{"id":"https://openalex.org/W2079611466","doi":"https://doi.org/10.1109/glocom.2011.6133604","title":"Analytical Bounds on the Critical Density for Percolation in Wireless Multi-Hop Networks","display_name":"Analytical Bounds on the Critical Density for Percolation in Wireless Multi-Hop Networks","publication_year":2011,"publication_date":"2011-12-01","ids":{"openalex":"https://openalex.org/W2079611466","doi":"https://doi.org/10.1109/glocom.2011.6133604","mag":"2079611466"},"language":"en","primary_location":{"id":"doi:10.1109/glocom.2011.6133604","is_oa":false,"landing_page_url":"https://doi.org/10.1109/glocom.2011.6133604","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2011 IEEE Global Telecommunications Conference - GLOBECOM 2011","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/A5035126587","display_name":"Seh Chun Ng","orcid":null},"institutions":[{"id":"https://openalex.org/I129604602","display_name":"University of Sydney","ror":"https://ror.org/0384j8v12","country_code":"AU","type":"education","lineage":["https://openalex.org/I129604602"]},{"id":"https://openalex.org/I42894916","display_name":"Data61","ror":"https://ror.org/03q397159","country_code":"AU","type":"other","lineage":["https://openalex.org/I1292875679","https://openalex.org/I2801453606","https://openalex.org/I42894916","https://openalex.org/I4387156119"]}],"countries":["AU"],"is_corresponding":true,"raw_author_name":"Seh Chun Ng","raw_affiliation_strings":["NICTA, Australia","School of Electrical and Information Engineering, University of Sydney, Australia"],"affiliations":[{"raw_affiliation_string":"NICTA, Australia","institution_ids":["https://openalex.org/I42894916"]},{"raw_affiliation_string":"School of Electrical and Information Engineering, University of Sydney, Australia","institution_ids":["https://openalex.org/I129604602"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5036000787","display_name":"Guoqiang Mao","orcid":"https://orcid.org/0000-0002-3598-4949"},"institutions":[{"id":"https://openalex.org/I42894916","display_name":"Data61","ror":"https://ror.org/03q397159","country_code":"AU","type":"other","lineage":["https://openalex.org/I1292875679","https://openalex.org/I2801453606","https://openalex.org/I42894916","https://openalex.org/I4387156119"]},{"id":"https://openalex.org/I129604602","display_name":"University of Sydney","ror":"https://ror.org/0384j8v12","country_code":"AU","type":"education","lineage":["https://openalex.org/I129604602"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Guoqiang Mao","raw_affiliation_strings":["NICTA, Australia","School of Electrical and Information Engineering, University of Sydney, Australia"],"affiliations":[{"raw_affiliation_string":"NICTA, Australia","institution_ids":["https://openalex.org/I42894916"]},{"raw_affiliation_string":"School of Electrical and Information Engineering, University of Sydney, Australia","institution_ids":["https://openalex.org/I129604602"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5015736743","display_name":"Brian D. O. Anderson","orcid":"https://orcid.org/0000-0002-1493-4774"},"institutions":[{"id":"https://openalex.org/I118347636","display_name":"Australian National University","ror":"https://ror.org/019wvm592","country_code":"AU","type":"education","lineage":["https://openalex.org/I118347636"]},{"id":"https://openalex.org/I42894916","display_name":"Data61","ror":"https://ror.org/03q397159","country_code":"AU","type":"other","lineage":["https://openalex.org/I1292875679","https://openalex.org/I2801453606","https://openalex.org/I42894916","https://openalex.org/I4387156119"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"B. D. O. Anderson","raw_affiliation_strings":["NICTA, Australia","Research School of Information Sciences and Engineering, Australian National University, Australia"],"affiliations":[{"raw_affiliation_string":"NICTA, Australia","institution_ids":["https://openalex.org/I42894916"]},{"raw_affiliation_string":"Research School of Information Sciences and Engineering, Australian National University, Australia","institution_ids":["https://openalex.org/I118347636"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5035126587"],"corresponding_institution_ids":["https://openalex.org/I129604602","https://openalex.org/I42894916"],"apc_list":null,"apc_paid":null,"fwci":1.2293,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.7602258,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":null,"issue":null,"first_page":"1","last_page":"6"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.9995999932289124,"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"}},"topics":[{"id":"https://openalex.org/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.9995999932289124,"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"}},{"id":"https://openalex.org/T10246","display_name":"Mobile Ad Hoc Networks","score":0.9994999766349792,"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/T10796","display_name":"Cooperative Communication and Network Coding","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"}}],"keywords":[{"id":"https://openalex.org/keywords/connection","display_name":"Connection (principal bundle)","score":0.7591471672058105},{"id":"https://openalex.org/keywords/hop","display_name":"Hop (telecommunications)","score":0.5668097138404846},{"id":"https://openalex.org/keywords/wireless-network","display_name":"Wireless network","score":0.5414202213287354},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.49790215492248535},{"id":"https://openalex.org/keywords/percolation-theory","display_name":"Percolation theory","score":0.49610814452171326},{"id":"https://openalex.org/keywords/monotonic-function","display_name":"Monotonic function","score":0.4803827404975891},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4565219283103943},{"id":"https://openalex.org/keywords/node","display_name":"Node (physics)","score":0.4501127004623413},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.43395593762397766},{"id":"https://openalex.org/keywords/wireless","display_name":"Wireless","score":0.42999470233917236},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.40974128246307373},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.2550150752067566},{"id":"https://openalex.org/keywords/computer-network","display_name":"Computer network","score":0.1670016348361969},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.09118536114692688},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.08252424001693726},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.07552176713943481}],"concepts":[{"id":"https://openalex.org/C13355873","wikidata":"https://www.wikidata.org/wiki/Q2920850","display_name":"Connection (principal bundle)","level":2,"score":0.7591471672058105},{"id":"https://openalex.org/C25906391","wikidata":"https://www.wikidata.org/wiki/Q1432381","display_name":"Hop (telecommunications)","level":2,"score":0.5668097138404846},{"id":"https://openalex.org/C108037233","wikidata":"https://www.wikidata.org/wiki/Q11375","display_name":"Wireless network","level":3,"score":0.5414202213287354},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.49790215492248535},{"id":"https://openalex.org/C11557063","wikidata":"https://www.wikidata.org/wiki/Q900918","display_name":"Percolation theory","level":3,"score":0.49610814452171326},{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.4803827404975891},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4565219283103943},{"id":"https://openalex.org/C62611344","wikidata":"https://www.wikidata.org/wiki/Q1062658","display_name":"Node (physics)","level":2,"score":0.4501127004623413},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.43395593762397766},{"id":"https://openalex.org/C555944384","wikidata":"https://www.wikidata.org/wiki/Q249","display_name":"Wireless","level":2,"score":0.42999470233917236},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.40974128246307373},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2550150752067566},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.1670016348361969},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09118536114692688},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.08252424001693726},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.07552176713943481},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/glocom.2011.6133604","is_oa":false,"landing_page_url":"https://doi.org/10.1109/glocom.2011.6133604","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2011 IEEE Global Telecommunications Conference - GLOBECOM 2011","raw_type":"proceedings-article"},{"id":"pmh:oai:opus.lib.uts.edu.au:10453/29478","is_oa":false,"landing_page_url":"http://hdl.handle.net/10453/29478","pdf_url":null,"source":{"id":"https://openalex.org/S4306401357","display_name":"UTS ePRESS (University of Technology Sydney)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I114017466","host_organization_name":"University of Technology Sydney","host_organization_lineage":["https://openalex.org/I114017466"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Conference Proceeding"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W587813246","https://openalex.org/W617886523","https://openalex.org/W630423399","https://openalex.org/W1981101107","https://openalex.org/W2035732731","https://openalex.org/W2037697450","https://openalex.org/W2111205830","https://openalex.org/W2112280103","https://openalex.org/W2161575750","https://openalex.org/W4247703164","https://openalex.org/W4249774010"],"related_works":["https://openalex.org/W2077314575","https://openalex.org/W4315701745","https://openalex.org/W1990290471","https://openalex.org/W2117210722","https://openalex.org/W4380682190","https://openalex.org/W587735977","https://openalex.org/W2005710836","https://openalex.org/W2589759689","https://openalex.org/W2102386043","https://openalex.org/W2945307361"],"abstract_inverted_index":{"In":[0,132],"this":[1,133],"paper":[2,134],"we":[3,135],"develop":[4],"analytical":[5],"bounds":[6,138,170],"on":[7,139],"the":[8,35,79,117,137,140,148,157,173,182],"critical":[9,89,141],"density":[10,90],"for":[11],"percolation":[12],"in":[13,19,34],"wireless":[14,187],"multi-":[15],"hop":[16],"networks,":[17],"but":[18,97],"contrast":[20],"to":[21,107,121,172],"other":[22,111,126],"studies,":[23],"under":[24,78,151],"a":[25,45,53,88,95,129,152],"random":[26,54],"connection":[27,47,55,84,154],"model":[28,56,82,85],"and":[29,64,70,83,114,162],"with":[30,128,147],"nodes":[31,51,112,127],"Poissonly":[32],"distributed":[33],"plane":[36],"R":[37],"<sup":[38],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[39],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">2</sup>":[40],".":[41],"The":[42,143,176],"establishment":[43],"of":[44,110,125,184],"direct":[46],"between":[48],"any":[49],"two":[50],"follows":[52],"satisfying":[57],"some":[58],"intuitively":[59],"reasonable":[60],"conditions,":[61],"i.e.":[62,156],"rotational":[63],"translational":[65],"invariance,":[66],"non-":[67],"increasing":[68],"monotonicity":[69],"integral":[71],"boundedness.":[72],"It":[73],"is":[74,100,119,145,164],"well":[75],"known":[76,174],"that":[77,166],"above":[80,115],"network":[81],"there":[86],"exists":[87],"below":[91],"which":[92,116],"almost":[93],"surely":[94],"fixed":[96],"arbitrary":[98],"node":[99,118],"connected":[101,120],"(via":[102],"single":[103],"or":[104],"multi-hop":[105,188],"path)":[106],"finite":[108],"number":[109,124],"only,":[113],"an":[122],"infinite":[123],"positive":[130],"probability.":[131],"investigate":[136],"density.":[142],"result":[144,177],"compared":[146],"existing":[149],"results":[150],"specific":[153],"model,":[155,161],"unit":[158],"disk":[159],"communication":[160],"it":[163],"shown":[165],"our":[167],"method":[168],"generates":[169],"close":[171],"ones.":[175],"provides":[178],"valuable":[179],"insight":[180],"into":[181],"design":[183],"large-":[185],"scale":[186],"networks.":[189]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2013,"cited_by_count":2}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}