{"id":"https://openalex.org/W2030106244","doi":"https://doi.org/10.1145/1998196.1998264","title":"Covering cubes and the closest vector problem","display_name":"Covering cubes and the closest vector problem","publication_year":2011,"publication_date":"2011-06-13","ids":{"openalex":"https://openalex.org/W2030106244","doi":"https://doi.org/10.1145/1998196.1998264","mag":"2030106244"},"language":"en","primary_location":{"id":"doi:10.1145/1998196.1998264","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1998196.1998264","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-seventh annual symposium on Computational geometry","raw_type":"proceedings-article"},"type":"conference-paper","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://infoscience.epfl.ch/record/163430","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5000598657","display_name":"Friedrich Eisenbrand","orcid":"https://orcid.org/0000-0001-7928-1076"},"institutions":[{"id":"https://openalex.org/I5124864","display_name":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne","ror":"https://ror.org/02s376052","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I5124864"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Friedrich Eisenbrand","raw_affiliation_strings":["\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne, Lausanne, Switzerland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne, Lausanne, Switzerland","institution_ids":["https://openalex.org/I5124864"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5009815551","display_name":"Nicolai H\u00e4hnle","orcid":null},"institutions":[{"id":"https://openalex.org/I5124864","display_name":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne","ror":"https://ror.org/02s376052","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I5124864"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Nicolai H\u00e4hnle","raw_affiliation_strings":["\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne, Lausanne, Switzerland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne, Lausanne, Switzerland","institution_ids":["https://openalex.org/I5124864"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5027003285","display_name":"Martin Niemeier","orcid":null},"institutions":[{"id":"https://openalex.org/I5124864","display_name":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne","ror":"https://ror.org/02s376052","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I5124864"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Martin Niemeier","raw_affiliation_strings":["\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne, Lausanne, Switzerland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne, Lausanne, Switzerland","institution_ids":["https://openalex.org/I5124864"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I5124864"],"apc_list":null,"apc_paid":null,"fwci":2.0021,"has_fulltext":false,"cited_by_count":28,"citation_normalized_percentile":{"value":0.86315106,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":null,"issue":null,"first_page":"417","last_page":"423"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12288","display_name":"Optimization and Search Problems","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/T12288","display_name":"Optimization and Search Problems","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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":0.9991999864578247,"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9987000226974487,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.48069697618484497},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4318598210811615},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3658320903778076}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.48069697618484497},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4318598210811615},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3658320903778076}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1145/1998196.1998264","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1998196.1998264","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-seventh annual symposium on Computational geometry","raw_type":"proceedings-article"},{"id":"pmh:oai:infoscience.tind.io:163430","is_oa":true,"landing_page_url":"http://infoscience.epfl.ch/record/163430","pdf_url":null,"source":{"id":"https://openalex.org/S4306400487","display_name":"Infoscience (Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"conference proceedings"}],"best_oa_location":{"id":"pmh:oai:infoscience.tind.io:163430","is_oa":true,"landing_page_url":"http://infoscience.epfl.ch/record/163430","pdf_url":null,"source":{"id":"https://openalex.org/S4306400487","display_name":"Infoscience (Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"conference proceedings"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W109797903","https://openalex.org/W846986113","https://openalex.org/W1595252626","https://openalex.org/W2000956176","https://openalex.org/W2026129593","https://openalex.org/W2050689197","https://openalex.org/W2070971235","https://openalex.org/W2114616381","https://openalex.org/W2119945951","https://openalex.org/W2157396841","https://openalex.org/W3014312596","https://openalex.org/W3217775779"],"related_works":["https://openalex.org/W2748952813","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W1587224694","https://openalex.org/W2042127053","https://openalex.org/W2142036596"],"abstract_inverted_index":{"We":[0,98],"provide":[1,99],"the":[2,9,15,25,29,39,44,60,81,93,105,108],"currently":[3],"fastest":[4],"randomized":[5],"(1+epsilon)-approximation":[6],"algorithm":[7,47,53],"for":[8,104],"closest":[10],"lattice":[11],"vector":[12],"problem":[13,64],"in":[14,92],"infinity-norm.":[16],"The":[17],"running":[18,41],"time":[19,42],"of":[20,43,59,67,69],"our":[21],"method":[22],"depends":[23],"on":[24,56],"dimension":[26],"n":[27],"and":[28,50],"approximation":[30],"guarantee":[31],"epsilon":[32],"by":[33,48],"2(O(n))":[34],"(log(1/epsilon))(O(n))":[35],"which":[36],"improves":[37],"upon":[38],"(2+1/epsilon)(O(n))":[40],"previously":[45],"best":[46],"Bl\u00f6mer":[49],"Naewe.":[51],"Our":[52],"is":[54,66],"based":[55],"a":[57],"solution":[58],"following":[61],"geometric":[62],"covering":[63],"that":[65],"interest":[68],"its":[70],"own:":[71],"Given":[72],"epsilon>0,":[73],"how":[74],"many":[75],"ellipsoids":[76,89,109],"are":[77,90,110],"necessary":[78],"to":[79,112],"cover":[80],"scaled":[82],"unit":[83,95],"cube":[84,96],"[-1+epsilon,":[85],"1-epsilon]n":[86],"such":[87],"all":[88],"contained":[91],"standard":[94],"[-1,1]n.":[97],"an":[100],"almost":[101],"optimal":[102],"bound":[103],"case":[106],"where":[107],"restricted":[111],"be":[113],"axis-parallel.":[114]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":5},{"year":2016,"cited_by_count":1},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":3}],"updated_date":"2026-07-29T14:22:42.915294","created_date":"2025-10-10T00:00:00"}