{"id":"https://openalex.org/W2126893614","doi":"https://doi.org/10.1109/tit.2010.2046254","title":"Asymptotic Critical Transmission Radius for $k$-Connectivity in Wireless <i>Ad Hoc</i> Networks","display_name":"Asymptotic Critical Transmission Radius for $k$-Connectivity in Wireless <i>Ad Hoc</i> Networks","publication_year":2010,"publication_date":"2010-05-27","ids":{"openalex":"https://openalex.org/W2126893614","doi":"https://doi.org/10.1109/tit.2010.2046254","mag":"2126893614"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2010.2046254","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2010.2046254","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Theory","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/A5036031118","display_name":"Peng\u2010Jun Wan","orcid":"https://orcid.org/0000-0001-7926-5711"},"institutions":[{"id":"https://openalex.org/I180949307","display_name":"Illinois Institute of Technology","ror":"https://ror.org/037t3ry66","country_code":"US","type":"education","lineage":["https://openalex.org/I180949307"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Peng-Jun Wan","raw_affiliation_strings":["Department of Computer Science, Illinois Institute of Technology, Chicago, IL, USA","Department of Computer Science, Illinois Institute of Technology, Chicago, IL, USA#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Illinois Institute of Technology, Chicago, IL, USA","institution_ids":["https://openalex.org/I180949307"]},{"raw_affiliation_string":"Department of Computer Science, Illinois Institute of Technology, Chicago, IL, USA#TAB#","institution_ids":["https://openalex.org/I180949307"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5111428778","display_name":"Chih\u2010Wei Yi","orcid":null},"institutions":[{"id":"https://openalex.org/I148366613","display_name":"National Yang Ming Chiao Tung University","ror":"https://ror.org/00se2k293","country_code":"TW","type":"education","lineage":["https://openalex.org/I148366613"]}],"countries":["TW"],"is_corresponding":false,"raw_author_name":"Chih-Wei Yi","raw_affiliation_strings":["Department of Computer Science, National Chiao Tung University, Hsinchu, Taiwan","Department of Computer Science; National Chiao Tung University; Hsinchu; Taiwan"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, National Chiao Tung University, Hsinchu, Taiwan","institution_ids":["https://openalex.org/I148366613"]},{"raw_affiliation_string":"Department of Computer Science; National Chiao Tung University; Hsinchu; Taiwan","institution_ids":["https://openalex.org/I148366613"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100331163","display_name":"Lixin Wang","orcid":"https://orcid.org/0000-0003-0797-3596"},"institutions":[{"id":"https://openalex.org/I180949307","display_name":"Illinois Institute of Technology","ror":"https://ror.org/037t3ry66","country_code":"US","type":"education","lineage":["https://openalex.org/I180949307"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Lixin Wang","raw_affiliation_strings":["Department of Computer Science, Illinois Institute of Technology, Chicago, IL, USA","Department of Computer Science, Illinois Institute of Technology, Chicago, IL, USA#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Illinois Institute of Technology, Chicago, IL, USA","institution_ids":["https://openalex.org/I180949307"]},{"raw_affiliation_string":"Department of Computer Science, Illinois Institute of Technology, Chicago, IL, USA#TAB#","institution_ids":["https://openalex.org/I180949307"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5036031118"],"corresponding_institution_ids":["https://openalex.org/I180949307"],"apc_list":null,"apc_paid":null,"fwci":2.4929,"has_fulltext":false,"cited_by_count":33,"citation_normalized_percentile":{"value":0.89993795,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"56","issue":"6","first_page":"2867","last_page":"2874"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10246","display_name":"Mobile Ad Hoc Networks","score":1.0,"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":1.0,"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":0.9991999864578247,"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/T11896","display_name":"Opportunistic and Delay-Tolerant Networks","score":0.9990000128746033,"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/wireless-ad-hoc-network","display_name":"Wireless ad hoc network","score":0.6449244618415833},{"id":"https://openalex.org/keywords/radius","display_name":"RADIUS","score":0.6218831539154053},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5028602480888367},{"id":"https://openalex.org/keywords/network-topology","display_name":"Network topology","score":0.4500848650932312},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.42889833450317383},{"id":"https://openalex.org/keywords/transmission","display_name":"Transmission (telecommunications)","score":0.4246904253959656},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3795374035835266},{"id":"https://openalex.org/keywords/wireless","display_name":"Wireless","score":0.33964964747428894},{"id":"https://openalex.org/keywords/computer-network","display_name":"Computer network","score":0.3330857455730438},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.321130633354187},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.2775494456291199},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.13293275237083435}],"concepts":[{"id":"https://openalex.org/C94523657","wikidata":"https://www.wikidata.org/wiki/Q4085781","display_name":"Wireless ad hoc network","level":3,"score":0.6449244618415833},{"id":"https://openalex.org/C178635117","wikidata":"https://www.wikidata.org/wiki/Q747499","display_name":"RADIUS","level":2,"score":0.6218831539154053},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5028602480888367},{"id":"https://openalex.org/C199845137","wikidata":"https://www.wikidata.org/wiki/Q145490","display_name":"Network topology","level":2,"score":0.4500848650932312},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.42889833450317383},{"id":"https://openalex.org/C761482","wikidata":"https://www.wikidata.org/wiki/Q118093","display_name":"Transmission (telecommunications)","level":2,"score":0.4246904253959656},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3795374035835266},{"id":"https://openalex.org/C555944384","wikidata":"https://www.wikidata.org/wiki/Q249","display_name":"Wireless","level":2,"score":0.33964964747428894},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.3330857455730438},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.321130633354187},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2775494456291199},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.13293275237083435}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tit.2010.2046254","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2010.2046254","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Theory","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.298.9913","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.298.9913","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.iit.edu/~wan/Journal/tit10.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":24,"referenced_works":["https://openalex.org/W1918250237","https://openalex.org/W1967533244","https://openalex.org/W2004100454","https://openalex.org/W2015812003","https://openalex.org/W2018438786","https://openalex.org/W2020122265","https://openalex.org/W2056986231","https://openalex.org/W2102041871","https://openalex.org/W2108986762","https://openalex.org/W2130820552","https://openalex.org/W2131205845","https://openalex.org/W2139894910","https://openalex.org/W2139924859","https://openalex.org/W2142346726","https://openalex.org/W2148565706","https://openalex.org/W2148577786","https://openalex.org/W2161429738","https://openalex.org/W2163219774","https://openalex.org/W2169293240","https://openalex.org/W2738722302","https://openalex.org/W3012992223","https://openalex.org/W6640281494","https://openalex.org/W6741938958","https://openalex.org/W6775144453"],"related_works":["https://openalex.org/W2086397253","https://openalex.org/W2133122801","https://openalex.org/W600422426","https://openalex.org/W2007156430","https://openalex.org/W2170882281","https://openalex.org/W3081478936","https://openalex.org/W2785612136","https://openalex.org/W1539291615","https://openalex.org/W1988224651","https://openalex.org/W2096179639"],"abstract_inverted_index":{"A":[0],"range":[1],"assignment":[2],"to":[3,155],"the":[4,49,60,67,80,118,129,139,156,168,178,197],"nodes":[5,25,58,99],"in":[6,17,90,105],"a":[7,15,91,106,113],"wireless":[8,92],"<i":[9,44,51,63,71,86,93,123,134,142,162,173,183,202],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[10,45,52,64,72,87,94,124,135,143,163,174,184,203],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">ad":[11,95],"hoc</i>":[12,96],"network":[13,97],"induces":[14],"topology":[16,69,171],"which":[18],"there":[19],"is":[20,48,70,138,172],"an":[21,190],"edge":[22],"between":[23,158],"two":[24],"if":[26,29,56,147],"and":[27,102,160],"only":[28],"both":[30],"of":[31,117],"them":[32],"are":[33,100],"within":[34],"each":[35],"other's":[36],"transmission":[37,41,61,83,120,152,180],"range.":[38],"The":[39],"critical":[40,82,119,130,179,198],"radius":[42,62,84,121,153,181],"for":[43,85,122,133,182,201],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">k</i>":[46,73,88,125,136,175,185,204],"-connectivity":[47,89,137],"smallest":[50,140],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">r</i>":[53,65],"such":[54,145],"that":[55,146],"all":[57],"have":[59],",":[66],"induced":[68,169],"-connected.":[74,176],"In":[75,127],"this":[76],"paper,":[77],"we":[78,187],"study":[79],"asymptotic":[81,115,191],"whose":[98],"uniformly":[101],"independently":[103],"distributed":[104],"unit-area":[107],"square":[108],"or":[109],"disk.":[110],"We":[111],"provide":[112],"precise":[114],"distribution":[116],"-connectivity.":[126,205],"addition,":[128],"neighbor":[131,199],"number":[132,200],"integer":[141],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">l</i>":[144,164],"every":[148],"node":[149],"sets":[150],"its":[151,161],"equal":[154],"distance":[157],"itself":[159],"-th":[165],"nearest":[166],"neighbor,":[167],"(symmetric)":[170],"Applying":[177],"-connectivity,":[186],"can":[188],"obtain":[189],"almost":[192],"sure":[193],"upper":[194],"bound":[195],"on":[196]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":5},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
