"},"type":"conference-paper","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/A5017968782","display_name":"Mohammad Ali Abam","orcid":"https://orcid.org/0000-0002-8345-8783"},"institutions":[{"id":"https://openalex.org/I83019370","display_name":"Eindhoven University of Technology","ror":"https://ror.org/02c2kyt77","country_code":"NL","type":"education","lineage":["https://openalex.org/I83019370"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Mohammad Ali Abam","raw_affiliation_strings":["TU Eindhoven","TU, Eindhoven"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"TU Eindhoven","institution_ids":["https://openalex.org/I83019370"]},{"raw_affiliation_string":"TU, Eindhoven","institution_ids":["https://openalex.org/I83019370"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5028410825","display_name":"Mark de Berg","orcid":"https://orcid.org/0000-0001-5770-3784"},"institutions":[{"id":"https://openalex.org/I83019370","display_name":"Eindhoven University of Technology","ror":"https://ror.org/02c2kyt77","country_code":"NL","type":"education","lineage":["https://openalex.org/I83019370"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Mark de Berg","raw_affiliation_strings":["TU Eindhoven","TU, Eindhoven"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"TU Eindhoven","institution_ids":["https://openalex.org/I83019370"]},{"raw_affiliation_string":"TU, Eindhoven","institution_ids":["https://openalex.org/I83019370"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I83019370"],"apc_list":null,"apc_paid":null,"fwci":1.0012,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.72758152,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"190","last_page":"197"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9997000098228455,"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":0.9997000098228455,"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/T11106","display_name":"Data Management and Algorithms","score":0.9994999766349792,"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/T10627","display_name":"Advanced Image and Video Retrieval Techniques","score":0.9958000183105469,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/convex-hull","display_name":"Convex hull","score":0.7686831951141357},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6891571283340454},{"id":"https://openalex.org/keywords/extreme-point","display_name":"Extreme point","score":0.6873611807823181},{"id":"https://openalex.org/keywords/sorting","display_name":"Sorting","score":0.5815683603286743},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.5562312602996826},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.532188892364502},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5236594080924988},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.509007453918457},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.4866224229335785},{"id":"https://openalex.org/keywords/plane","display_name":"Plane (geometry)","score":0.4720141589641571},{"id":"https://openalex.org/keywords/real-line","display_name":"Real line","score":0.45055440068244934},{"id":"https://openalex.org/keywords/convex-set","display_name":"Convex set","score":0.4467059075832367},{"id":"https://openalex.org/keywords/convex-combination","display_name":"Convex combination","score":0.4438720941543579},{"id":"https://openalex.org/keywords/line","display_name":"Line (geometry)","score":0.44019004702568054},{"id":"https://openalex.org/keywords/hull","display_name":"Hull","score":0.43052399158477783},{"id":"https://openalex.org/keywords/kinetic-energy","display_name":"Kinetic energy","score":0.4221554100513458},{"id":"https://openalex.org/keywords/line-segment","display_name":"Line segment","score":0.4152408540248871},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.36071860790252686},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.31228360533714294},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.3039458394050598},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.24486824870109558},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.17766299843788147},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.177433043718338}],"concepts":[{"id":"https://openalex.org/C206194317","wikidata":"https://www.wikidata.org/wiki/Q1138624","display_name":"Convex hull","level":3,"score":0.7686831951141357},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6891571283340454},{"id":"https://openalex.org/C39847760","wikidata":"https://www.wikidata.org/wiki/Q1385465","display_name":"Extreme point","level":2,"score":0.6873611807823181},{"id":"https://openalex.org/C111696304","wikidata":"https://www.wikidata.org/wiki/Q2303697","display_name":"Sorting","level":2,"score":0.5815683603286743},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.5562312602996826},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.532188892364502},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5236594080924988},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.509007453918457},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.4866224229335785},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.4720141589641571},{"id":"https://openalex.org/C75432250","wikidata":"https://www.wikidata.org/wiki/Q29654355","display_name":"Real line","level":2,"score":0.45055440068244934},{"id":"https://openalex.org/C49870271","wikidata":"https://www.wikidata.org/wiki/Q193657","display_name":"Convex set","level":4,"score":0.4467059075832367},{"id":"https://openalex.org/C111110010","wikidata":"https://www.wikidata.org/wiki/Q2627315","display_name":"Convex combination","level":4,"score":0.4438720941543579},{"id":"https://openalex.org/C198352243","wikidata":"https://www.wikidata.org/wiki/Q37105","display_name":"Line (geometry)","level":2,"score":0.44019004702568054},{"id":"https://openalex.org/C37423430","wikidata":"https://www.wikidata.org/wiki/Q6750281","display_name":"Hull","level":2,"score":0.43052399158477783},{"id":"https://openalex.org/C135889238","wikidata":"https://www.wikidata.org/wiki/Q46276","display_name":"Kinetic energy","level":2,"score":0.4221554100513458},{"id":"https://openalex.org/C182124507","wikidata":"https://www.wikidata.org/wiki/Q166154","display_name":"Line segment","level":2,"score":0.4152408540248871},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.36071860790252686},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.31228360533714294},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.3039458394050598},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.24486824870109558},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.17766299843788147},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.177433043718338},{"id":"https://openalex.org/C199104240","wikidata":"https://www.wikidata.org/wiki/Q118291","display_name":"Marine engineering","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.1145/1064092.1064122","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1064092.1064122","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the twenty-first annual symposium on Computational geometry","raw_type":"proceedings-article"},{"id":"pmh:oai:pure.tue.nl:openaire_cris_publications/d07e1862-5c70-4f67-b3e7-bf9646582b0f","is_oa":false,"landing_page_url":"https://research.tue.nl/en/publications/d07e1862-5c70-4f67-b3e7-bf9646582b0f","pdf_url":null,"source":{"id":"https://openalex.org/S4406922641","display_name":"TU/e Research Portal","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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Abam, M A & Berg, de, M 2005, Kinetic sorting and kinetic convex hulls. in J S B Mitchell & G Rote (eds), Proceedings 21st Annual ACM Symposium on Computational Geometry (Pisa, Italy, June 6-8, 2005). Association for Computing Machinery, Inc., New York, pp. 190-197.","raw_type":"info:eu-repo/semantics/conferenceObject"},{"id":"pmh:624379","is_oa":false,"landing_page_url":"http://library.tue.nl/csp/dare/LinkToRepository.csp?recordnumber=624379","pdf_url":null,"source":{"id":"https://openalex.org/S4406922641","display_name":"TU/e Research Portal","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ISSN:0925-7721","raw_type":"Article / Letter to the editor"},{"id":"pmh:oai:library.tue.nl:624379","is_oa":false,"landing_page_url":"http://repository.tue.nl/624379","pdf_url":null,"source":{"id":"https://openalex.org/S4406922641","display_name":"TU/e Research Portal","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ISSN:0925-7721","raw_type":"Article / Letter to the editor"},{"id":"pmh:oai:pure.tue.nl:publications/d07e1862-5c70-4f67-b3e7-bf9646582b0f","is_oa":false,"landing_page_url":"http://doi.acm.org/10.1145/1064092.1064122","pdf_url":null,"source":{"id":"https://openalex.org/S4406922641","display_name":"TU/e Research Portal","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Abam, M A & Berg, de, M 2005, Kinetic sorting and kinetic convex hulls. in J S B Mitchell & G Rote (eds), Proceedings 21st Annual ACM Symposium on Computational Geometry (Pisa, Italy, June 6-8, 2005). Association for Computing Machinery, Inc., New York, pp. 190-197.","raw_type":"info:eu-repo/semantics/conferenceObject"},{"id":"pmh:tue:oai:pure.tue.nl:publications/d07e1862-5c70-4f67-b3e7-bf9646582b0f","is_oa":false,"landing_page_url":"https://research.tue.nl/nl/publications/d07e1862-5c70-4f67-b3e7-bf9646582b0f","pdf_url":null,"source":{"id":"https://openalex.org/S4306401843","display_name":"Data Archiving and Networked Services (DANS)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1322597698","host_organization_name":"Royal Netherlands Academy of Arts and Sciences","host_organization_lineage":["https://openalex.org/I1322597698"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Proceedings 21st Annual ACM Symposium on Computational Geometry (Pisa, Italy, June 6-8, 2005), 190 - 197","raw_type":"info:eu-repo/semantics/conferencepaper"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W243610207","https://openalex.org/W1513818018","https://openalex.org/W1520144421","https://openalex.org/W1537692524","https://openalex.org/W1816717522","https://openalex.org/W1972449607","https://openalex.org/W1979207937","https://openalex.org/W1982042357","https://openalex.org/W1998566446","https://openalex.org/W2011467929","https://openalex.org/W2019186067","https://openalex.org/W2057958932","https://openalex.org/W2058127000","https://openalex.org/W2069716316","https://openalex.org/W2080570254","https://openalex.org/W2086449672","https://openalex.org/W2086474457","https://openalex.org/W2101429492","https://openalex.org/W2103893986","https://openalex.org/W2106136378","https://openalex.org/W2149906774","https://openalex.org/W2170881625","https://openalex.org/W4206231591","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W142701514","https://openalex.org/W2223571892","https://openalex.org/W2391247224","https://openalex.org/W2061565576","https://openalex.org/W2363904277","https://openalex.org/W1992352038","https://openalex.org/W1913561908","https://openalex.org/W2806627627","https://openalex.org/W2793184312","https://openalex.org/W1970905676"],"abstract_inverted_index":{"Let":[0],"S":[1,26,103,126,139,240],"be":[2],"a":[3,20,34,59,92,101,112,116,152,180,231,252],"set":[4,25,102],"of":[5,37,104,132,192,198,213],"n":[6,105],"points":[7,39,107,124,214],"moving":[8,106],"on":[9,23,69,100,128,215],"the":[10,24,38,56,70,75,80,109,129,155,159,189,193,196,199,206,211,216,237,259],"real":[11],"line.":[12],"The":[13,221],"kinetic":[14,93],"sorting":[15],"problem":[16],"is":[17,140,145,188,219,236,242,256],"to":[18,31,73,79,204,226],"maintain":[19],"data":[21,94],"structure":[22,95,222],"that":[27,122,182,241],"makes":[28],"it":[29],"possible":[30],"quickly":[32,209],"generate":[33,74],"sorted":[35,76],"list":[36,77],"in":[40,108,244],"S,":[41],"at":[42],"any":[43,66,163],"given":[44,111],"time.":[45],"We":[46],"prove":[47],"tight":[48],"lower":[49],"bounds":[50],"for":[51,87,96,162],"this":[52],"problem,":[53],"which":[54,135],"show":[55],"following:":[57],"with":[58,165,179],"subquadratic":[60],"maintenance":[61,160],"cost":[62],"one":[63],"cannot":[64],"obtain":[65],"significant":[67],"speed-up":[68],"time":[71,157,178],"needed":[72],"(compared":[78],"trivial":[81],"O(n":[82],"log":[83,175],"n)":[84,176],"time),":[85],"even":[86],"linear":[88],"motions.We":[89],"also":[90,223],"describe":[91],"so-called":[97],"gift-wrapping":[98],"queries":[99,229,250],"plane:":[110],"point":[113,136,238,254],"q":[114,120,257],"and":[115,158,247],"line":[117],"l":[118,144],"through":[119],"such":[121],"all":[123],"from":[125,239],"lie":[127],"same":[130],"side":[131],"l,":[133],"report":[134],"pi":[137],"\u2208":[138],"hit":[141],"first":[142],"when":[143,210],"rotated":[146],"around":[147],"q.":[148],"Our":[149],"KDS":[150,181],"allows":[151,202,224],"trade-off":[153],"between":[154],"query":[156,177,232,253],"cost:":[161],"Q":[164,168],"1":[166],"\u2264":[167,169],"n,":[170],"we":[171],"can":[172],"achieve":[173],"O(Q":[174],"processes":[183],"O(n2+\u03b5/Q1+1/\u03b4)":[184],"events,":[185],"where":[186],"\u03b4":[187],"maximum":[190],"degree":[191],"polynomials":[194],"describing":[195],"motions":[197],"points.":[200],"This":[201],"us":[203,225],"reconstruct":[205],"convex":[207,217,261],"hull":[208,218],"number":[212],"small.":[220],"answer":[227],"extreme-point":[228],"(given":[230,251],"direction":[233,245],"\u20d7d,":[234],"what":[235],"extreme":[243],"\u20d7d?)":[246],"convex-hull":[248],"containment":[249],"q,":[255],"inside":[258],"current":[260],"hull?).":[262]},"counts_by_year":[{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":1}],"updated_date":"2026-07-29T14:22:42.915294","created_date":"2025-10-10T00:00:00"}