{"id":"https://openalex.org/W2115622430","doi":"https://doi.org/10.1109/infcom.2011.5935327","title":"Asymptotic distribution of critical transmission radius for greedy forward routing","display_name":"Asymptotic distribution of critical transmission radius for greedy forward routing","publication_year":2011,"publication_date":"2011-04-01","ids":{"openalex":"https://openalex.org/W2115622430","doi":"https://doi.org/10.1109/infcom.2011.5935327","mag":"2115622430"},"language":"en","primary_location":{"id":"doi:10.1109/infcom.2011.5935327","is_oa":false,"landing_page_url":"https://doi.org/10.1109/infcom.2011.5935327","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2011 Proceedings IEEE INFOCOM","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/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":false,"raw_author_name":"Peng-Jun Wan","raw_affiliation_strings":["Department of Computer Science, Illinois Institute of Technology, Chicago, IL, USA","Dept. of Computer Science, Illinois Institute of Technology, Chicago, 60616, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Illinois Institute of Technology, Chicago, IL, USA","institution_ids":["https://openalex.org/I180949307"]},{"raw_affiliation_string":"Dept. of Computer Science, Illinois Institute of Technology, Chicago, 60616, USA","institution_ids":["https://openalex.org/I180949307"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100331160","display_name":"Lixin Wang","orcid":"https://orcid.org/0000-0002-9497-461X"},"institutions":[{"id":"https://openalex.org/I19989617","display_name":"Paine College","ror":"https://ror.org/00hveka38","country_code":"US","type":"education","lineage":["https://openalex.org/I19989617"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Lixin Wang","raw_affiliation_strings":["Department of Math and Computer Science, Paine College, Augusta, GA, USA","Department of Math and Computer Science, Paine College, Augusta, GA 30901, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Math and Computer Science, Paine College, Augusta, GA, USA","institution_ids":["https://openalex.org/I19989617"]},{"raw_affiliation_string":"Department of Math and Computer Science, Paine College, Augusta, GA 30901, USA","institution_ids":["https://openalex.org/I19989617"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"981","last_page":"989"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10246","display_name":"Mobile Ad Hoc Networks","score":0.9984999895095825,"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":0.9984999895095825,"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/T11830","display_name":"Point processes and geometric inequalities","score":0.9943000078201294,"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9865999817848206,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"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/combinatorics","display_name":"Combinatorics","score":0.5515515804290771},{"id":"https://openalex.org/keywords/radius","display_name":"RADIUS","score":0.5059143900871277},{"id":"https://openalex.org/keywords/poisson-distribution","display_name":"Poisson distribution","score":0.5031909346580505},{"id":"https://openalex.org/keywords/routing","display_name":"Routing (electronic design automation)","score":0.4965980648994446},{"id":"https://openalex.org/keywords/poisson-point-process","display_name":"Poisson point process","score":0.457711398601532},{"id":"https://openalex.org/keywords/distribution","display_name":"Distribution (mathematics)","score":0.45172637701034546},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.41714975237846375},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4021534323692322},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.39961761236190796},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.37645387649536133},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.18236622214317322},{"id":"https://openalex.org/keywords/computer-network","display_name":"Computer network","score":0.13250064849853516},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1278192400932312},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.07746466994285583}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5515515804290771},{"id":"https://openalex.org/C178635117","wikidata":"https://www.wikidata.org/wiki/Q747499","display_name":"RADIUS","level":2,"score":0.5059143900871277},{"id":"https://openalex.org/C100906024","wikidata":"https://www.wikidata.org/wiki/Q205692","display_name":"Poisson distribution","level":2,"score":0.5031909346580505},{"id":"https://openalex.org/C74172769","wikidata":"https://www.wikidata.org/wiki/Q1446839","display_name":"Routing (electronic design automation)","level":2,"score":0.4965980648994446},{"id":"https://openalex.org/C16757284","wikidata":"https://www.wikidata.org/wiki/Q1145117","display_name":"Poisson point process","level":3,"score":0.457711398601532},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.45172637701034546},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.41714975237846375},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4021534323692322},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.39961761236190796},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.37645387649536133},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.18236622214317322},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.13250064849853516},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1278192400932312},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07746466994285583}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/infcom.2011.5935327","is_oa":false,"landing_page_url":"https://doi.org/10.1109/infcom.2011.5935327","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2011 Proceedings IEEE INFOCOM","raw_type":"proceedings-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.220.8506","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.220.8506","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/%7Ewan/Conference/infocom111.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":18,"referenced_works":["https://openalex.org/W630423399","https://openalex.org/W1518780012","https://openalex.org/W1550444125","https://openalex.org/W2027532437","https://openalex.org/W2063295648","https://openalex.org/W2101963262","https://openalex.org/W2111057502","https://openalex.org/W2120447359","https://openalex.org/W2135572590","https://openalex.org/W2137563374","https://openalex.org/W2148565706","https://openalex.org/W2149136852","https://openalex.org/W2156689181","https://openalex.org/W3012992223","https://openalex.org/W3145008664","https://openalex.org/W6631139668","https://openalex.org/W6632945411","https://openalex.org/W6775144453"],"related_works":["https://openalex.org/W1488915263","https://openalex.org/W2077799587","https://openalex.org/W2081706695","https://openalex.org/W2138098899","https://openalex.org/W1977638783","https://openalex.org/W2749866257","https://openalex.org/W2312435285","https://openalex.org/W2950739675","https://openalex.org/W2612834665","https://openalex.org/W3022821365"],"abstract_inverted_index":{"Consider":[0],"a":[1,8,13],"random":[2],"multihop":[3],"wireless":[4],"network":[5],"represented":[6],"by":[7],"Poisson":[9],"point":[10],"process":[11],"over":[12],"unit-area":[14],"disk":[15],"with":[16],"mean":[17],"n.":[18],"Let":[19],"\u00f8":[20,38,53],"<sub":[21,39,54],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[22,40,55,92],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">n</sub>":[23,41,56],"denote":[24],"its":[25,30],"critical":[26],"transmission":[27],"radius":[28],"for":[29,75],"greedy":[31],"forward":[32],"routing.":[33],"Recently,":[34],"asymptotic":[35,49,80],"bounds":[36],"on":[37],"have":[42],"been":[43],"progressively":[44],"improved.":[45],"However,":[46],"the":[47,79],"precise":[48],"probability":[50,81],"distribution":[51],"of":[52,82],"remains":[57],"open.":[58],"In":[59],"this":[60,64],"paper,":[61],"we":[62],"settle":[63],"open":[65],"problem.":[66],"Specifically,":[67],"let":[68],"\u03c3":[69],"=":[70],"2\u03c0/3":[71],"-":[72],"\u221a3/2.":[73],"Then":[74],"any":[76],"constant":[77],"c,":[78],"equation":[83],"is":[84],"proved":[85],"to":[86],"be":[87],"exactly":[88],"exp":[89],"(-(1/\u03c3/\u03c0-1/3-\u03c0/2\u03c3)e":[90],"<sup":[91],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">-c</sup>":[93],").":[94]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-07-14T23:27:15.235271","created_date":"2025-10-10T00:00:00"}
