{"id":"https://openalex.org/W4387455167","doi":"https://doi.org/10.3390/a16100471","title":"Computation of the Hausdorff Distance between Two Compact Convex Sets","display_name":"Computation of the Hausdorff Distance between Two Compact Convex Sets","publication_year":2023,"publication_date":"2023-10-06","ids":{"openalex":"https://openalex.org/W4387455167","doi":"https://doi.org/10.3390/a16100471","pmid":"https://pubmed.ncbi.nlm.nih.gov/38529123"},"language":"en","primary_location":{"id":"doi:10.3390/a16100471","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a16100471","pdf_url":"https://www.mdpi.com/1999-4893/16/10/471/pdf?version=1696598994","source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj","pubmed"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1999-4893/16/10/471/pdf?version=1696598994","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5070269135","display_name":"Kenneth Lange","orcid":"https://orcid.org/0000-0002-1313-5030"},"institutions":[{"id":"https://openalex.org/I161318765","display_name":"University of California, Los Angeles","ror":"https://ror.org/046rm7j60","country_code":"US","type":"education","lineage":["https://openalex.org/I161318765"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Kenneth Lange","raw_affiliation_strings":["Department of Computational Medicine, University of California, Los Angeles, CA 90095, USA","Department of Human Genetics, University of California, Los Angeles, CA 90095, USA","Department of Statistics, University of California, Los Angeles, CA 90095, USA","Department of Computational Medicine, University of California, Los Angeles, CA 90095, USA;"],"raw_orcid":"https://orcid.org/0000-0002-1313-5030","affiliations":[{"raw_affiliation_string":"Department of Computational Medicine, University of California, Los Angeles, CA 90095, USA","institution_ids":["https://openalex.org/I161318765"]},{"raw_affiliation_string":"Department of Human Genetics, University of California, Los Angeles, CA 90095, USA","institution_ids":["https://openalex.org/I161318765"]},{"raw_affiliation_string":"Department of Statistics, University of California, Los Angeles, CA 90095, USA","institution_ids":["https://openalex.org/I161318765"]},{"raw_affiliation_string":"Department of Computational Medicine, University of California, Los Angeles, CA 90095, USA;","institution_ids":["https://openalex.org/I161318765"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5070269135"],"corresponding_institution_ids":["https://openalex.org/I161318765"],"apc_list":{"value":1600,"currency":"CHF","value_usd":1782},"apc_paid":{"value":1600,"currency":"CHF","value_usd":1782},"fwci":0.2872,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.58485846,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":95},"biblio":{"volume":"16","issue":"10","first_page":"471","last_page":"471"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12536","display_name":"Topological and Geometric Data Analysis","score":0.986299991607666,"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"}},"topics":[{"id":"https://openalex.org/T12536","display_name":"Topological and Geometric Data Analysis","score":0.986299991607666,"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/mathematics","display_name":"Mathematics","score":0.7438089847564697},{"id":"https://openalex.org/keywords/hausdorff-distance","display_name":"Hausdorff distance","score":0.6851025819778442},{"id":"https://openalex.org/keywords/hausdorff-space","display_name":"Hausdorff space","score":0.4908645749092102},{"id":"https://openalex.org/keywords/unit-sphere","display_name":"Unit sphere","score":0.45946574211120605},{"id":"https://openalex.org/keywords/ball","display_name":"Ball (mathematics)","score":0.457030713558197},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.4530215263366699},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4183773398399353},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.32629555463790894},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.17845061421394348},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.15143516659736633}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7438089847564697},{"id":"https://openalex.org/C141898687","wikidata":"https://www.wikidata.org/wiki/Q1501997","display_name":"Hausdorff distance","level":2,"score":0.6851025819778442},{"id":"https://openalex.org/C191399826","wikidata":"https://www.wikidata.org/wiki/Q326908","display_name":"Hausdorff space","level":2,"score":0.4908645749092102},{"id":"https://openalex.org/C191948623","wikidata":"https://www.wikidata.org/wiki/Q1307800","display_name":"Unit sphere","level":2,"score":0.45946574211120605},{"id":"https://openalex.org/C122041747","wikidata":"https://www.wikidata.org/wiki/Q838611","display_name":"Ball (mathematics)","level":2,"score":0.457030713558197},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.4530215263366699},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4183773398399353},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.32629555463790894},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.17845061421394348},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.15143516659736633}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.3390/a16100471","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a16100471","pdf_url":"https://www.mdpi.com/1999-4893/16/10/471/pdf?version=1696598994","source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithms","raw_type":"journal-article"},{"id":"pmid:38529123","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/38529123","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithms","raw_type":null},{"id":"pmh:oai:pubmedcentral.nih.gov:10961591","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/10961591","pdf_url":"https://pmc.ncbi.nlm.nih.gov/articles/PMC10961591/pdf/nihms-1942714.pdf","source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Algorithms","raw_type":"Text"},{"id":"pmh:oai:doaj.org/article:a005768787b4481ab71346c1167f1d40","is_oa":true,"landing_page_url":"https://doaj.org/article/a005768787b4481ab71346c1167f1d40","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","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":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Algorithms, Vol 16, Iss 10, p 471 (2023)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/a16100471","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a16100471","pdf_url":"https://www.mdpi.com/1999-4893/16/10/471/pdf?version=1696598994","source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithms","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2196735445","display_name":null,"funder_award_id":"R35 GM141798","funder_id":"https://openalex.org/F4320337354","funder_display_name":"National Institute of General Medical Sciences"},{"id":"https://openalex.org/G5088041617","display_name":null,"funder_award_id":"HG006139","funder_id":"https://openalex.org/F4320332505","funder_display_name":"U.S. Public Health Service"},{"id":"https://openalex.org/G8009928313","display_name":null,"funder_award_id":"R01 GM053275","funder_id":"https://openalex.org/F4320337354","funder_display_name":"National Institute of General Medical Sciences"},{"id":"https://openalex.org/G8583520036","display_name":null,"funder_award_id":"GM53275","funder_id":"https://openalex.org/F4320332505","funder_display_name":"U.S. Public Health Service"},{"id":"https://openalex.org/G950618099","display_name":null,"funder_award_id":"R01 HG006139","funder_id":"https://openalex.org/F4320337348","funder_display_name":"National Human Genome Research Institute"}],"funders":[{"id":"https://openalex.org/F4320332505","display_name":"U.S. Public Health Service","ror":"https://ror.org/05xf94514"},{"id":"https://openalex.org/F4320337348","display_name":"National Human Genome Research Institute","ror":"https://ror.org/00baak391"},{"id":"https://openalex.org/F4320337354","display_name":"National Institute of General Medical Sciences","ror":"https://ror.org/04q48ey07"}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4387455167.pdf"},"referenced_works_count":42,"referenced_works":["https://openalex.org/W905619","https://openalex.org/W75930369","https://openalex.org/W205960364","https://openalex.org/W416122618","https://openalex.org/W1494466405","https://openalex.org/W1517128391","https://openalex.org/W1971675470","https://openalex.org/W1977957682","https://openalex.org/W2023753054","https://openalex.org/W2028344184","https://openalex.org/W2044632218","https://openalex.org/W2061075701","https://openalex.org/W2068373432","https://openalex.org/W2075711464","https://openalex.org/W2103404435","https://openalex.org/W2107105977","https://openalex.org/W2135500318","https://openalex.org/W2136885855","https://openalex.org/W2149008940","https://openalex.org/W2149414429","https://openalex.org/W2160754664","https://openalex.org/W2162896357","https://openalex.org/W2168655828","https://openalex.org/W2169371923","https://openalex.org/W2489539531","https://openalex.org/W2498094064","https://openalex.org/W2624570034","https://openalex.org/W2763081248","https://openalex.org/W2802300911","https://openalex.org/W2887462883","https://openalex.org/W2913596570","https://openalex.org/W2945443581","https://openalex.org/W2951081229","https://openalex.org/W2963842279","https://openalex.org/W3001495598","https://openalex.org/W4244393449","https://openalex.org/W4247591450","https://openalex.org/W4392102439","https://openalex.org/W6681978318","https://openalex.org/W6703754205","https://openalex.org/W6753743610","https://openalex.org/W6758789481"],"related_works":["https://openalex.org/W2886349793","https://openalex.org/W2387072865","https://openalex.org/W2804455714","https://openalex.org/W1530081058","https://openalex.org/W1144450175","https://openalex.org/W2388183907","https://openalex.org/W4231727339","https://openalex.org/W1991371429","https://openalex.org/W2314727157","https://openalex.org/W2031465436"],"abstract_inverted_index":{"The":[0,45,99],"Hausdorff":[1,58,161],"distance":[2,59,162],"between":[3,60],"two":[4,61,92,96,108],"closed":[5],"sets":[6,33],"has":[7],"important":[8],"theoretical":[9],"and":[10,39,50,101,125,134,138,145,174],"practical":[11],"applications.":[12],"Yet":[13],"apart":[14],"from":[15],"finite":[16],"point":[17],"clouds,":[18],"there":[19],"appear":[20],"to":[21,70],"be":[22],"no":[23],"generic":[24],"algorithms":[25,54,67,104,188],"for":[26,55],"computing":[27,56],"this":[28,41,82],"quantity.":[29],"Because":[30],"many":[31],"infinite":[32],"are":[34,68,105],"defined":[35],"by":[36,77,123,153],"algebraic":[37],"equalities":[38],"inequalities,":[40],"a":[42,86],"huge":[43],"gap.":[44],"current":[46],"paper":[47],"constructs":[48],"Frank\u2013Wolfe":[49,100,172],"projected":[51,102],"gradient":[52,103,165],"ascent":[53,166],"the":[57,95,119,128,131,135,142,148,160,171,176,184,190],"compact":[62,112],"convex":[63,113],"sets.":[64,98],"Although":[65],"these":[66],"guaranteed":[69],"go":[71],"uphill,":[72],"they":[73],"can":[74],"become":[75],"trapped":[76],"local":[78],"maxima.":[79],"To":[80],"avoid":[81],"defect,":[83],"we":[84,158],"investigate":[85],"homotopy":[87],"method":[88],"that":[89],"gradually":[90],"deforms":[91],"balls":[93],"into":[94],"target":[97],"tested":[106],"on":[107],"pairs":[109],"(A,B)":[110],"of":[111,130,179,186],"sets,":[114],"where:":[115],"(1)":[116],"A":[117,140],"is":[118,127,141,147,167,193],"box":[120],"[\u22121,1]":[121],"translated":[122,152],"1":[124],"B":[126,146],"intersection":[129],"unit":[132,150],"ball":[133,151],"non-negative":[136],"orthant;":[137],"(2)":[139],"probability":[143],"simplex":[144],"\u21131":[149],"1.":[154],"For":[155],"problem":[156,180],"(2),":[157],"find":[159],"analytically.":[163],"Projected":[164],"more":[168],"reliable":[169],"than":[170],"algorithm":[173],"finds":[175],"exact":[177,191],"solution":[178,192],"(2).":[181],"Homotopy":[182],"improves":[183],"performance":[185],"both":[187],"when":[189],"unknown":[194],"or":[195],"unattained.":[196]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1}],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2025-10-10T00:00:00"}