{"id":"https://openalex.org/W2172249426","doi":"https://doi.org/10.1142/s0218195905001828","title":"A LOWER BOUND FOR LEBESGUE'S UNIVERSAL COVER PROBLEM","display_name":"A LOWER BOUND FOR LEBESGUE'S UNIVERSAL COVER PROBLEM","publication_year":2005,"publication_date":"2005-10-01","ids":{"openalex":"https://openalex.org/W2172249426","doi":"https://doi.org/10.1142/s0218195905001828","mag":"2172249426"},"language":"en","primary_location":{"id":"doi:10.1142/s0218195905001828","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218195905001828","pdf_url":null,"source":{"id":"https://openalex.org/S25827807","display_name":"International Journal of Computational Geometry & Applications","issn_l":"0218-1959","issn":["0218-1959","1793-6357"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computational Geometry &amp; Applications","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/A5021293894","display_name":"Peter Bra\u00df","orcid":"https://orcid.org/0009-0001-0247-8329"},"institutions":[{"id":"https://openalex.org/I125687163","display_name":"City College of New York","ror":"https://ror.org/00wmhkr98","country_code":"US","type":"education","lineage":["https://openalex.org/I125687163"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"PETER BRASS","raw_affiliation_strings":["Department of Computer Science,  City College of New York, 138th Street at Convent Avenue,  New York, NY 10031, USA"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science,  City College of New York, 138th Street at Convent Avenue,  New York, NY 10031, USA","institution_ids":["https://openalex.org/I125687163"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5019884726","display_name":"Mehrbod Sharifi","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"MEHRBOD SHARIFI","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5021293894"],"corresponding_institution_ids":["https://openalex.org/I125687163"],"apc_list":null,"apc_paid":null,"fwci":1.3929,"has_fulltext":false,"cited_by_count":17,"citation_normalized_percentile":{"value":0.80519099,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"15","issue":"05","first_page":"537","last_page":"544"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11830","display_name":"Point processes and geometric inequalities","score":0.996999979019165,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T11830","display_name":"Point processes and geometric inequalities","score":0.996999979019165,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9886000156402588,"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/cover","display_name":"Cover (algebra)","score":0.8674138784408569},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7800359725952148},{"id":"https://openalex.org/keywords/lebesgue-integration","display_name":"Lebesgue integration","score":0.7410502433776855},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.6017507910728455},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.5824210047721863},{"id":"https://openalex.org/keywords/covering-space","display_name":"Covering space","score":0.5433716177940369},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5413361191749573},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5001227855682373},{"id":"https://openalex.org/keywords/set-cover-problem","display_name":"Set cover problem","score":0.46201956272125244},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4216897487640381},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.14706331491470337},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.12533169984817505},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.09836071729660034}],"concepts":[{"id":"https://openalex.org/C2780428219","wikidata":"https://www.wikidata.org/wiki/Q16952335","display_name":"Cover (algebra)","level":2,"score":0.8674138784408569},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7800359725952148},{"id":"https://openalex.org/C14158598","wikidata":"https://www.wikidata.org/wiki/Q853831","display_name":"Lebesgue integration","level":2,"score":0.7410502433776855},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.6017507910728455},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5824210047721863},{"id":"https://openalex.org/C162329640","wikidata":"https://www.wikidata.org/wiki/Q332648","display_name":"Covering space","level":2,"score":0.5433716177940369},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5413361191749573},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5001227855682373},{"id":"https://openalex.org/C100808899","wikidata":"https://www.wikidata.org/wiki/Q1192100","display_name":"Set cover problem","level":3,"score":0.46201956272125244},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4216897487640381},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.14706331491470337},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.12533169984817505},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.09836071729660034},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218195905001828","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218195905001828","pdf_url":null,"source":{"id":"https://openalex.org/S25827807","display_name":"International Journal of Computational Geometry & Applications","issn_l":"0218-1959","issn":["0218-1959","1793-6357"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computational Geometry &amp; Applications","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":8,"referenced_works":["https://openalex.org/W1514016901","https://openalex.org/W1539895965","https://openalex.org/W1595327909","https://openalex.org/W1763364262","https://openalex.org/W2006792557","https://openalex.org/W2018931513","https://openalex.org/W2021425705","https://openalex.org/W2152514307"],"related_works":["https://openalex.org/W2383500046","https://openalex.org/W3145090562","https://openalex.org/W2951839510","https://openalex.org/W384763036","https://openalex.org/W3006241023","https://openalex.org/W2088414519","https://openalex.org/W179341918","https://openalex.org/W3048660185","https://openalex.org/W2163081350","https://openalex.org/W2172249426"],"abstract_inverted_index":{"In":[0],"the":[1,30],"following":[2],"we":[3],"show":[4],"that":[5,9],"any":[6,15],"convex":[7],"set":[8,16],"contains":[10],"a":[11,39],"congruent":[12],"copy":[13],"of":[14,17,41],"diameter":[18],"one":[19],"(universal":[20],"cover)":[21],"has":[22],"area":[23],"at":[24],"least":[25],"0.832.":[26],"This":[27],"considerably":[28],"improves":[29],"lower":[31],"bound":[32],"for":[33],"Lebesgue's":[34],"universal":[35],"cover":[36],"problem,":[37],"using":[38],"combination":[40],"computer":[42],"search":[43],"and":[44],"geometric":[45],"bounds.":[46]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2020,"cited_by_count":3},{"year":2018,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
