{"id":"https://openalex.org/W2114804538","doi":"https://doi.org/10.1145/2151171.2151173","title":"Succinct geometric indexes supporting point location queries","display_name":"Succinct geometric indexes supporting point location queries","publication_year":2012,"publication_date":"2012-04-01","ids":{"openalex":"https://openalex.org/W2114804538","doi":"https://doi.org/10.1145/2151171.2151173","mag":"2114804538"},"language":"en","primary_location":{"id":"doi:10.1145/2151171.2151173","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2151171.2151173","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":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://ir.library.carleton.ca/pub/6072","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5013674788","display_name":"Prosenjit Bose","orcid":"https://orcid.org/0000-0002-8906-0573"},"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":true,"raw_author_name":"Prosenjit Bose","raw_affiliation_strings":["Carleton University, Canada"],"affiliations":[{"raw_affiliation_string":"Carleton University, Canada","institution_ids":["https://openalex.org/I67031392"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100731451","display_name":"Eric Chen","orcid":"https://orcid.org/0000-0002-5247-3593"},"institutions":[{"id":"https://openalex.org/I1291425158","display_name":"Google (United States)","ror":"https://ror.org/00njsd438","country_code":"US","type":"company","lineage":["https://openalex.org/I1291425158","https://openalex.org/I4210128969"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Eric Y. Chen","raw_affiliation_strings":["Google Inc., California","Google Inc., California#TAB#"],"affiliations":[{"raw_affiliation_string":"Google Inc., California","institution_ids":["https://openalex.org/I1291425158"]},{"raw_affiliation_string":"Google Inc., California#TAB#","institution_ids":["https://openalex.org/I1291425158"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5009017533","display_name":"Meng He","orcid":"https://orcid.org/0000-0003-0358-7102"},"institutions":[{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Meng He","raw_affiliation_strings":["University of Waterloo, Canada"],"affiliations":[{"raw_affiliation_string":"University of Waterloo, Canada","institution_ids":["https://openalex.org/I151746483"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5103136561","display_name":"Anil Maheshwari","orcid":"https://orcid.org/0000-0002-1274-4598"},"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":"Anil Maheshwari","raw_affiliation_strings":["Carleton University, Canada"],"affiliations":[{"raw_affiliation_string":"Carleton University, Canada","institution_ids":["https://openalex.org/I67031392"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5045902784","display_name":"Pat Morin","orcid":"https://orcid.org/0000-0003-0471-4118"},"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":"Pat Morin","raw_affiliation_strings":["Carleton University, Canada"],"affiliations":[{"raw_affiliation_string":"Carleton University, Canada","institution_ids":["https://openalex.org/I67031392"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5013674788"],"corresponding_institution_ids":["https://openalex.org/I67031392"],"apc_list":null,"apc_paid":null,"fwci":3.5282,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.92501693,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"8","issue":"2","first_page":"1","last_page":"26"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":1.0,"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":1.0,"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":0.9987999796867371,"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/T11269","display_name":"Algorithms and Data Compression","score":0.9976000189781189,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/point-location","display_name":"Point location","score":0.6990451812744141},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.6305716037750244},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5632773041725159},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.539326548576355},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5357391834259033},{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.5201140642166138},{"id":"https://openalex.org/keywords/planar","display_name":"Planar","score":0.45637616515159607},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.44411951303482056},{"id":"https://openalex.org/keywords/line-segment","display_name":"Line segment","score":0.435916543006897},{"id":"https://openalex.org/keywords/computational-geometry","display_name":"Computational geometry","score":0.41585856676101685},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3585357666015625},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.33972281217575073},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.30756473541259766},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.22251546382904053}],"concepts":[{"id":"https://openalex.org/C186750021","wikidata":"https://www.wikidata.org/wiki/Q7208210","display_name":"Point location","level":3,"score":0.6990451812744141},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.6305716037750244},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5632773041725159},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.539326548576355},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5357391834259033},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.5201140642166138},{"id":"https://openalex.org/C134786449","wikidata":"https://www.wikidata.org/wiki/Q3391255","display_name":"Planar","level":2,"score":0.45637616515159607},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.44411951303482056},{"id":"https://openalex.org/C182124507","wikidata":"https://www.wikidata.org/wiki/Q166154","display_name":"Line segment","level":2,"score":0.435916543006897},{"id":"https://openalex.org/C29123130","wikidata":"https://www.wikidata.org/wiki/Q874709","display_name":"Computational geometry","level":2,"score":0.41585856676101685},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3585357666015625},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.33972281217575073},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.30756473541259766},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.22251546382904053},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"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/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1145/2151171.2151173","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2151171.2151173","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:carleton.ca:6072","is_oa":true,"landing_page_url":"https://ir.library.carleton.ca/pub/6072","pdf_url":null,"source":{"id":"https://openalex.org/S4306402514","display_name":"Carleton University's Institutional Repository (MacOdrum Library, Carleton University)","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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ACM Transactions on Algorithms vol. 8 no. 2","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:carleton.ca:6072","is_oa":true,"landing_page_url":"https://ir.library.carleton.ca/pub/6072","pdf_url":null,"source":{"id":"https://openalex.org/S4306402514","display_name":"Carleton University's Institutional Repository (MacOdrum Library, Carleton University)","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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ACM Transactions on Algorithms vol. 8 no. 2","raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":47,"referenced_works":["https://openalex.org/W43719964","https://openalex.org/W73389528","https://openalex.org/W1557435441","https://openalex.org/W1969046465","https://openalex.org/W1971550377","https://openalex.org/W1974033543","https://openalex.org/W1974844978","https://openalex.org/W1974876810","https://openalex.org/W1978294273","https://openalex.org/W1982180670","https://openalex.org/W1985174631","https://openalex.org/W1990921890","https://openalex.org/W2002322113","https://openalex.org/W2011024091","https://openalex.org/W2011297770","https://openalex.org/W2014563459","https://openalex.org/W2035836235","https://openalex.org/W2041808700","https://openalex.org/W2047497406","https://openalex.org/W2056531186","https://openalex.org/W2061916218","https://openalex.org/W2065457428","https://openalex.org/W2068912469","https://openalex.org/W2080845014","https://openalex.org/W2106413026","https://openalex.org/W2113438075","https://openalex.org/W2114400222","https://openalex.org/W2118486794","https://openalex.org/W2120424341","https://openalex.org/W2126876121","https://openalex.org/W2132026455","https://openalex.org/W2134696992","https://openalex.org/W2148659572","https://openalex.org/W2149243190","https://openalex.org/W2149906774","https://openalex.org/W2150580945","https://openalex.org/W2156305878","https://openalex.org/W2161403911","https://openalex.org/W2570771845","https://openalex.org/W2609210027","https://openalex.org/W2609482647","https://openalex.org/W2763207634","https://openalex.org/W2913887712","https://openalex.org/W2914932700","https://openalex.org/W3123513344","https://openalex.org/W4206206918","https://openalex.org/W4252017042"],"related_works":["https://openalex.org/W2107368692","https://openalex.org/W3021181284","https://openalex.org/W1974844978","https://openalex.org/W2011903683","https://openalex.org/W2168320878","https://openalex.org/W2042426695","https://openalex.org/W3037561104","https://openalex.org/W2199106736","https://openalex.org/W2132026455","https://openalex.org/W1575958304"],"abstract_inverted_index":{"We":[0,74,176],"propose":[1],"designing":[2],"data":[3,203],"structures":[4,156,204],"called":[5],"succinct":[6,50,179],"geometric":[7,21,51,180],"indexes":[8,187],"of":[9,29,79,142,152,174,191],"negligible":[10],"space":[11],"(more":[12],"precisely,":[13],"o":[14,107],"(":[15,131,160],"n":[16,31,71,89,92,97,109,161,167,213],")":[17,72,98,110,162,168,214],"bits)":[18],"that":[19,53,157,205],"support":[20,206],"queries":[22,128],"in":[23,33,62,68,106,129,209],"optimal":[24],"time,":[25,136],"by":[26,118],"taking":[27],"advantage":[28],"the":[30,34,113,140,143,149,200],"points":[32],"dataset":[35],"permuted":[36],"and":[37,45,185],"stored":[38],"elsewhere":[39],"as":[40],"a":[41,49,59],"sequence.":[42],"Our":[43],"first":[44,83,201],"main":[46],"result":[47],"is":[48,139],"index":[52,181],"can":[54,124],"answer":[55,125],"point":[56,85,104,126,154,207],"location":[57,86,105,127,155,208],"queries,":[58],"fundamental":[60],"problem":[61],"computational":[63],"geometry,":[64],"on":[65],"planar":[66,183],"triangulations":[67],"O":[69,94,130,159,210],"(lg":[70,95,108,211],"time.":[73,215],"also":[75],"design":[76,186,199],"three":[77],"variants":[78],"this":[80],"index.":[81],"The":[82,101,121],"supports":[84,103],"using":[87],"lg":[88,166],"+":[90,93,133],"2\u221alg":[91],"1/4":[96],"point-line":[99],"comparisons.":[100],"second":[102],"time":[111],"when":[112],"coordinates":[114],"are":[115],"integers":[116],"bounded":[117],"U":[119],".":[120],"last":[122],"variant":[123],"H":[132,138],"1)":[134],"expected":[135],"where":[137],"entropy":[141],"query":[144,150],"distribution.":[145],"These":[146],"results":[147],"match":[148],"efficiency":[151],"previous":[153],"occupy":[158],"words":[163],"or":[164],"O(n":[165],"bits,":[169],"while":[170],"saving":[171],"drastic":[172],"amounts":[173],"space.":[175],"generalize":[177],"our":[178,196],"to":[182,198],"subdivisions,":[184],"for":[188],"other":[189],"types":[190],"queries.":[192],"Finally,":[193],"we":[194],"apply":[195],"techniques":[197],"implicit":[202],"2":[212]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}