{"id":"https://openalex.org/W2959712748","doi":"https://doi.org/10.1515/jmc-2020-0074","title":"Approximate Voronoi cells for lattices, revisited","display_name":"Approximate Voronoi cells for lattices, revisited","publication_year":2020,"publication_date":"2020-11-17","ids":{"openalex":"https://openalex.org/W2959712748","doi":"https://doi.org/10.1515/jmc-2020-0074","mag":"2959712748"},"language":"en","primary_location":{"id":"doi:10.1515/jmc-2020-0074","is_oa":true,"landing_page_url":"https://doi.org/10.1515/jmc-2020-0074","pdf_url":"https://www.degruyter.com/document/doi/10.1515/jmc-2020-0074/pdf","source":{"id":"https://openalex.org/S100611479","display_name":"Journal of Mathematical Cryptology","issn_l":"1862-2976","issn":["1862-2976","1862-2984"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Mathematical Cryptology","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.degruyter.com/document/doi/10.1515/jmc-2020-0074/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5023482258","display_name":"Thijs Laarhoven","orcid":"https://orcid.org/0000-0002-2369-9067"},"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":true,"raw_author_name":"Thijs Laarhoven","raw_affiliation_strings":["Eindhoven University of Technology , Eindhoven , The Netherlands","Eindhoven University of Technology, Eindhoven, The Netherlands"],"affiliations":[{"raw_affiliation_string":"Eindhoven University of Technology , Eindhoven , The Netherlands","institution_ids":["https://openalex.org/I83019370"]},{"raw_affiliation_string":"Eindhoven University of Technology, Eindhoven, The Netherlands","institution_ids":["https://openalex.org/I83019370"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5023482258"],"corresponding_institution_ids":["https://openalex.org/I83019370"],"apc_list":{"value":1000,"currency":"EUR","value_usd":1078},"apc_paid":{"value":1000,"currency":"EUR","value_usd":1078},"fwci":0.1359,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.52218865,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"15","issue":"1","first_page":"60","last_page":"71"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10237","display_name":"Cryptography and Data Security","score":1.0,"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"}},"topics":[{"id":"https://openalex.org/T10237","display_name":"Cryptography and Data Security","score":1.0,"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"}},{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9998000264167786,"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/T12072","display_name":"Machine Learning and Algorithms","score":0.9980000257492065,"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":0.8149219751358032},{"id":"https://openalex.org/keywords/enumeration","display_name":"Enumeration","score":0.6543385982513428},{"id":"https://openalex.org/keywords/heuristic","display_name":"Heuristic","score":0.6352781057357788},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5546942353248596},{"id":"https://openalex.org/keywords/matching","display_name":"Matching (statistics)","score":0.5395711064338684},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.5320530533790588},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4867105782032013},{"id":"https://openalex.org/keywords/preprocessor","display_name":"Preprocessor","score":0.47345322370529175},{"id":"https://openalex.org/keywords/scaling","display_name":"Scaling","score":0.45142310857772827},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.44862842559814453},{"id":"https://openalex.org/keywords/computational-complexity-theory","display_name":"Computational complexity theory","score":0.41619521379470825},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3919506072998047},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.35160213708877563},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.32624542713165283},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.2935255169868469},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.0925913155078888},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.09072324633598328},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.0775509774684906}],"concepts":[{"id":"https://openalex.org/C24881265","wikidata":"https://www.wikidata.org/wiki/Q757267","display_name":"Voronoi diagram","level":2,"score":0.8149219751358032},{"id":"https://openalex.org/C156340839","wikidata":"https://www.wikidata.org/wiki/Q2704791","display_name":"Enumeration","level":2,"score":0.6543385982513428},{"id":"https://openalex.org/C173801870","wikidata":"https://www.wikidata.org/wiki/Q201413","display_name":"Heuristic","level":2,"score":0.6352781057357788},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5546942353248596},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.5395711064338684},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.5320530533790588},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4867105782032013},{"id":"https://openalex.org/C34736171","wikidata":"https://www.wikidata.org/wiki/Q918333","display_name":"Preprocessor","level":2,"score":0.47345322370529175},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.45142310857772827},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.44862842559814453},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.41619521379470825},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3919506072998047},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.35160213708877563},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.32624542713165283},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2935255169868469},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0925913155078888},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.09072324633598328},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0775509774684906},{"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":7,"locations":[{"id":"doi:10.1515/jmc-2020-0074","is_oa":true,"landing_page_url":"https://doi.org/10.1515/jmc-2020-0074","pdf_url":"https://www.degruyter.com/document/doi/10.1515/jmc-2020-0074/pdf","source":{"id":"https://openalex.org/S100611479","display_name":"Journal of Mathematical Cryptology","issn_l":"1862-2976","issn":["1862-2976","1862-2984"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Mathematical Cryptology","raw_type":"journal-article"},{"id":"pmh:oai:pure.tue.nl:openaire/bba51f4b-e4f4-49dd-8779-0a9dbab4439d","is_oa":true,"landing_page_url":"https://research.tue.nl/en/publications/bba51f4b-e4f4-49dd-8779-0a9dbab4439d","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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Laarhoven, T 2021, 'Approximate Voronoi cells for lattices, revisited', Journal of Mathematical Cryptology, vol. 15, no. 1, pp. 60-71. https://doi.org/10.1515/jmc-2020-0074","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:arXiv.org:1907.04630","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1907.04630","pdf_url":"https://arxiv.org/pdf/1907.04630","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":"","raw_type":"text"},{"id":"mag:2959712748","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1907.04630.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:pure.tue.nl:publications/bba51f4b-e4f4-49dd-8779-0a9dbab4439d","is_oa":true,"landing_page_url":"http://www.scopus.com/inward/record.url?scp=85097144448&partnerID=8YFLogxK","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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Laarhoven, T 2021, 'Approximate Voronoi cells for lattices, revisited', Journal of Mathematical Cryptology, vol. 15, no. 1, pp. 60-71. https://doi.org/10.1515/jmc-2020-0074","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:tue:oai:pure.tue.nl:publications/bba51f4b-e4f4-49dd-8779-0a9dbab4439d","is_oa":true,"landing_page_url":"https://research.tue.nl/nl/publications/bba51f4b-e4f4-49dd-8779-0a9dbab4439d","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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal of Mathematical Cryptology, 15(1), 60 - 71. Walter de Gruyter GmbH","raw_type":"info:eu-repo/semantics/article"},{"id":"doi:10.48550/arxiv.1907.04630","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1907.04630","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.1515/jmc-2020-0074","is_oa":true,"landing_page_url":"https://doi.org/10.1515/jmc-2020-0074","pdf_url":"https://www.degruyter.com/document/doi/10.1515/jmc-2020-0074/pdf","source":{"id":"https://openalex.org/S100611479","display_name":"Journal of Mathematical Cryptology","issn_l":"1862-2976","issn":["1862-2976","1862-2984"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Mathematical Cryptology","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G7010378412","display_name":null,"funder_award_id":"016.Veni","funder_id":"https://openalex.org/F4320321800","funder_display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek"},{"id":"https://openalex.org/G8335564440","display_name":null,"funder_award_id":"016.Veni.192.005","funder_id":"https://openalex.org/F4320321800","funder_display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek"}],"funders":[{"id":"https://openalex.org/F4320321800","display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek","ror":"https://ror.org/04jsz6e67"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2959712748.pdf","grobid_xml":"https://content.openalex.org/works/W2959712748.grobid-xml"},"referenced_works_count":45,"referenced_works":["https://openalex.org/W1447686308","https://openalex.org/W1491861813","https://openalex.org/W1496447390","https://openalex.org/W1540698682","https://openalex.org/W1572143270","https://openalex.org/W1572529050","https://openalex.org/W1845765495","https://openalex.org/W1992938819","https://openalex.org/W1996271812","https://openalex.org/W1997002146","https://openalex.org/W2000956176","https://openalex.org/W2010219188","https://openalex.org/W2021907057","https://openalex.org/W2037426925","https://openalex.org/W2040996999","https://openalex.org/W2044180609","https://openalex.org/W2050689197","https://openalex.org/W2061949491","https://openalex.org/W2069278600","https://openalex.org/W2077244027","https://openalex.org/W2101362102","https://openalex.org/W2133083701","https://openalex.org/W2155178472","https://openalex.org/W2160639384","https://openalex.org/W2167382625","https://openalex.org/W2168676717","https://openalex.org/W2268911554","https://openalex.org/W2295744963","https://openalex.org/W2499625922","https://openalex.org/W2601026052","https://openalex.org/W2774544939","https://openalex.org/W2789825276","https://openalex.org/W2794791038","https://openalex.org/W2795008797","https://openalex.org/W2890428003","https://openalex.org/W2916071429","https://openalex.org/W2920734175","https://openalex.org/W2946791252","https://openalex.org/W2949722426","https://openalex.org/W2951649498","https://openalex.org/W2952033682","https://openalex.org/W2959677688","https://openalex.org/W2991397127","https://openalex.org/W3104264786","https://openalex.org/W4297991408"],"related_works":["https://openalex.org/W2244310358","https://openalex.org/W1622655993","https://openalex.org/W2152564789","https://openalex.org/W2764685090","https://openalex.org/W3095065183","https://openalex.org/W2990730306","https://openalex.org/W2982545082","https://openalex.org/W2499957808","https://openalex.org/W1506630368","https://openalex.org/W2055558637","https://openalex.org/W3112211311","https://openalex.org/W2011525357","https://openalex.org/W3002379878","https://openalex.org/W2059273723","https://openalex.org/W1531964914","https://openalex.org/W2997803662","https://openalex.org/W2261727491","https://openalex.org/W2569902587","https://openalex.org/W1911336049","https://openalex.org/W2036686829"],"abstract_inverted_index":{"Abstract":[0],"We":[1,123],"revisit":[2],"the":[3,10,22,35,42,54,58,126,135,138,141,146,188,197],"approximate":[4],"Voronoi":[5,39],"cells":[6,40],"approach":[7,154],"for":[8,196],"solving":[9],"closest":[11,198],"vector":[12,199],"problem":[13,24,128],"with":[14,149],"preprocessing":[15],"(CVPP)":[16],"on":[17,34,53],"high-dimensional":[18],"lattices,":[19],"and":[20,88,140,186],"settle":[21,125],"open":[23,127],"of":[25,30,37,57,129,137],"Doulgerakis\u2013Laarhoven\u2013De":[26],"Weger":[27],"[PQCrypto,":[28],"2019]":[29],"determining":[31],"exact":[32],"asymptotics":[33],"volume":[36],"these":[38],"under":[41],"Gaussian":[43],"heuristic.":[44],"As":[45],"a":[46,131],"result,":[47],"we":[48,89],"obtain":[49,93],"improved":[50],"upper":[51],"bounds":[52],"time":[55,143,147],"complexity":[56,148],"randomized":[59],"iterative":[60],"slicer":[61],"when":[62,97],"using":[63,98],"less":[64,99],"than":[65,100],"<m:math":[66,101,157],"xmlns:m=\"http://www.w3.org/1998/Math/MathML\">":[67,102,158],"<m:msup>":[68,103,159],"<m:mn>2</m:mn>":[69,104,168],"<m:mrow":[70,105,161,164],"class=\"MJX-TeXAtom-ORD\">":[71,106,162,165],"<m:mn>0.076</m:mn>":[72],"<m:mi>d</m:mi>":[73,78,108,113,160,163,173],"<m:mo>+</m:mo>":[74,109,169],"<m:mi>o</m:mi>":[75,110,170],"<m:mo":[76,79,111,114,171,174],"stretchy=\"false\">(</m:mo>":[77,112,172],"stretchy=\"false\">)</m:mo>":[80,115,175],"</m:mrow>":[81,116,167,176],"</m:msup>":[82,117,177],"</m:math>":[83,118,178],"$2^{0.076d":[84],"+":[85,120,180],"o(d)}$":[86,121,181],"memory,":[87],"show":[90],"how":[91],"to":[92],"time\u2013memory":[94],"trade-offs":[95],"even":[96],"<m:mn>0.048</m:mn>":[107],"$2^{0.048d":[119],"memory.":[122],"also":[124],"obtaining":[130],"continuous":[132],"trade-off":[133],"between":[134],"size":[136],"advice":[139,151],"query":[142],"complexity,":[144],"as":[145,156,192],"subexponential":[150],"in":[152],"our":[153],"scales":[155],"<m:mo>/</m:mo>":[166],"$d^{d/2":[179],"matching":[182],"worst-case":[183],"enumeration":[184,194],"bounds,":[185],"achieving":[187],"same":[189],"asymptotic":[190],"scaling":[191],"average-case":[193],"algorithms":[195],"problem.":[200]},"counts_by_year":[{"year":2020,"cited_by_count":1}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}