{"id":"https://openalex.org/W3037345875","doi":"https://doi.org/10.20382/jocg.v13i1a8","title":"A near-linear time approximation scheme for geometric transportation with arbitrary supplies and spread","display_name":"A near-linear time approximation scheme for geometric transportation with arbitrary supplies and spread","publication_year":2022,"publication_date":"2022-06-06","ids":{"openalex":"https://openalex.org/W3037345875","doi":"https://doi.org/10.20382/jocg.v13i1a8","mag":"3037345875"},"language":"en","primary_location":{"id":"pmh:oai:ojs.library.carleton.ca:article/3865","is_oa":false,"landing_page_url":"https://jocg.org/index.php/jocg/article/view/3865","pdf_url":null,"source":{"id":"https://openalex.org/S4306400962","display_name":"Journal of Computational Geometry (Carleton University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I67031392","host_organization_name":"Carleton University","host_organization_lineage":["https://openalex.org/I67031392"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Computational Geometry; Vol. 13 No. 1 (2022); 204\u2013225","raw_type":"info:eu-repo/semantics/article"},"type":"article","indexed_in":["datacite","doaj"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://arxiv.org/abs/1907.04426","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5013518909","display_name":"Kyle Fox","orcid":"https://orcid.org/0000-0002-2446-8594"},"institutions":[{"id":"https://openalex.org/I162577319","display_name":"The University of Texas at Dallas","ror":"https://ror.org/049emcs32","country_code":"US","type":"education","lineage":["https://openalex.org/I162577319"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Fox, Kyle","raw_affiliation_strings":["The University of Texas at Dallas, Richardson, United States"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"The University of Texas at Dallas, Richardson, United States","institution_ids":["https://openalex.org/I162577319"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5018204830","display_name":"Jiashuai Lu","orcid":null},"institutions":[{"id":"https://openalex.org/I162577319","display_name":"The University of Texas at Dallas","ror":"https://ror.org/049emcs32","country_code":"US","type":"education","lineage":["https://openalex.org/I162577319"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Lu, Jiashuai","raw_affiliation_strings":["The University of Texas at Dallas, Richardson, United States"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"The University of Texas at Dallas, Richardson, United States","institution_ids":["https://openalex.org/I162577319"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I162577319"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.00359853,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11502","display_name":"Facility Location and Emergency Management","score":0.9797000288963318,"subfield":{"id":"https://openalex.org/subfields/1407","display_name":"Organizational Behavior and Human Resource Management"},"field":{"id":"https://openalex.org/fields/14","display_name":"Business, Management and Accounting"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T11502","display_name":"Facility Location and Emergency Management","score":0.9797000288963318,"subfield":{"id":"https://openalex.org/subfields/1407","display_name":"Organizational Behavior and Human Resource Management"},"field":{"id":"https://openalex.org/fields/14","display_name":"Business, Management and Accounting"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T12709","display_name":"Optimization and Mathematical Programming","score":0.9710999727249146,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10698","display_name":"Transportation Planning and Optimization","score":0.9563999772071838,"subfield":{"id":"https://openalex.org/subfields/3313","display_name":"Transportation"},"field":{"id":"https://openalex.org/fields/33","display_name":"Social Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/euclidean-space","display_name":"Euclidean space","score":0.6884816884994507},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6020501852035522},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5560365915298462},{"id":"https://openalex.org/keywords/approximation-algorithm","display_name":"Approximation algorithm","score":0.5440863370895386},{"id":"https://openalex.org/keywords/transportation-theory","display_name":"Transportation theory","score":0.5339589715003967},{"id":"https://openalex.org/keywords/linear-space","display_name":"Linear space","score":0.5282449126243591},{"id":"https://openalex.org/keywords/euclidean-distance","display_name":"Euclidean distance","score":0.5161086320877075},{"id":"https://openalex.org/keywords/euclidean-geometry","display_name":"Euclidean geometry","score":0.5062021613121033},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.48478811979293823},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4511158764362335},{"id":"https://openalex.org/keywords/facility-location-problem","display_name":"Facility location problem","score":0.4313046336174011},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.4309488832950592},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4004228115081787},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3289486765861511},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1908644735813141},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.12605562806129456}],"concepts":[{"id":"https://openalex.org/C186450821","wikidata":"https://www.wikidata.org/wiki/Q17295","display_name":"Euclidean space","level":2,"score":0.6884816884994507},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6020501852035522},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5560365915298462},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.5440863370895386},{"id":"https://openalex.org/C31829261","wikidata":"https://www.wikidata.org/wiki/Q1929885","display_name":"Transportation theory","level":2,"score":0.5339589715003967},{"id":"https://openalex.org/C176370821","wikidata":"https://www.wikidata.org/wiki/Q1826459","display_name":"Linear space","level":2,"score":0.5282449126243591},{"id":"https://openalex.org/C120174047","wikidata":"https://www.wikidata.org/wiki/Q847073","display_name":"Euclidean distance","level":2,"score":0.5161086320877075},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.5062021613121033},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.48478811979293823},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4511158764362335},{"id":"https://openalex.org/C108005400","wikidata":"https://www.wikidata.org/wiki/Q1305598","display_name":"Facility location problem","level":2,"score":0.4313046336174011},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.4309488832950592},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4004228115081787},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3289486765861511},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1908644735813141},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.12605562806129456},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"pmh:oai:ojs.library.carleton.ca:article/3865","is_oa":false,"landing_page_url":"https://jocg.org/index.php/jocg/article/view/3865","pdf_url":null,"source":{"id":"https://openalex.org/S4306400962","display_name":"Journal of Computational Geometry (Carleton University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I67031392","host_organization_name":"Carleton University","host_organization_lineage":["https://openalex.org/I67031392"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Computational Geometry; Vol. 13 No. 1 (2022); 204\u2013225","raw_type":"info:eu-repo/semantics/article"},{"id":"mag:3037345875","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1907.04426","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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:doaj.org/article:21750ea23d9742a6bd9dccf8b5fbf924","is_oa":true,"landing_page_url":"https://doaj.org/article/21750ea23d9742a6bd9dccf8b5fbf924","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":"Journal of Computational Geometry, Vol 13, Iss 1 (2022)","raw_type":"article"},{"id":"doi:10.20382/jocg.v13i1a8","is_oa":true,"landing_page_url":"https://doi.org/10.20382/jocg.v13i1a8","pdf_url":null,"source":{"id":"https://openalex.org/S4306400962","display_name":"Journal of Computational Geometry (Carleton University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I67031392","host_organization_name":"Carleton University","host_organization_lineage":["https://openalex.org/I67031392"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"mag:3037345875","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1907.04426","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2996255997","https://openalex.org/W2102302396","https://openalex.org/W1933526215","https://openalex.org/W3165080458","https://openalex.org/W2956137402","https://openalex.org/W3199722554","https://openalex.org/W1810702064","https://openalex.org/W1552496115","https://openalex.org/W1983067644","https://openalex.org/W2018557292","https://openalex.org/W2210270306","https://openalex.org/W2099217816","https://openalex.org/W2387333975","https://openalex.org/W3004921380","https://openalex.org/W2407517109","https://openalex.org/W1575344150","https://openalex.org/W1982475381","https://openalex.org/W2084822306","https://openalex.org/W2188685519","https://openalex.org/W111486705"],"abstract_inverted_index":{"$\\newcommand{\\R}{\\mathbb{R}}\\DeclareMathOperator{\\poly}{poly}\\DeclareMathOperator{\\polylog}{polylog}$The":[0],"geometric":[1],"transportation":[2,31,126],"problem":[3,113],"takes":[4],"as":[5],"input":[6],"a":[7,17,30,33,119],"set":[8],"of":[9,46,88,152,155,160],"points":[10,76],"\\(P\\)":[11,156],"in":[12,128],"\\(d\\)-dimensional":[13],"Euclidean":[14,89],"space":[15],"and":[16,157],"supply":[18],"function":[19],"\\(\\mu":[20],":":[21,37],"P":[22,38,40,97],"\\to":[23,41],"\\R\\).":[24],"The":[25,80],"goal":[26,81],"is":[27,55,82,150],"to":[28,44,57,83,123,137],"find":[29],"map,":[32],"non-negative":[34],"assignment":[35,51],"\\(\\tau":[36],"\\times":[39,98],"\\R_{\\geq":[42],"0}\\)":[43],"pairs":[45],"points,":[47],"so":[48],"the":[49,85,92,108,124,138,153,158],"total":[50],"leaving":[52],"each":[53],"point":[54],"equal":[56],"its":[58,161],"supply,":[59],"i.e.,":[60],"\\(\\sum_{r":[61],"\\in":[62,68,78,96],"P}":[63,69,99],"\\tau(q,":[64],"r)":[65],"-":[66,104],"\\sum_{p":[67],"\\tau(p,":[70,100],"q)":[71,95,101],"=":[72],"\\mu(q)\\)":[73],"for":[74,91,111,142],"all":[75],"\\(q":[77],"P\\).":[79],"minimize":[84],"weighted":[86],"sum":[87],"distances":[90],"pairs,":[93],"\\(\\sum_{(p,":[94],"\\cdot":[102],"||q":[103],"p||_2\\).":[105],"We":[106],"describe":[107],"first":[109],"algorithm":[110],"this":[112,143],"that":[114],"returns,":[115],"with":[116],"high":[117],"probability,":[118],"\\((1":[120],"+":[121],"\\epsilon)\\)-approximation":[122],"optimal":[125],"map":[127],"\\(O(n":[129],"\\poly(1":[130],"/":[131],"\\epsilon)":[132],"\\polylog{n})\\)":[133],"time.":[134],"In":[135],"contrast":[136],"previous":[139],"best":[140],"algorithms":[141],"problem,":[144],"our":[145],"near-linear":[146],"running":[147],"time":[148],"bound":[149],"independent":[151],"spread":[154],"magnitude":[159],"real-valued":[162],"supplies.":[163]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1}],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2025-10-10T00:00:00"}