{"id":"https://openalex.org/W2141565952","doi":"https://doi.org/10.1145/2229163.2229173","title":"Entropy, triangulation, and point location in planar subdivisions","display_name":"Entropy, triangulation, and point location in planar subdivisions","publication_year":2012,"publication_date":"2012-07-01","ids":{"openalex":"https://openalex.org/W2141565952","doi":"https://doi.org/10.1145/2229163.2229173","mag":"2141565952"},"language":"en","primary_location":{"id":"doi:10.1145/2229163.2229173","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2229163.2229173","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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Algorithms","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/0901.1908","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"S\u00e9bastien Collette","orcid":null},"institutions":[{"id":"https://openalex.org/I132053463","display_name":"Universit\u00e9 Libre de Bruxelles","ror":"https://ror.org/01r9htc13","country_code":"BE","type":"education","lineage":["https://openalex.org/I132053463"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"S\u00e9bastien Collette","raw_affiliation_strings":["Universit\u00e9 Libre de Bruxelles"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universit\u00e9 Libre de Bruxelles","institution_ids":["https://openalex.org/I132053463"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Vida Dujmovi\u0107","orcid":null},"institutions":[{"id":"https://openalex.org/I67031392","display_name":"Carleton University","ror":"https://ror.org/02qtvee93","country_code":"CA","type":"education","lineage":["https://openalex.org/I67031392"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Vida Dujmovi\u0107","raw_affiliation_strings":["Carleton University, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Carleton University, Canada","institution_ids":["https://openalex.org/I67031392"]}]},{"author_position":"middle","author":{"id":null,"display_name":"John Iacono","orcid":null},"institutions":[{"id":"https://openalex.org/I90965887","display_name":"SUNY Polytechnic Institute","ror":"https://ror.org/000fxgx19","country_code":"US","type":"education","lineage":["https://openalex.org/I90965887"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"John Iacono","raw_affiliation_strings":["Polytechnic Institute of NYU, Brooklyn, NY"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Polytechnic Institute of NYU, Brooklyn, NY","institution_ids":["https://openalex.org/I90965887"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Stefan Langerman","orcid":null},"institutions":[{"id":"https://openalex.org/I132053463","display_name":"Universit\u00e9 Libre de Bruxelles","ror":"https://ror.org/01r9htc13","country_code":"BE","type":"education","lineage":["https://openalex.org/I132053463"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"Stefan Langerman","raw_affiliation_strings":["Universit\u00e9 Libre de Bruxelles"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universit\u00e9 Libre de Bruxelles","institution_ids":["https://openalex.org/I132053463"]}]},{"author_position":"last","author":{"id":null,"display_name":"Pat Morin","orcid":null},"institutions":[{"id":"https://openalex.org/I129604602","display_name":"The University of Sydney","ror":"https://ror.org/0384j8v12","country_code":"AU","type":"education","lineage":["https://openalex.org/I129604602"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Pat Morin","raw_affiliation_strings":["Universit\u00e9 Libre de Bruxelles, Natural ICT Australia, University of Sydney, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universit\u00e9 Libre de Bruxelles, Natural ICT Australia, University of Sydney, Canada","institution_ids":["https://openalex.org/I129604602"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.4333,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.87201908,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"8","issue":"3","first_page":"1","last_page":"18"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9223999977111816,"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":0.9223999977111816,"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":0.01590000092983246,"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/T11522","display_name":"VLSI and FPGA Design Techniques","score":0.010700000450015068,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/point-location","display_name":"Point location","score":0.7731999754905701},{"id":"https://openalex.org/keywords/subdivision","display_name":"Subdivision","score":0.7192999720573425},{"id":"https://openalex.org/keywords/triangulation","display_name":"Triangulation","score":0.5658000111579895},{"id":"https://openalex.org/keywords/data-structure","display_name":"Data structure","score":0.5593000054359436},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.5267000198364258},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.5192999839782715},{"id":"https://openalex.org/keywords/preprocessor","display_name":"Preprocessor","score":0.4537000060081482},{"id":"https://openalex.org/keywords/distribution","display_name":"Distribution (mathematics)","score":0.42739999294281006},{"id":"https://openalex.org/keywords/computational-geometry","display_name":"Computational geometry","score":0.42089998722076416}],"concepts":[{"id":"https://openalex.org/C186750021","wikidata":"https://www.wikidata.org/wiki/Q7208210","display_name":"Point location","level":3,"score":0.7731999754905701},{"id":"https://openalex.org/C143392562","wikidata":"https://www.wikidata.org/wiki/Q449111","display_name":"Subdivision","level":2,"score":0.7192999720573425},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5990999937057495},{"id":"https://openalex.org/C135981907","wikidata":"https://www.wikidata.org/wiki/Q188056","display_name":"Triangulation","level":2,"score":0.5658000111579895},{"id":"https://openalex.org/C162319229","wikidata":"https://www.wikidata.org/wiki/Q175263","display_name":"Data structure","level":2,"score":0.5593000054359436},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.5267000198364258},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5192999839782715},{"id":"https://openalex.org/C34736171","wikidata":"https://www.wikidata.org/wiki/Q918333","display_name":"Preprocessor","level":2,"score":0.4537000060081482},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4372999966144562},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.42739999294281006},{"id":"https://openalex.org/C29123130","wikidata":"https://www.wikidata.org/wiki/Q874709","display_name":"Computational geometry","level":2,"score":0.42089998722076416},{"id":"https://openalex.org/C118317068","wikidata":"https://www.wikidata.org/wiki/Q2100760","display_name":"Point distribution model","level":2,"score":0.4196000099182129},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.4172999858856201},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.40959998965263367},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.40959998965263367},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.39329999685287476},{"id":"https://openalex.org/C134786449","wikidata":"https://www.wikidata.org/wiki/Q3391255","display_name":"Planar","level":2,"score":0.3896999955177307},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3544999957084656},{"id":"https://openalex.org/C21080849","wikidata":"https://www.wikidata.org/wiki/Q13611879","display_name":"Data point","level":2,"score":0.3407000005245209},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.302700012922287},{"id":"https://openalex.org/C108882938","wikidata":"https://www.wikidata.org/wiki/Q274506","display_name":"Uniform distribution (continuous)","level":2,"score":0.28850001096725464},{"id":"https://openalex.org/C33721204","wikidata":"https://www.wikidata.org/wiki/Q309949","display_name":"k-d tree","level":3,"score":0.2563999891281128},{"id":"https://openalex.org/C94557470","wikidata":"https://www.wikidata.org/wiki/Q2377385","display_name":"Segment tree","level":5,"score":0.2554999887943268},{"id":"https://openalex.org/C10390562","wikidata":"https://www.wikidata.org/wiki/Q581809","display_name":"Spline (mechanical)","level":2,"score":0.25369998812675476},{"id":"https://openalex.org/C136736807","wikidata":"https://www.wikidata.org/wiki/Q818943","display_name":"Range query (database)","level":5,"score":0.2524999976158142},{"id":"https://openalex.org/C167117609","wikidata":"https://www.wikidata.org/wiki/Q17078161","display_name":"Point set triangulation","level":3,"score":0.25200000405311584}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1145/2229163.2229173","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2229163.2229173","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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Algorithms","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:0901.1908","is_oa":true,"landing_page_url":"http://arxiv.org/abs/0901.1908","pdf_url":"https://arxiv.org/pdf/0901.1908","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:dipot.ulb.ac.be:2013/191468","is_oa":false,"landing_page_url":"http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/191468","pdf_url":null,"source":{"id":"https://openalex.org/S4306401063","display_name":"D\u00e9p\u00f4t institutionnel de l'Universit\u00e9 libre de Bruxelles (Universit\u00e9 Libre de Bruxelles)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I132053463","host_organization_name":"Universit\u00e9 Libre de Bruxelles","host_organization_lineage":["https://openalex.org/I132053463"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ACM transactions on algorithms, 8 (3","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:0901.1908","is_oa":true,"landing_page_url":"http://arxiv.org/abs/0901.1908","pdf_url":"https://arxiv.org/pdf/0901.1908","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3392395684","display_name":null,"funder_award_id":"OISE-0334653 and CCF-0430849","funder_id":"https://openalex.org/F4320337387","funder_display_name":"Division of Computing and Communication Foundations"},{"id":"https://openalex.org/G5499465162","display_name":null,"funder_award_id":"OISE-0334653 and CCF-0430849","funder_id":"https://openalex.org/F4320337370","funder_display_name":"Office of International Science and Engineering"}],"funders":[{"id":"https://openalex.org/F4320337370","display_name":"Office of International Science and Engineering","ror":"https://ror.org/01k638r21"},{"id":"https://openalex.org/F4320337387","display_name":"Division of Computing and Communication Foundations","ror":"https://ror.org/01mng8331"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W1974844978","https://openalex.org/W1998909289","https://openalex.org/W2004389974","https://openalex.org/W2011297770","https://openalex.org/W2041551783","https://openalex.org/W2041808700","https://openalex.org/W2067994867","https://openalex.org/W2068376033","https://openalex.org/W2080845014","https://openalex.org/W2092885083","https://openalex.org/W2126876121","https://openalex.org/W2132026455","https://openalex.org/W2150122711","https://openalex.org/W2150580945","https://openalex.org/W6664576613","https://openalex.org/W6702197583"],"related_works":[],"abstract_inverted_index":{"A":[0],"data":[1,22,63,77,142],"structure":[2,23,64,143],"is":[3,17,30,41,88,99],"presented":[4,42],"for":[5,65,116],"point":[6,61,117],"location":[7,62,118],"in":[8,19,119,131],"connected":[9,46],"planar":[10,47],"subdivisions":[11],"when":[12,79],"the":[13,80,104,122],"distribution":[14,56,124],"of":[15,35,50,71,107,144,159],"queries":[16,81],"known":[18],"advance.":[20],"The":[21,68,127],"has":[24,162],"an":[25,39],"expected":[26,69,105],"query":[27,55,123],"time":[28,138],"that":[29,43,161],"within":[31],"a":[32,45,54,60,100,141,156],"constant":[33],"factor":[34],"optimal.":[36],"More":[37],"specifically,":[38],"algorithm":[40,129],"preprocesses":[44],"subdivision":[48],"G":[49,66,120,160],"size":[51,145],"n":[52,134,136,148],"and":[53,139],"D":[57,86,125],"to":[58,85],"produce":[59],".":[67,126],"number":[70,106],"point-line":[72,108],"comparisons":[73,109],"performed":[74,110],"by":[75,111,154],"this":[76],"structure,":[78],"are":[82,152],"distributed":[83],"according":[84],",":[87],"H\u02dc":[89],"+":[90],"O":[91,132,146],"(H\u02dc":[92],"1/2":[93],"+1)":[94],"where":[95],"H\u02dc=H\u02dc(":[96],"G,D":[97],")":[98,137],"lower":[101],"bound":[102],"on":[103],"any":[112],"linear":[113],"decision":[114],"tree":[115],"under":[121],"preprocessing":[128],"runs":[130],"(":[133,147],"log":[135],"produces":[140],").":[149],"These":[150],"results":[151],"obtained":[153],"creating":[155],"Steiner":[157],"triangulation":[158],"near-minimum":[163],"entropy.":[164]},"counts_by_year":[{"year":2021,"cited_by_count":2},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2016-06-24T00:00:00"}
