{"id":"https://openalex.org/W2063921098","doi":"https://doi.org/10.1137/140952806","title":"Finding a Closest Point in a Lattice of Voronoi's First Kind","display_name":"Finding a Closest Point in a Lattice of Voronoi's First Kind","publication_year":2014,"publication_date":"2014-01-01","ids":{"openalex":"https://openalex.org/W2063921098","doi":"https://doi.org/10.1137/140952806","mag":"2063921098"},"language":"en","primary_location":{"id":"doi:10.1137/140952806","is_oa":false,"landing_page_url":"https://doi.org/10.1137/140952806","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","raw_type":"journal-article"},"type":"article","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/A5018311451","display_name":"Robby G. McKilliam","orcid":"https://orcid.org/0000-0002-7341-8964"},"institutions":[{"id":"https://openalex.org/I170239107","display_name":"University of South Australia","ror":"https://ror.org/01p93h210","country_code":"AU","type":"education","lineage":["https://openalex.org/I170239107"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Robby G. McKilliam","raw_affiliation_strings":["University of South Australia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of South Australia","institution_ids":["https://openalex.org/I170239107"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5072485708","display_name":"Alex Grant","orcid":"https://orcid.org/0000-0002-5345-7771"},"institutions":[{"id":"https://openalex.org/I170239107","display_name":"University of South Australia","ror":"https://ror.org/01p93h210","country_code":"AU","type":"education","lineage":["https://openalex.org/I170239107"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Alex Grant","raw_affiliation_strings":["University of South Australia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of South Australia","institution_ids":["https://openalex.org/I170239107"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5004300153","display_name":"I. Vaughan L. Clarkson","orcid":null},"institutions":[{"id":"https://openalex.org/I165143802","display_name":"The University of Queensland","ror":"https://ror.org/00rqy9422","country_code":"AU","type":"education","lineage":["https://openalex.org/I165143802"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"I. Vaughan L. Clarkson","raw_affiliation_strings":["University of Queensland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Queensland","institution_ids":["https://openalex.org/I165143802"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.7488,"has_fulltext":false,"cited_by_count":14,"citation_normalized_percentile":{"value":0.93200469,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"28","issue":"3","first_page":"1405","last_page":"1422"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9975000023841858,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9975000023841858,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.994700014591217,"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/T10237","display_name":"Cryptography and Data Security","score":0.9944000244140625,"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/voronoi-diagram","display_name":"Voronoi diagram","score":0.81291663646698},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7537108659744263},{"id":"https://openalex.org/keywords/lattice","display_name":"Lattice (music)","score":0.7363858222961426},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6335625648498535},{"id":"https://openalex.org/keywords/series","display_name":"Series (stratigraphy)","score":0.4419041872024536},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4174846112728119},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.4104793071746826},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.16802191734313965}],"concepts":[{"id":"https://openalex.org/C24881265","wikidata":"https://www.wikidata.org/wiki/Q757267","display_name":"Voronoi diagram","level":2,"score":0.81291663646698},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7537108659744263},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.7363858222961426},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6335625648498535},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.4419041872024536},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4174846112728119},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.4104793071746826},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.16802191734313965},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","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/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"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:10.1137/140952806","is_oa":false,"landing_page_url":"https://doi.org/10.1137/140952806","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":56,"referenced_works":["https://openalex.org/W21857574","https://openalex.org/W73629738","https://openalex.org/W151157452","https://openalex.org/W1512015702","https://openalex.org/W1578099820","https://openalex.org/W1589331344","https://openalex.org/W1761303171","https://openalex.org/W1888890775","https://openalex.org/W1964083244","https://openalex.org/W1981326822","https://openalex.org/W1996271812","https://openalex.org/W1997086908","https://openalex.org/W2026129593","https://openalex.org/W2028576516","https://openalex.org/W2029495080","https://openalex.org/W2030065557","https://openalex.org/W2034056530","https://openalex.org/W2036845965","https://openalex.org/W2037426925","https://openalex.org/W2048695439","https://openalex.org/W2058852236","https://openalex.org/W2059504953","https://openalex.org/W2060296335","https://openalex.org/W2065550084","https://openalex.org/W2069278600","https://openalex.org/W2083175934","https://openalex.org/W2088227123","https://openalex.org/W2094837187","https://openalex.org/W2095093213","https://openalex.org/W2096221836","https://openalex.org/W2098170033","https://openalex.org/W2101362102","https://openalex.org/W2105019546","https://openalex.org/W2110400683","https://openalex.org/W2110764235","https://openalex.org/W2111416661","https://openalex.org/W2114616381","https://openalex.org/W2117723531","https://openalex.org/W2119352491","https://openalex.org/W2122621581","https://openalex.org/W2123806189","https://openalex.org/W2127393508","https://openalex.org/W2131392072","https://openalex.org/W2133465710","https://openalex.org/W2140940105","https://openalex.org/W2141040012","https://openalex.org/W2148907454","https://openalex.org/W2149342630","https://openalex.org/W2165523162","https://openalex.org/W2295187311","https://openalex.org/W2340365916","https://openalex.org/W2885882229","https://openalex.org/W3014312596","https://openalex.org/W3145128584","https://openalex.org/W4253905290","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W3020555194","https://openalex.org/W2793256277","https://openalex.org/W2348235448","https://openalex.org/W4360958759","https://openalex.org/W2116218375","https://openalex.org/W2389906634","https://openalex.org/W288156810","https://openalex.org/W176898926","https://openalex.org/W1562406979","https://openalex.org/W2962797788"],"abstract_inverted_index":{"We":[0,50],"show":[1,51],"that":[2,41,52],"for":[3],"those":[4],"lattices":[5],"of":[6,29,37],"Voronoi's":[7],"first":[8],"kind":[9],"with":[10],"known":[11],"obtuse":[12],"superbasis,":[13],"a":[14,35,44,78],"closest":[15,45],"lattice":[16,39,46],"point":[17,47],"can":[18,66],"be":[19,67],"computed":[20,69],"in":[21,63,70,81],"$O(n^4)$":[22],"operations,":[23],"where":[24],"$n$":[25,59],"is":[26,48],"the":[27,30,53,64],"dimension":[28],"lattice.":[31],"To":[32],"achieve":[33],"this":[34],"series":[36,54,65],"relevant":[38],"vectors":[40],"converges":[42,55],"to":[43,76],"found.":[49],"after":[56],"at":[57],"most":[58],"terms.":[60],"Each":[61],"vector":[62],"efficiently":[68],"$O(n^3)$":[71],"operations":[72],"using":[73],"an":[74,82],"algorithm":[75],"compute":[77],"minimum":[79],"cut":[80],"undirected":[83],"flow":[84],"network.":[85]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
