{"id":"https://openalex.org/W1569888385","doi":"https://doi.org/10.1093/comjnl/bxv124","title":"Area and Perimeter of the Convex Hull of Stochastic Points","display_name":"Area and Perimeter of the Convex Hull of Stochastic Points","publication_year":2016,"publication_date":"2016-01-07","ids":{"openalex":"https://openalex.org/W1569888385","doi":"https://doi.org/10.1093/comjnl/bxv124","mag":"1569888385"},"language":"en","primary_location":{"id":"doi:10.1093/comjnl/bxv124","is_oa":false,"landing_page_url":"https://doi.org/10.1093/comjnl/bxv124","pdf_url":null,"source":{"id":"https://openalex.org/S44643521","display_name":"The Computer Journal","issn_l":"0010-4620","issn":["0010-4620","1460-2067"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311648","host_organization_name":"Oxford University Press","host_organization_lineage":["https://openalex.org/P4310311648","https://openalex.org/P4310311647"],"host_organization_lineage_names":["Oxford University Press","University of Oxford"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Computer Journal","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1412.5153","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5082230826","display_name":"Pablo P\u00e9rez-Lantero","orcid":"https://orcid.org/0000-0002-8703-8970"},"institutions":[{"id":"https://openalex.org/I79274474","display_name":"University of Valpara\u00edso","ror":"https://ror.org/00h9jrb69","country_code":"CL","type":"education","lineage":["https://openalex.org/I79274474"]}],"countries":["CL"],"is_corresponding":true,"raw_author_name":"Pablo P\u00e9rez-Lantero","raw_affiliation_strings":["Escuela de Ingenier\u00eda Civil en Inform\u00e1tica, Universidad de Valpara\u00edso, Valparaiso, Chile"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Escuela de Ingenier\u00eda Civil en Inform\u00e1tica, Universidad de Valpara\u00edso, Valparaiso, Chile","institution_ids":["https://openalex.org/I79274474"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5082230826"],"corresponding_institution_ids":["https://openalex.org/I79274474"],"apc_list":{"value":2635,"currency":"GBP","value_usd":3232},"apc_paid":null,"fwci":0.8848,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.78823529,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"59","issue":"8","first_page":"1144","last_page":"1154"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9998999834060669,"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"}},{"id":"https://openalex.org/T11106","display_name":"Data Management and Algorithms","score":0.9987999796867371,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.9976000189781189,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7845211029052734},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7155977487564087},{"id":"https://openalex.org/keywords/convex-hull","display_name":"Convex hull","score":0.6601606011390686},{"id":"https://openalex.org/keywords/probability-measure","display_name":"Probability measure","score":0.6515858769416809},{"id":"https://openalex.org/keywords/perimeter","display_name":"Perimeter","score":0.6500970125198364},{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.5931384563446045},{"id":"https://openalex.org/keywords/expected-value","display_name":"Expected value","score":0.5644832253456116},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.5413873195648193},{"id":"https://openalex.org/keywords/probability-distribution","display_name":"Probability distribution","score":0.5162875056266785},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4872955083847046},{"id":"https://openalex.org/keywords/geometric-probability","display_name":"Geometric probability","score":0.4392244219779968},{"id":"https://openalex.org/keywords/plane","display_name":"Plane (geometry)","score":0.4215894937515259},{"id":"https://openalex.org/keywords/convex-combination","display_name":"Convex combination","score":0.4124622046947479},{"id":"https://openalex.org/keywords/monte-carlo-method","display_name":"Monte Carlo method","score":0.41136741638183594},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.36259329319000244},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.18839091062545776},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.1712583303451538},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.15269288420677185},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.11182361841201782},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.08043983578681946}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7845211029052734},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7155977487564087},{"id":"https://openalex.org/C206194317","wikidata":"https://www.wikidata.org/wiki/Q1138624","display_name":"Convex hull","level":3,"score":0.6601606011390686},{"id":"https://openalex.org/C21031990","wikidata":"https://www.wikidata.org/wiki/Q355020","display_name":"Probability measure","level":2,"score":0.6515858769416809},{"id":"https://openalex.org/C98503990","wikidata":"https://www.wikidata.org/wiki/Q28474","display_name":"Perimeter","level":2,"score":0.6500970125198364},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.5931384563446045},{"id":"https://openalex.org/C141042865","wikidata":"https://www.wikidata.org/wiki/Q200125","display_name":"Expected value","level":2,"score":0.5644832253456116},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.5413873195648193},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.5162875056266785},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4872955083847046},{"id":"https://openalex.org/C7605037","wikidata":"https://www.wikidata.org/wiki/Q327164","display_name":"Geometric probability","level":2,"score":0.4392244219779968},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.4215894937515259},{"id":"https://openalex.org/C111110010","wikidata":"https://www.wikidata.org/wiki/Q2627315","display_name":"Convex combination","level":4,"score":0.4124622046947479},{"id":"https://openalex.org/C19499675","wikidata":"https://www.wikidata.org/wiki/Q232207","display_name":"Monte Carlo method","level":2,"score":0.41136741638183594},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.36259329319000244},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.18839091062545776},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.1712583303451538},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.15269288420677185},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.11182361841201782},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.08043983578681946},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1093/comjnl/bxv124","is_oa":false,"landing_page_url":"https://doi.org/10.1093/comjnl/bxv124","pdf_url":null,"source":{"id":"https://openalex.org/S44643521","display_name":"The Computer Journal","issn_l":"0010-4620","issn":["0010-4620","1460-2067"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311648","host_organization_name":"Oxford University Press","host_organization_lineage":["https://openalex.org/P4310311648","https://openalex.org/P4310311647"],"host_organization_lineage_names":["Oxford University Press","University of Oxford"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Computer Journal","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1412.5153","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1412.5153","pdf_url":"https://arxiv.org/pdf/1412.5153","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"mag:1569888385","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1412.5153.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:open-archive.highwire.org:comjnl:59/8/1144","is_oa":false,"landing_page_url":"http://comjnl.oxfordjournals.org/cgi/content/short/59/8/1144","pdf_url":null,"source":{"id":"https://openalex.org/S4406923041","display_name":"HighWire Press Open Archive","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"TEXT"},{"id":"doi:10.48550/arxiv.1412.5153","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1412.5153","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1412.5153","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1412.5153","pdf_url":"https://arxiv.org/pdf/1412.5153","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1569888385.pdf","grobid_xml":"https://content.openalex.org/works/W1569888385.grobid-xml"},"referenced_works_count":20,"referenced_works":["https://openalex.org/W3557434","https://openalex.org/W581837698","https://openalex.org/W1496278954","https://openalex.org/W1507039213","https://openalex.org/W1539720494","https://openalex.org/W1572529050","https://openalex.org/W1676035630","https://openalex.org/W2011039300","https://openalex.org/W2036686829","https://openalex.org/W2041916646","https://openalex.org/W2057213951","https://openalex.org/W2068164539","https://openalex.org/W2080255048","https://openalex.org/W2088422262","https://openalex.org/W2089984367","https://openalex.org/W2129047612","https://openalex.org/W2140237757","https://openalex.org/W2157754768","https://openalex.org/W2951335702","https://openalex.org/W3022077708"],"related_works":["https://openalex.org/W2963059745","https://openalex.org/W3099777322","https://openalex.org/W1585848810","https://openalex.org/W593147561","https://openalex.org/W2006081156","https://openalex.org/W2912659905","https://openalex.org/W3099038112","https://openalex.org/W3209196676","https://openalex.org/W3098145066","https://openalex.org/W1992963068","https://openalex.org/W2296334090","https://openalex.org/W2950187912","https://openalex.org/W2049562387","https://openalex.org/W2009451893","https://openalex.org/W2963685758","https://openalex.org/W2963988444","https://openalex.org/W1984547003","https://openalex.org/W1549761076","https://openalex.org/W2949112689","https://openalex.org/W2737593370"],"abstract_inverted_index":{"Given":[0],"a":[1,34,66,98,128,165,207],"set":[2],"|":[3,5,7,9,37,39,41,43,48,50,57,59,61,63,70,73,101,103,106,111,120,124,141,143,154,158,170,174,178,184,192,200,216,219,224,228,238,240],"$P$":[4,42,62],"of":[6,18,23,29,33,40,60,78,212],"$n$":[8],"points":[10],"in":[11,119,169],"the":[12,16,19,25,30,79,90,93,133,136,146,149,161,230,233],"plane,":[13],"we":[14,82,113,163,189],"study":[15],"computation":[17],"probability":[20,69,91,134,147,211,231],"distribution":[21],"function":[22],"both":[24,76],"area":[26,137,150],"and":[27,126,145,185],"perimeter":[28],"convex":[31,80],"hull":[32],"random":[35,46],"subset":[36,47],"$S$":[38,49],".":[44,74,104,159,241],"The":[45],"is":[51,86,95,131,138,151,235],"formed":[52],"by":[53],"drawing":[54],"each":[55],"point":[56],"$p$":[58],"independently":[64],"with":[65,210],"given":[67,99,177],"rational":[68],"$\\pi":[71],"_p$":[72],"For":[75,105,160],"measures":[77],"hull,":[81],"show":[83,164,190],"that":[84,92,117,130,135,148,205,232],"it":[85],"#P-hard":[87],"to":[88],"compute":[89],"measure":[94,234],"at":[96,139,152,214,222,236],"least":[97,140,153,215,237],"bound":[100],"$w$":[102,142,239],"$":[107,179,218,225,227],"\\varepsilon":[108,122,156,172,180,196,226],"\\in":[109,182],"(0,1)$":[110,183],",":[112,144,220],"provide":[114],"an":[115,191],"algorithm":[116,167,204],"runs":[118],"$O(n^{6}/":[121,171],")$":[123,173],"time":[125],"returns":[127,206],"value":[129,208],"between":[132],"$(1-":[155],")w$":[157],"perimeter,":[162],"similar":[166],"running":[168],"time.":[175],"Finally,":[176],",\\delta":[181],"for":[186],"any":[187],"measure,":[188],"$O(n\\log":[193],"n+":[194],"(n/":[195],"^2)\\log":[197],"(1/\\delta":[198],"))$":[199],"-time":[201],"Monte":[202],"Carlo":[203],"that,":[209],"success":[213],"$1-\\delta":[217],"differs":[221],"most":[223],"from":[229]},"counts_by_year":[{"year":2016,"cited_by_count":1}],"updated_date":"2026-07-15T18:14:33.161393","created_date":"2025-10-10T00:00:00"}