{"id":"https://openalex.org/W2026109416","doi":"https://doi.org/10.1109/wiopt.2009.5291570","title":"Finite random geometric graphs by circular and square coverage","display_name":"Finite random geometric graphs by circular and square coverage","publication_year":2009,"publication_date":"2009-06-01","ids":{"openalex":"https://openalex.org/W2026109416","doi":"https://doi.org/10.1109/wiopt.2009.5291570","mag":"2026109416"},"language":"en","primary_location":{"id":"doi:10.1109/wiopt.2009.5291570","is_oa":false,"landing_page_url":"https://doi.org/10.1109/wiopt.2009.5291570","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2009 7th International Symposium on Modeling and Optimization in Mobile, Ad Hoc, and Wireless Networks","raw_type":"proceedings-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/A5023916531","display_name":"Chi-Kin Chau","orcid":"https://orcid.org/0000-0003-0362-2844"},"institutions":[{"id":"https://openalex.org/I241749","display_name":"University of Cambridge","ror":"https://ror.org/013meh722","country_code":"GB","type":"education","lineage":["https://openalex.org/I241749"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Chi-Kin Chau","raw_affiliation_strings":["University of Cambridge, UK","Univ. Of Cambridge, UK"],"affiliations":[{"raw_affiliation_string":"University of Cambridge, UK","institution_ids":["https://openalex.org/I241749"]},{"raw_affiliation_string":"Univ. Of Cambridge, UK","institution_ids":["https://openalex.org/I241749"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5023916531"],"corresponding_institution_ids":["https://openalex.org/I241749"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.11644075,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"1","last_page":"8"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10246","display_name":"Mobile Ad Hoc Networks","score":0.9980999827384949,"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/T10246","display_name":"Mobile Ad Hoc Networks","score":0.9980999827384949,"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/T14445","display_name":"Transportation Safety and Impact Analysis","score":0.9731000065803528,"subfield":{"id":"https://openalex.org/subfields/2205","display_name":"Civil and Structural Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10069","display_name":"Antenna Design and Analysis","score":0.9679999947547913,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/random-graph","display_name":"Random graph","score":0.7821118831634521},{"id":"https://openalex.org/keywords/square","display_name":"Square (algebra)","score":0.5089375972747803},{"id":"https://openalex.org/keywords/wireless-ad-hoc-network","display_name":"Wireless ad hoc network","score":0.5088682174682617},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.50409996509552},{"id":"https://openalex.org/keywords/random-geometric-graph","display_name":"Random geometric graph","score":0.503936231136322},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.42944806814193726},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.39797452092170715},{"id":"https://openalex.org/keywords/wireless","display_name":"Wireless","score":0.19865134358406067},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.14607688784599304},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.1365014612674713}],"concepts":[{"id":"https://openalex.org/C47458327","wikidata":"https://www.wikidata.org/wiki/Q910404","display_name":"Random graph","level":3,"score":0.7821118831634521},{"id":"https://openalex.org/C135692309","wikidata":"https://www.wikidata.org/wiki/Q111124","display_name":"Square (algebra)","level":2,"score":0.5089375972747803},{"id":"https://openalex.org/C94523657","wikidata":"https://www.wikidata.org/wiki/Q4085781","display_name":"Wireless ad hoc network","level":3,"score":0.5088682174682617},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.50409996509552},{"id":"https://openalex.org/C30609935","wikidata":"https://www.wikidata.org/wiki/Q7291969","display_name":"Random geometric graph","level":5,"score":0.503936231136322},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.42944806814193726},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.39797452092170715},{"id":"https://openalex.org/C555944384","wikidata":"https://www.wikidata.org/wiki/Q249","display_name":"Wireless","level":2,"score":0.19865134358406067},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.14607688784599304},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.1365014612674713},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.0},{"id":"https://openalex.org/C22149727","wikidata":"https://www.wikidata.org/wiki/Q7940747","display_name":"Voltage graph","level":4,"score":0.0},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/wiopt.2009.5291570","is_oa":false,"landing_page_url":"https://doi.org/10.1109/wiopt.2009.5291570","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2009 7th International Symposium on Modeling and Optimization in Mobile, Ad Hoc, and Wireless Networks","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W630423399","https://openalex.org/W1519389809","https://openalex.org/W1544368832","https://openalex.org/W1918250237","https://openalex.org/W1943309769","https://openalex.org/W2077353774","https://openalex.org/W2084234679","https://openalex.org/W2085356235","https://openalex.org/W2106963018","https://openalex.org/W2119221712","https://openalex.org/W2138561727","https://openalex.org/W2163219774","https://openalex.org/W2169293240","https://openalex.org/W2322524800","https://openalex.org/W2795444554","https://openalex.org/W3148070887","https://openalex.org/W6640281494","https://openalex.org/W6671559892"],"related_works":["https://openalex.org/W117858965","https://openalex.org/W2782929340","https://openalex.org/W2179240077","https://openalex.org/W59125150","https://openalex.org/W2963133557","https://openalex.org/W1590359421","https://openalex.org/W1992227230","https://openalex.org/W2130919150","https://openalex.org/W2155003029","https://openalex.org/W4214904560"],"abstract_inverted_index":{"Random":[0],"geometric":[1,27,61,97,145],"graphs":[2,28,98],"are":[3,13,29,47],"widely-used":[4],"for":[5,66,85,137],"modelling":[6],"wireless":[7],"ad":[8],"hoc":[9],"networks,":[10],"where":[11],"nodes":[12],"randomly":[14],"deployed":[15],"with":[16,70,126],"each":[17],"covering":[18],"a":[19,80],"finite":[20,68,143],"region.":[21],"The":[22],"fundamental":[23],"properties":[24],"of":[25,39,88,140],"random":[26,42,60,91,96,144],"often":[30],"studied":[31],"in":[32,57,142],"the":[33,37,53,67,86,95,116,127,138],"literature,":[34],"such":[35],"as":[36],"probability":[38,87,139],"connectivity":[40,89,141],"and":[41,90,102],"coverage":[43,92,104],"area.":[44],"While":[45],"there":[46],"numerous":[48],"asymptotic":[49],"results":[50,113,128],"that":[51],"concern":[52],"related":[54],"scaling":[55],"laws":[56],"very":[58],"large":[59],"graphs,":[62],"more":[63,134],"accurate":[64,135],"estimation":[65,136],"cases":[69],"moderate-sized":[71],"networks":[72],"remains":[73],"challenging.":[74],"In":[75],"this":[76],"paper,":[77],"we":[78],"present":[79],"remarkably":[81],"good":[82,117],"approximation":[83,118],"relationship":[84,121],"area":[93],"between":[94],"induced":[99],"by":[100],"circular":[101],"square":[103],"models,":[105],"under":[106],"suitable":[107],"normalisation.":[108],"We":[109],"also":[110],"provide":[111],"analytical":[112],"towards":[114],"justifying":[115],"relationship.":[119],"This":[120],"is":[122],"then":[123],"exploited,":[124],"combining":[125],"from":[129],"reliability":[130],"studies,":[131],"to":[132],"obtain":[133],"graphs.":[146]},"counts_by_year":[{"year":2019,"cited_by_count":1},{"year":2016,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}