{"id":"https://openalex.org/W2156787018","doi":"https://doi.org/10.1109/wiopt.2009.5291571","title":"On the k-coverage of line segments by a non homogeneous Poisson-Boolean model","display_name":"On the k-coverage of line segments by a non homogeneous Poisson-Boolean model","publication_year":2009,"publication_date":"2009-06-01","ids":{"openalex":"https://openalex.org/W2156787018","doi":"https://doi.org/10.1109/wiopt.2009.5291571","mag":"2156787018"},"language":"en","primary_location":{"id":"doi:10.1109/wiopt.2009.5291571","is_oa":false,"landing_page_url":"https://doi.org/10.1109/wiopt.2009.5291571","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/A5062610685","display_name":"Sundar Aditya","orcid":"https://orcid.org/0000-0003-3818-2332"},"institutions":[{"id":"https://openalex.org/I162827531","display_name":"Indian Institute of Technology Bombay","ror":"https://ror.org/02qyf5152","country_code":"IN","type":"education","lineage":["https://openalex.org/I162827531"]}],"countries":["IN"],"is_corresponding":true,"raw_author_name":"S.T. Aditya","raw_affiliation_strings":["Department of Electrical Engineering, IIT Bombay, Mumbai, India"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, IIT Bombay, Mumbai, India","institution_ids":["https://openalex.org/I162827531"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5001739759","display_name":"Pallavi Manohar","orcid":null},"institutions":[{"id":"https://openalex.org/I162827531","display_name":"Indian Institute of Technology Bombay","ror":"https://ror.org/02qyf5152","country_code":"IN","type":"education","lineage":["https://openalex.org/I162827531"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"P. Manohar","raw_affiliation_strings":["Department of Electrical Engineering, IIT Bombay, Mumbai, India"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, IIT Bombay, Mumbai, India","institution_ids":["https://openalex.org/I162827531"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5017359920","display_name":"D. Manjunath","orcid":"https://orcid.org/0000-0001-7302-284X"},"institutions":[{"id":"https://openalex.org/I162827531","display_name":"Indian Institute of Technology Bombay","ror":"https://ror.org/02qyf5152","country_code":"IN","type":"education","lineage":["https://openalex.org/I162827531"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"D. Manjunath","raw_affiliation_strings":["Department of Electrical Engineering, IIT Bombay, Mumbai, India"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, IIT Bombay, Mumbai, India","institution_ids":["https://openalex.org/I162827531"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5062610685"],"corresponding_institution_ids":["https://openalex.org/I162827531"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.19921412,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"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/T11830","display_name":"Point processes and geometric inequalities","score":0.9940000176429749,"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"}},"topics":[{"id":"https://openalex.org/T11830","display_name":"Point processes and geometric inequalities","score":0.9940000176429749,"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/T13187","display_name":"Diffusion and Search Dynamics","score":0.963699996471405,"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9312000274658203,"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/boolean-model","display_name":"Boolean model","score":0.7947991490364075},{"id":"https://openalex.org/keywords/extension","display_name":"Extension (predicate logic)","score":0.707781970500946},{"id":"https://openalex.org/keywords/poisson-distribution","display_name":"Poisson distribution","score":0.6105867624282837},{"id":"https://openalex.org/keywords/point-process","display_name":"Point process","score":0.5468473434448242},{"id":"https://openalex.org/keywords/line","display_name":"Line (geometry)","score":0.5244588851928711},{"id":"https://openalex.org/keywords/markov-chain","display_name":"Markov chain","score":0.5011847019195557},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.48483550548553467},{"id":"https://openalex.org/keywords/real-line","display_name":"Real line","score":0.47123441100120544},{"id":"https://openalex.org/keywords/homogeneous","display_name":"Homogeneous","score":0.46501094102859497},{"id":"https://openalex.org/keywords/markov-process","display_name":"Markov process","score":0.4613040089607239},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4493206739425659},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.437601238489151},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4374259114265442},{"id":"https://openalex.org/keywords/process","display_name":"Process (computing)","score":0.4249003529548645},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3657628297805786},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.36047452688217163},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.1239686906337738},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.08123907446861267},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.07826927304267883}],"concepts":[{"id":"https://openalex.org/C67499762","wikidata":"https://www.wikidata.org/wiki/Q4943358","display_name":"Boolean model","level":2,"score":0.7947991490364075},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.707781970500946},{"id":"https://openalex.org/C100906024","wikidata":"https://www.wikidata.org/wiki/Q205692","display_name":"Poisson distribution","level":2,"score":0.6105867624282837},{"id":"https://openalex.org/C88871306","wikidata":"https://www.wikidata.org/wiki/Q7208287","display_name":"Point process","level":2,"score":0.5468473434448242},{"id":"https://openalex.org/C198352243","wikidata":"https://www.wikidata.org/wiki/Q37105","display_name":"Line (geometry)","level":2,"score":0.5244588851928711},{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.5011847019195557},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.48483550548553467},{"id":"https://openalex.org/C75432250","wikidata":"https://www.wikidata.org/wiki/Q29654355","display_name":"Real line","level":2,"score":0.47123441100120544},{"id":"https://openalex.org/C66882249","wikidata":"https://www.wikidata.org/wiki/Q169336","display_name":"Homogeneous","level":2,"score":0.46501094102859497},{"id":"https://openalex.org/C159886148","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov process","level":2,"score":0.4613040089607239},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4493206739425659},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.437601238489151},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4374259114265442},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.4249003529548645},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3657628297805786},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.36047452688217163},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.1239686906337738},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.08123907446861267},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07826927304267883},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/wiopt.2009.5291571","is_oa":false,"landing_page_url":"https://doi.org/10.1109/wiopt.2009.5291571","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":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":6,"referenced_works":["https://openalex.org/W1983003702","https://openalex.org/W2092510684","https://openalex.org/W2118166339","https://openalex.org/W2160013177","https://openalex.org/W2334895121","https://openalex.org/W2798062075"],"related_works":["https://openalex.org/W4298392797","https://openalex.org/W2086605530","https://openalex.org/W1979678609","https://openalex.org/W2093139423","https://openalex.org/W2180122548","https://openalex.org/W4233361775","https://openalex.org/W2068352195","https://openalex.org/W2615845803","https://openalex.org/W3169048396","https://openalex.org/W2101969505"],"abstract_inverted_index":{"We":[0,19,78],"consider":[1],"k-coverage":[2],"of":[3,23,64,67,86],"a":[4,7,38,54,65],"line":[5,69],"by":[6,73,82],"two-dimensional,":[8],"non":[9],"homogeneous":[10],"Poisson-Boolean":[11],"model.":[12],"This":[13,56],"has":[14],"applications":[15],"in":[16],"sensor":[17],"networks.":[18],"extend":[20],"the":[21,26,44,49,62,68,80,84],"analysis":[22],"[1]":[24],"to":[25,36,60],"case":[27,85],"for":[28],"k":[29,45,74,87],">":[30],"1.":[31],"The":[32],"extension":[33,81],"requires":[34],"us":[35],"define":[37],"vector":[39],"Markov":[40],"process":[41,57],"that":[42,47],"tracks":[43],"segments":[46],"have":[48],"longest":[50],"residual":[51],"coverage":[52],"at":[53],"point.":[55],"is":[58],"used":[59],"determine":[61],"probability":[63],"segment":[66],"being":[70],"completely":[71],"covered":[72],"or":[75],"more":[76],"sensors.":[77],"illustrate":[79],"considering":[83],"=":[88],"2.":[89]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}