{"id":"https://openalex.org/W3113114146","doi":"https://doi.org/10.1137/19m1301837","title":"Solutions to the Minimum Variance Problem Using Delaunay Triangulation","display_name":"Solutions to the Minimum Variance Problem Using Delaunay Triangulation","publication_year":2020,"publication_date":"2020-01-01","ids":{"openalex":"https://openalex.org/W3113114146","doi":"https://doi.org/10.1137/19m1301837","mag":"3113114146"},"language":"en","primary_location":{"id":"doi:10.1137/19m1301837","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1301837","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","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/A5036898670","display_name":"Alexander Strang","orcid":"https://orcid.org/0000-0001-6618-631X"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Alexander Strang","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0001-6618-631X","affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5036898670"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.15999741,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"34","issue":"4","first_page":"2510","last_page":"2531"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9945999979972839,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9945999979972839,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10621","display_name":"Gene Regulatory Network Analysis","score":0.9656000137329102,"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/T10848","display_name":"Advanced Multi-Objective Optimization Algorithms","score":0.9517999887466431,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/delaunay-triangulation","display_name":"Delaunay triangulation","score":0.9415977001190186},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8306554555892944},{"id":"https://openalex.org/keywords/minimum-weight-triangulation","display_name":"Minimum-weight triangulation","score":0.6463939547538757},{"id":"https://openalex.org/keywords/convex-hull","display_name":"Convex hull","score":0.6067403554916382},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5731579661369324},{"id":"https://openalex.org/keywords/pitteway-triangulation","display_name":"Pitteway triangulation","score":0.5568462610244751},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.5428036451339722},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.5285110473632812},{"id":"https://openalex.org/keywords/bowyer\u2013watson-algorithm","display_name":"Bowyer\u2013Watson algorithm","score":0.49563920497894287},{"id":"https://openalex.org/keywords/triangulation","display_name":"Triangulation","score":0.4940236210823059},{"id":"https://openalex.org/keywords/constrained-delaunay-triangulation","display_name":"Constrained Delaunay triangulation","score":0.4730355441570282},{"id":"https://openalex.org/keywords/covariance","display_name":"Covariance","score":0.43524619936943054},{"id":"https://openalex.org/keywords/extreme-point","display_name":"Extreme point","score":0.42557796835899353},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3276737928390503},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.11326274275779724},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.08515900373458862}],"concepts":[{"id":"https://openalex.org/C68010082","wikidata":"https://www.wikidata.org/wiki/Q192445","display_name":"Delaunay triangulation","level":2,"score":0.9415977001190186},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8306554555892944},{"id":"https://openalex.org/C39969762","wikidata":"https://www.wikidata.org/wiki/Q6865406","display_name":"Minimum-weight triangulation","level":4,"score":0.6463939547538757},{"id":"https://openalex.org/C206194317","wikidata":"https://www.wikidata.org/wiki/Q1138624","display_name":"Convex hull","level":3,"score":0.6067403554916382},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5731579661369324},{"id":"https://openalex.org/C178609930","wikidata":"https://www.wikidata.org/wiki/Q3538712","display_name":"Pitteway triangulation","level":3,"score":0.5568462610244751},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.5428036451339722},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.5285110473632812},{"id":"https://openalex.org/C121198538","wikidata":"https://www.wikidata.org/wiki/Q4951461","display_name":"Bowyer\u2013Watson algorithm","level":3,"score":0.49563920497894287},{"id":"https://openalex.org/C135981907","wikidata":"https://www.wikidata.org/wiki/Q188056","display_name":"Triangulation","level":2,"score":0.4940236210823059},{"id":"https://openalex.org/C128321387","wikidata":"https://www.wikidata.org/wiki/Q5164356","display_name":"Constrained Delaunay triangulation","level":3,"score":0.4730355441570282},{"id":"https://openalex.org/C178650346","wikidata":"https://www.wikidata.org/wiki/Q201984","display_name":"Covariance","level":2,"score":0.43524619936943054},{"id":"https://openalex.org/C39847760","wikidata":"https://www.wikidata.org/wiki/Q1385465","display_name":"Extreme point","level":2,"score":0.42557796835899353},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3276737928390503},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.11326274275779724},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.08515900373458862},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/19m1301837","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1301837","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G8831279422","display_name":null,"funder_award_id":"DEB-1654989","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W412911888","https://openalex.org/W1669686402","https://openalex.org/W1965896631","https://openalex.org/W1973890190","https://openalex.org/W1978939198","https://openalex.org/W2010441082","https://openalex.org/W2018825389","https://openalex.org/W2023222239","https://openalex.org/W2078734278","https://openalex.org/W2122844515","https://openalex.org/W2128014106","https://openalex.org/W2131566584","https://openalex.org/W2149616971","https://openalex.org/W2167154952","https://openalex.org/W2208229792","https://openalex.org/W2323484339","https://openalex.org/W2324040359","https://openalex.org/W2325955172","https://openalex.org/W2809229891","https://openalex.org/W2962880672","https://openalex.org/W2971167581"],"related_works":["https://openalex.org/W2350914983","https://openalex.org/W109258179","https://openalex.org/W2001351033","https://openalex.org/W2509795980","https://openalex.org/W2172589357","https://openalex.org/W2381084059","https://openalex.org/W149465645","https://openalex.org/W113718658","https://openalex.org/W2348486108","https://openalex.org/W2359979928"],"abstract_inverted_index":{"We":[0,48,81],"consider":[1],"the":[2,6,22,26,30,33,39,43,46,54,57,63,75,92,94,100,109,112,116,122,127,151],"problem":[3],"of":[4,8,16,25,56,77,89,108,124,129,132,159],"minimizing":[5],"variance":[7],"a":[9,13,105,147],"distribution":[10,31],"supported":[11],"on":[12,91,150],"finite":[14],"set":[15],"points":[17,71],"$\\Omega$":[18,73],"in":[19,36,38,62,74],"$\\mathbb{R}^n$":[20],"given":[21,42,97],"expected":[23],"value":[24],"distribution.":[27],"This":[28],"produces":[29],"with":[32,104,135,146],"least":[34],"uncertainty":[35],"$X$,":[37],"$l_2$":[40],"sense,":[41],"support":[44,55,110],"and":[45],"mean.":[47,113],"show":[49,83],"that,":[50,84],"for":[51],"general":[52],"norms,":[53],"solution":[58,95,149],"must":[59],"be":[60],"small":[61],"sense":[64],"that":[65],"it":[66],"does":[67],"not":[68,120],"contain":[69],"any":[70],"from":[72],"interior":[76],"its":[78],"convex":[79,130],"hull.":[80],"then":[82],"under":[85],"an":[86],"appropriate":[87],"choice":[88],"norm":[90],"covariance,":[93],"is":[96,119,126],"by":[98],"evaluating":[99],"tent":[101],"functions":[102],"associated":[103,134],"Delaunay":[106,117],"triangulation":[107,118],"at":[111],"Moreover,":[114],"when":[115],"unique":[121],"space":[123,128],"solutions":[125,133],"combinations":[131],"each":[136],"possible":[137],"triangulation.":[138],"Solutions":[139],"to":[140],"special":[141,148],"cases":[142],"are":[143],"presented,":[144],"along":[145],"lattice":[152],"which":[153],"simultaneously":[154],"minimizes":[155],"three":[156],"natural":[157],"choices":[158],"norm.":[160]},"counts_by_year":[],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2025-10-10T00:00:00"}
