{"id":"https://openalex.org/W2164275765","doi":"https://doi.org/10.1109/allerton.2012.6483478","title":"Covering arbitrary point patterns","display_name":"Covering arbitrary point patterns","publication_year":2012,"publication_date":"2012-10-01","ids":{"openalex":"https://openalex.org/W2164275765","doi":"https://doi.org/10.1109/allerton.2012.6483478","mag":"2164275765"},"language":"en","primary_location":{"id":"doi:10.1109/allerton.2012.6483478","is_oa":false,"landing_page_url":"https://doi.org/10.1109/allerton.2012.6483478","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2012 50th Annual Allerton Conference on Communication, Control, and Computing (Allerton)","raw_type":"proceedings-article"},"type":"conference-paper","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/A5051046818","display_name":"Arya Mazumdar","orcid":"https://orcid.org/0000-0003-4605-7996"},"institutions":[{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Arya Mazumdar","raw_affiliation_strings":["Department of EECS / Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of EECS / Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA, USA","institution_ids":["https://openalex.org/I63966007"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101842281","display_name":"Ligong Wang","orcid":"https://orcid.org/0000-0003-2342-4343"},"institutions":[{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Ligong Wang","raw_affiliation_strings":["Department of EECS / Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of EECS / Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA, USA","institution_ids":["https://openalex.org/I63966007"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I63966007"],"apc_list":null,"apc_paid":null,"fwci":0.9538,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.80256269,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":null,"issue":null,"first_page":"2075","last_page":"2080"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T13187","display_name":"Diffusion and Search Dynamics","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},"topics":[{"id":"https://openalex.org/T13187","display_name":"Diffusion and Search Dynamics","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T11830","display_name":"Point processes and geometric inequalities","score":0.9961000084877014,"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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9926000237464905,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/codebook","display_name":"Codebook","score":0.8715424537658691},{"id":"https://openalex.org/keywords/cover","display_name":"Cover (algebra)","score":0.7083491086959839},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6807525753974915},{"id":"https://openalex.org/keywords/lebesgue-measure","display_name":"Lebesgue measure","score":0.675197184085846},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.5523737072944641},{"id":"https://openalex.org/keywords/interval","display_name":"Interval (graph theory)","score":0.5300818681716919},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.5282646417617798},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5274305939674377},{"id":"https://openalex.org/keywords/infinity","display_name":"Infinity","score":0.5193008780479431},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5145809054374695},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.48487982153892517},{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.4509269595146179},{"id":"https://openalex.org/keywords/poisson-distribution","display_name":"Poisson distribution","score":0.44578444957733154},{"id":"https://openalex.org/keywords/lebesgue-integration","display_name":"Lebesgue integration","score":0.38154828548431396},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.26285773515701294},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.24892550706863403},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.14595165848731995},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.09130814671516418},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.07870548963546753}],"concepts":[{"id":"https://openalex.org/C127759330","wikidata":"https://www.wikidata.org/wiki/Q637416","display_name":"Codebook","level":2,"score":0.8715424537658691},{"id":"https://openalex.org/C2780428219","wikidata":"https://www.wikidata.org/wiki/Q16952335","display_name":"Cover (algebra)","level":2,"score":0.7083491086959839},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6807525753974915},{"id":"https://openalex.org/C2777105136","wikidata":"https://www.wikidata.org/wiki/Q827230","display_name":"Lebesgue measure","level":3,"score":0.675197184085846},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.5523737072944641},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.5300818681716919},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.5282646417617798},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5274305939674377},{"id":"https://openalex.org/C7321624","wikidata":"https://www.wikidata.org/wiki/Q205","display_name":"Infinity","level":2,"score":0.5193008780479431},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5145809054374695},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.48487982153892517},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.4509269595146179},{"id":"https://openalex.org/C100906024","wikidata":"https://www.wikidata.org/wiki/Q205692","display_name":"Poisson distribution","level":2,"score":0.44578444957733154},{"id":"https://openalex.org/C14158598","wikidata":"https://www.wikidata.org/wiki/Q853831","display_name":"Lebesgue integration","level":2,"score":0.38154828548431396},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.26285773515701294},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.24892550706863403},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.14595165848731995},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.09130814671516418},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.07870548963546753},{"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},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.0},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/allerton.2012.6483478","is_oa":false,"landing_page_url":"https://doi.org/10.1109/allerton.2012.6483478","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2012 50th Annual Allerton Conference on Communication, Control, and Computing (Allerton)","raw_type":"proceedings-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.395.6001","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.395.6001","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ece.umn.edu/users/arya/papers/adversarial_points.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W1606480398","https://openalex.org/W1608472120","https://openalex.org/W1990992471","https://openalex.org/W1995468345","https://openalex.org/W2050555115","https://openalex.org/W2062460958","https://openalex.org/W2115102992","https://openalex.org/W2131197204","https://openalex.org/W2141811876","https://openalex.org/W2150412388","https://openalex.org/W2155464965","https://openalex.org/W2156254348","https://openalex.org/W2219576505","https://openalex.org/W6679894317"],"related_works":["https://openalex.org/W2074721578","https://openalex.org/W928772053","https://openalex.org/W2917668491","https://openalex.org/W3008743878","https://openalex.org/W4287864225","https://openalex.org/W2963197230","https://openalex.org/W4394649689","https://openalex.org/W3184958942","https://openalex.org/W4244471727","https://openalex.org/W1567236373"],"abstract_inverted_index":{"This":[0],"paper":[1],"considers":[2],"the":[3,18,49,52,56,88,93,96,109,116,118,124,128,131,143],"problem":[4,57,81],"of":[5,14,26,48,82,95,140],"covering":[6],"an":[7,148],"arbitrary":[8],"point":[9],"pattern":[10],"-":[11,22],"a":[12,24,33,45,77,137],"set":[13],"\u03bbT":[15],"points":[16,50,132],"in":[17,51,62,127,147],"interval":[19],"[0,":[20,27],"T]":[21,28],"with":[23],"subset":[25,37,110],"that":[29],"is":[30,38,76,85,111],"drawn":[31],"from":[32],"predefined":[34],"codebook.":[35,97],"The":[36,80],"required":[39,112],"to":[40,86,106,113,122],"contain":[41],"either":[42],"all":[43,60,115],"or":[44],"certain":[46],"proportion":[47],"pattern,":[53],"depending":[54],"on":[55],"setting.":[58],"Also,":[59],"subsets":[61],"this":[63,100],"codebook":[64],"must":[65],"have":[66],"Lebesgue":[67],"measure":[68],"not":[69],"exceeding":[70],"dT":[71],"where":[72,130],"d":[73,91],"\u2264":[74],"1":[75],"given":[78],"constant.":[79],"interest":[83],"here":[84],"find":[87,99],"trade-off":[89,101],"between":[90],"and":[92],"size":[94],"We":[98],"asymptotically":[102],"as":[103,126],"T":[104],"goes":[105],"infinity.":[107],"When":[108],"cover":[114],"points,":[117],"answer":[119],"turns":[120],"out":[121],"be":[123],"same":[125],"case":[129],"were":[133],"randomly":[134],"generated":[135],"by":[136],"Poisson":[138],"process":[139],"intensity":[141],"\u03bb,":[142],"latter":[144],"being":[145],"obtained":[146],"earlier":[149],"work.":[150]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2026-07-29T14:22:42.915294","created_date":"2025-10-10T00:00:00"}
