{"id":"https://openalex.org/W1985901118","doi":"https://doi.org/10.1137/s0097539792236729","title":"Efficient Algorithms for the Hitchcock Transportation Problem","display_name":"Efficient Algorithms for the Hitchcock Transportation Problem","publication_year":1995,"publication_date":"1995-06-01","ids":{"openalex":"https://openalex.org/W1985901118","doi":"https://doi.org/10.1137/s0097539792236729","mag":"1985901118"},"language":"en","primary_location":{"id":"doi:10.1137/s0097539792236729","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0097539792236729","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"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 Computing","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/A5031520565","display_name":"Takeshi Tokuyama","orcid":"https://orcid.org/0000-0002-9400-8729"},"institutions":[{"id":"https://openalex.org/I1341412227","display_name":"IBM (United States)","ror":"https://ror.org/05hh8d621","country_code":"US","type":"company","lineage":["https://openalex.org/I1341412227"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Takeshi Tokuyama","raw_affiliation_strings":["IBM, ,"],"affiliations":[{"raw_affiliation_string":"IBM, ,","institution_ids":["https://openalex.org/I1341412227"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5004135985","display_name":"Jun Nakano","orcid":null},"institutions":[{"id":"https://openalex.org/I1341412227","display_name":"IBM (United States)","ror":"https://ror.org/05hh8d621","country_code":"US","type":"company","lineage":["https://openalex.org/I1341412227"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jun Nakano","raw_affiliation_strings":["IBM, ,"],"affiliations":[{"raw_affiliation_string":"IBM, ,","institution_ids":["https://openalex.org/I1341412227"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5031520565"],"corresponding_institution_ids":["https://openalex.org/I1341412227"],"apc_list":null,"apc_paid":null,"fwci":0.521,"has_fulltext":false,"cited_by_count":26,"citation_normalized_percentile":{"value":0.61506781,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"24","issue":"3","first_page":"563","last_page":"578"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9994000196456909,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9994000196456909,"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/T12288","display_name":"Optimization and Search Problems","score":0.996999979019165,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9861000180244446,"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/binary-logarithm","display_name":"Binary logarithm","score":0.7091831564903259},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6664121747016907},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5914089679718018},{"id":"https://openalex.org/keywords/omega","display_name":"Omega","score":0.5711619257926941},{"id":"https://openalex.org/keywords/log-log-plot","display_name":"Log-log plot","score":0.47851598262786865},{"id":"https://openalex.org/keywords/running-time","display_name":"Running time","score":0.4389723837375641},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.4257553815841675},{"id":"https://openalex.org/keywords/randomized-algorithm","display_name":"Randomized algorithm","score":0.4108174443244934},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.37924838066101074},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3235844373703003},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.12222912907600403}],"concepts":[{"id":"https://openalex.org/C63553672","wikidata":"https://www.wikidata.org/wiki/Q581168","display_name":"Binary logarithm","level":2,"score":0.7091831564903259},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6664121747016907},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5914089679718018},{"id":"https://openalex.org/C2779557605","wikidata":"https://www.wikidata.org/wiki/Q9890","display_name":"Omega","level":2,"score":0.5711619257926941},{"id":"https://openalex.org/C195292467","wikidata":"https://www.wikidata.org/wiki/Q2091879","display_name":"Log-log plot","level":3,"score":0.47851598262786865},{"id":"https://openalex.org/C3017489831","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Running time","level":2,"score":0.4389723837375641},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.4257553815841675},{"id":"https://openalex.org/C128669082","wikidata":"https://www.wikidata.org/wiki/Q583461","display_name":"Randomized algorithm","level":2,"score":0.4108174443244934},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.37924838066101074},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3235844373703003},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.12222912907600403},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/s0097539792236729","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0097539792236729","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"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 Computing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W261423654","https://openalex.org/W1967290491","https://openalex.org/W1989070206","https://openalex.org/W2010997912","https://openalex.org/W2053760675","https://openalex.org/W2056991815","https://openalex.org/W2084224084","https://openalex.org/W2149342630","https://openalex.org/W2150154671","https://openalex.org/W2214462370","https://openalex.org/W4255338942","https://openalex.org/W4300640952"],"related_works":["https://openalex.org/W2055932080","https://openalex.org/W2011106535","https://openalex.org/W4377371889","https://openalex.org/W2113270940","https://openalex.org/W1992470151","https://openalex.org/W1541068124","https://openalex.org/W1994598067","https://openalex.org/W1992104669","https://openalex.org/W2521054645","https://openalex.org/W2018076478"],"abstract_inverted_index":{"We":[0],"consider":[1],"the":[2,57,61,65,69,118],"Hitchcock":[3],"transportation":[4],"problem":[5,22,119],"on":[6],"n":[7,15,29,96],"supply":[8,67,71],"points":[9,13],"and":[10,50,93,114],"k":[11],"demand":[12],"when":[14,60],"is":[16,40,72,83,120,126],"much":[17],"greater":[18],"than":[19],"k.":[20],"The":[21,75],"can":[23,55],"be":[24],"solved":[25,121],"in":[26,122],"$O(kn^{2}":[27],"\\log":[28,97],"+":[30],"n^{2}\\log^{2}":[31],"n)$":[32],"time":[33,58,78],"if":[34,87,100],"an":[35],"efficient":[36],"minimum-cost":[37],"flow":[38],"algorithm":[39,82],"directly":[41],"applied.":[42],"Applying":[43],"a":[44,51],"geometric":[45],"method":[46],"named":[47],"splitter":[48],"finding":[49],"randomization":[52],"technique,":[53],"we":[54],"improve":[56],"complexity":[59],"ratio":[62],"c":[63],"of":[64,79],"maximum":[66],"to":[68],"minimum":[70],"sufficiently":[73],"small.":[74],"expected":[76],"running":[77],"our":[80],"randomized":[81],"$O(\\frac{kn\\log":[84],"cn}{\\log(n/k^{4}":[85],"\\log^{2}k)})$":[86],"$n":[88,101,107],">":[89,112],"k^{4}":[90,103],"\\log^{2}":[91,95,104],"k$,":[92],"$O(k^{5}":[94],"cn":[98],")$":[99],"\\leq":[102],"k$.":[105],"If":[106],"=":[108,116],"\\Omega":[109],"(k^{4+\\epsilon})":[110],"(\\epsilon":[111],"0)$":[113],"$c":[115],"\\operatorname{poly}(n)$,":[117],"$O(kn)$":[123],"time,":[124],"which":[125],"optimal.":[127]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}