{"id":"https://openalex.org/W2139158290","doi":"https://doi.org/10.1155/2011/379505","title":"Noniterative Solution of Some Fermat-Weber Location Problems","display_name":"Noniterative Solution of Some Fermat-Weber Location Problems","publication_year":2011,"publication_date":"2011-01-01","ids":{"openalex":"https://openalex.org/W2139158290","doi":"https://doi.org/10.1155/2011/379505","mag":"2139158290"},"language":"en","primary_location":{"id":"doi:10.1155/2011/379505","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2011/379505","pdf_url":"https://downloads.hindawi.com/journals/aor/2011/379505.pdf","source":{"id":"https://openalex.org/S33782831","display_name":"Advances in Operations Research","issn_l":"1687-9147","issn":["1687-9147","1687-9155"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Operations Research","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://downloads.hindawi.com/journals/aor/2011/379505.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5012989644","display_name":"Reuven Chen","orcid":"https://orcid.org/0000-0001-5177-4039"},"institutions":[{"id":"https://openalex.org/I16391192","display_name":"Tel Aviv University","ror":"https://ror.org/04mhzgx49","country_code":"IL","type":"education","lineage":["https://openalex.org/I16391192"]}],"countries":["IL"],"is_corresponding":true,"raw_author_name":"Reuven Chen","raw_affiliation_strings":["The Raymond & Beverly Sackler School of Physics and Astronomy, Tel Aviv University, Tel Aviv 69978, Israel"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"The Raymond & Beverly Sackler School of Physics and Astronomy, Tel Aviv University, Tel Aviv 69978, Israel","institution_ids":["https://openalex.org/I16391192"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5012989644"],"corresponding_institution_ids":["https://openalex.org/I16391192"],"apc_list":{"value":1050,"currency":"USD","value_usd":1050},"apc_paid":{"value":1050,"currency":"USD","value_usd":1050},"fwci":1.8346,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.8822335,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"2011","issue":null,"first_page":"1","last_page":"10"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9986000061035156,"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":0.9986000061035156,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9983999729156494,"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"}},{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9923999905586243,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/mathematical-optimization","display_name":"Mathematical optimization","score":0.6270778179168701},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.573887825012207},{"id":"https://openalex.org/keywords/fermats-last-theorem","display_name":"Fermat's Last Theorem","score":0.5706778764724731},{"id":"https://openalex.org/keywords/analogy","display_name":"Analogy","score":0.5624236464500427},{"id":"https://openalex.org/keywords/euclidean-geometry","display_name":"Euclidean geometry","score":0.5612902045249939},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4875304400920868},{"id":"https://openalex.org/keywords/euclidean-space","display_name":"Euclidean space","score":0.4732395112514496},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4705130457878113},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4310896694660187},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.14854347705841064},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.10309818387031555},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.07826370000839233}],"concepts":[{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.6270778179168701},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.573887825012207},{"id":"https://openalex.org/C87670640","wikidata":"https://www.wikidata.org/wiki/Q132469","display_name":"Fermat's Last Theorem","level":2,"score":0.5706778764724731},{"id":"https://openalex.org/C521332185","wikidata":"https://www.wikidata.org/wiki/Q185816","display_name":"Analogy","level":2,"score":0.5624236464500427},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.5612902045249939},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4875304400920868},{"id":"https://openalex.org/C186450821","wikidata":"https://www.wikidata.org/wiki/Q17295","display_name":"Euclidean space","level":2,"score":0.4732395112514496},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4705130457878113},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4310896694660187},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.14854347705841064},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.10309818387031555},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.07826370000839233},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1155/2011/379505","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2011/379505","pdf_url":"https://downloads.hindawi.com/journals/aor/2011/379505.pdf","source":{"id":"https://openalex.org/S33782831","display_name":"Advances in Operations Research","issn_l":"1687-9147","issn":["1687-9147","1687-9155"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Operations Research","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:hin:jnlaor:379505","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/AOR/2011/379505.xml","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},{"id":"pmh:oai:doaj.org/article:5b871655f9bf4e2492d6073b217e7f74","is_oa":true,"landing_page_url":"https://doaj.org/article/5b871655f9bf4e2492d6073b217e7f74","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":"Advances in Operations Research, Vol 2011 (2011)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2011/379505","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2011/379505","pdf_url":"https://downloads.hindawi.com/journals/aor/2011/379505.pdf","source":{"id":"https://openalex.org/S33782831","display_name":"Advances in Operations Research","issn_l":"1687-9147","issn":["1687-9147","1687-9155"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Operations Research","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2139158290.pdf","grobid_xml":"https://content.openalex.org/works/W2139158290.grobid-xml"},"referenced_works_count":19,"referenced_works":["https://openalex.org/W49320045","https://openalex.org/W1970928279","https://openalex.org/W1978844855","https://openalex.org/W1987510210","https://openalex.org/W1990285857","https://openalex.org/W1999917983","https://openalex.org/W2018870832","https://openalex.org/W2020546119","https://openalex.org/W2028645072","https://openalex.org/W2031089375","https://openalex.org/W2031903553","https://openalex.org/W2043397919","https://openalex.org/W2060223209","https://openalex.org/W2075931423","https://openalex.org/W2076746488","https://openalex.org/W2090706255","https://openalex.org/W2111352009","https://openalex.org/W2161669108","https://openalex.org/W2163521247"],"related_works":["https://openalex.org/W2610298398","https://openalex.org/W4281992692","https://openalex.org/W2325263694","https://openalex.org/W2145396827","https://openalex.org/W2279239548","https://openalex.org/W4294294347","https://openalex.org/W63976795","https://openalex.org/W2404658402","https://openalex.org/W164473625","https://openalex.org/W2105228010"],"abstract_inverted_index":{"The":[0,31],"Fermat-Weber":[1],"problem":[2,132],"of":[3,64,87],"optimally":[4,113],"locating":[5],"a":[6,75,129],"service":[7],"facility":[8],"in":[9,42,45,118,125],"the":[10,19,43,47,58,65,81,84,88,101,122],"Euclidean":[11],"continuous":[12],"two-dimensional":[13],"space":[14],"is":[15,50,105],"usually":[16,34],"solved":[17,114,141],"by":[18,24,27],"iterative":[20,48],"process":[21],"first":[22],"suggested":[23],"Weiszfeld":[25],"or":[26,68],"later":[28],"versions":[29],"thereof.":[30],"methods":[32],"are":[33,40,55],"rather":[35],"efficient,":[36],"but":[37],"exceptional":[38],"problems":[39,54,109],"described":[41],"literature":[44],"which":[46,136],"solution":[49,59,102],"exceedingly":[51],"long.":[52],"These":[53,127],"such":[56],"that":[57,83,107],"either":[60],"coincides":[61,70],"with":[62,71,98,115],"one":[63],"demand":[66,90],"points":[67,91],"nearly":[69],"it.":[72],"We":[73],"describe":[74],"noniterative":[76],"direct":[77],"alternative,":[78],"based":[79],"on":[80],"insight":[82],"gradient":[85],"components":[86],"individual":[89],"can":[92,110,137],"be":[93,112,139],"considered":[94],"as":[95],"pooling":[96],"forces":[97],"respect":[99],"to":[100,120,142],"point.":[103],"It":[104],"demonstrated":[106],"symmetrical":[108],"thus":[111],"no":[116],"iterations,":[117],"analogy":[119],"finding":[121],"equilibrium":[123],"point":[124],"statics.":[126],"include":[128],"well-known":[130],"ill-conditioned":[131],"and":[133],"its":[134],"variants,":[135],"now":[138],"easily":[140],"optimality":[143],"using":[144],"geometrical":[145],"considerations.":[146]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-07-31T08:31:51.225901","created_date":"2025-10-10T00:00:00"}