{"id":"https://openalex.org/W1997710729","doi":"https://doi.org/10.1137/0211040","title":"Complexity Results for Scheduling Tasks in Fixed Intervals on Two Types of Machines","display_name":"Complexity Results for Scheduling Tasks in Fixed Intervals on Two Types of Machines","publication_year":1982,"publication_date":"1982-08-01","ids":{"openalex":"https://openalex.org/W1997710729","doi":"https://doi.org/10.1137/0211040","mag":"1997710729"},"language":"en","primary_location":{"id":"doi:10.1137/0211040","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0211040","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":true,"oa_status":"green","oa_url":"https://research.tue.nl/nl/publications/8e170695-4989-4522-9970-87196bed3f5e","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5071436542","display_name":"K. Nakajima","orcid":"https://orcid.org/0000-0001-7495-0445"},"institutions":[{"id":"https://openalex.org/I111979921","display_name":"Northwestern University","ror":"https://ror.org/000e0be47","country_code":"US","type":"education","lineage":["https://openalex.org/I111979921"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"K. Nakajima","raw_affiliation_strings":["Department of Electrical Engineering and Computer Science, Northwestern University, Evanston, Illinois 60201","Mathematisch Centrum, Amsterdam, the Netherlands"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering and Computer Science, Northwestern University, Evanston, Illinois 60201","institution_ids":["https://openalex.org/I111979921"]},{"raw_affiliation_string":"Mathematisch Centrum, Amsterdam, the Netherlands","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5073752732","display_name":"S. L. Hakimi","orcid":null},"institutions":[{"id":"https://openalex.org/I111979921","display_name":"Northwestern University","ror":"https://ror.org/000e0be47","country_code":"US","type":"education","lineage":["https://openalex.org/I111979921"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"S. L. Hakimi","raw_affiliation_strings":["Computer Science Division, Department of Electrical Engineering, Texas Tech University, Lubbock, Texas 79409. Formerly at Department of Electrical Engineering and Computer Science,","Northwestern University, Evanston, Illinois 60201"],"affiliations":[{"raw_affiliation_string":"Computer Science Division, Department of Electrical Engineering, Texas Tech University, Lubbock, Texas 79409. Formerly at Department of Electrical Engineering and Computer Science,","institution_ids":[]},{"raw_affiliation_string":"Northwestern University, Evanston, Illinois 60201","institution_ids":["https://openalex.org/I111979921"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5057978522","display_name":"Jan Karel Lenstra","orcid":null},"institutions":[{"id":"https://openalex.org/I111979921","display_name":"Northwestern University","ror":"https://ror.org/000e0be47","country_code":"US","type":"education","lineage":["https://openalex.org/I111979921"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"J. K. Lenstra","raw_affiliation_strings":["Northwestern University, Evanston, Illinois 60201","Computer Science Division, Department of Electrical Engineering, Texas Tech University, Lubbock, Texas 79409. Formerly at Department of Electrical Engineering and Computer Science,"],"affiliations":[{"raw_affiliation_string":"Northwestern University, Evanston, Illinois 60201","institution_ids":["https://openalex.org/I111979921"]},{"raw_affiliation_string":"Computer Science Division, Department of Electrical Engineering, Texas Tech University, Lubbock, Texas 79409. Formerly at Department of Electrical Engineering and Computer Science,","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5071436542"],"corresponding_institution_ids":["https://openalex.org/I111979921"],"apc_list":null,"apc_paid":null,"fwci":1.692,"has_fulltext":true,"cited_by_count":13,"citation_normalized_percentile":{"value":0.82509008,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"11","issue":"3","first_page":"512","last_page":"520"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10551","display_name":"Scheduling and Optimization Algorithms","score":0.9972000122070312,"subfield":{"id":"https://openalex.org/subfields/2209","display_name":"Industrial and Manufacturing Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10551","display_name":"Scheduling and Optimization Algorithms","score":0.9972000122070312,"subfield":{"id":"https://openalex.org/subfields/2209","display_name":"Industrial and Manufacturing 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/T10054","display_name":"Parallel Computing and Optimization Techniques","score":0.9896000027656555,"subfield":{"id":"https://openalex.org/subfields/1708","display_name":"Hardware and Architecture"},"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":0.9866999983787537,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/preemption","display_name":"Preemption","score":0.7662301063537598},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.7108933329582214},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.642156183719635},{"id":"https://openalex.org/keywords/scheduling","display_name":"Scheduling (production processes)","score":0.6048270463943481},{"id":"https://openalex.org/keywords/task","display_name":"Task (project management)","score":0.5699435472488403},{"id":"https://openalex.org/keywords/schedule","display_name":"Schedule","score":0.5093275308609009},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.42263472080230713},{"id":"https://openalex.org/keywords/parallel-computing","display_name":"Parallel computing","score":0.3260039985179901},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.2573004364967346},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.18886715173721313},{"id":"https://openalex.org/keywords/operating-system","display_name":"Operating system","score":0.06317567825317383}],"concepts":[{"id":"https://openalex.org/C206952183","wikidata":"https://www.wikidata.org/wiki/Q1193100","display_name":"Preemption","level":2,"score":0.7662301063537598},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.7108933329582214},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.642156183719635},{"id":"https://openalex.org/C206729178","wikidata":"https://www.wikidata.org/wiki/Q2271896","display_name":"Scheduling (production processes)","level":2,"score":0.6048270463943481},{"id":"https://openalex.org/C2780451532","wikidata":"https://www.wikidata.org/wiki/Q759676","display_name":"Task (project management)","level":2,"score":0.5699435472488403},{"id":"https://openalex.org/C68387754","wikidata":"https://www.wikidata.org/wiki/Q7271585","display_name":"Schedule","level":2,"score":0.5093275308609009},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.42263472080230713},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.3260039985179901},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2573004364967346},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.18886715173721313},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.06317567825317383},{"id":"https://openalex.org/C187736073","wikidata":"https://www.wikidata.org/wiki/Q2920921","display_name":"Management","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1137/0211040","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0211040","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"},{"id":"pmh:tue:oai:pure.tue.nl:publications/8e170695-4989-4522-9970-87196bed3f5e","is_oa":true,"landing_page_url":"https://research.tue.nl/nl/publications/8e170695-4989-4522-9970-87196bed3f5e","pdf_url":"https://research.tue.nl/nl/publications/8e170695-4989-4522-9970-87196bed3f5e","source":{"id":"https://openalex.org/S4306401843","display_name":"Data Archiving and Networked Services (DANS)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1322597698","host_organization_name":"Royal Netherlands Academy of Arts and Sciences","host_organization_lineage":["https://openalex.org/I1322597698"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Journal on Computing, 11(3), 512 - 520. Society for Industrial and Applied Mathematics (SIAM)","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:681659","is_oa":false,"landing_page_url":"http://library.tue.nl/csp/dare/LinkToRepository.csp?recordnumber=681659","pdf_url":null,"source":{"id":"https://openalex.org/S4406923046","display_name":"TU/e Research Portal (Eindhoven University of Technology)","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ISSN:0097-5397","raw_type":"Article / Letter to the editor"},{"id":"pmh:oai:library.tue.nl:681659","is_oa":false,"landing_page_url":"http://repository.tue.nl/681659","pdf_url":null,"source":{"id":"https://openalex.org/S4406923046","display_name":"TU/e Research Portal (Eindhoven University of Technology)","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ISSN:0097-5397","raw_type":"Article / Letter to the editor"},{"id":"pmh:oai:pure.tue.nl:publications/8e170695-4989-4522-9970-87196bed3f5e","is_oa":false,"landing_page_url":"https://research.tue.nl/en/publications/8e170695-4989-4522-9970-87196bed3f5e","pdf_url":null,"source":{"id":"https://openalex.org/S4406922641","display_name":"TU/e Research Portal","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":""}],"best_oa_location":{"id":"pmh:tue:oai:pure.tue.nl:publications/8e170695-4989-4522-9970-87196bed3f5e","is_oa":true,"landing_page_url":"https://research.tue.nl/nl/publications/8e170695-4989-4522-9970-87196bed3f5e","pdf_url":"https://research.tue.nl/nl/publications/8e170695-4989-4522-9970-87196bed3f5e","source":{"id":"https://openalex.org/S4306401843","display_name":"Data Archiving and Networked Services (DANS)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1322597698","host_organization_name":"Royal Netherlands Academy of Arts and Sciences","host_organization_lineage":["https://openalex.org/I1322597698"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Journal on Computing, 11(3), 512 - 520. Society for Industrial and Applied Mathematics (SIAM)","raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[{"display_name":"Decent work and economic growth","id":"https://metadata.un.org/sdg/8","score":0.44999998807907104}],"awards":[],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1997710729.pdf"},"referenced_works_count":8,"referenced_works":["https://openalex.org/W1488422606","https://openalex.org/W1655990431","https://openalex.org/W1761548667","https://openalex.org/W2009990213","https://openalex.org/W2029808296","https://openalex.org/W2119359259","https://openalex.org/W2146870367","https://openalex.org/W2401610261"],"related_works":["https://openalex.org/W3191866865","https://openalex.org/W840708677","https://openalex.org/W2361541374","https://openalex.org/W1439300391","https://openalex.org/W1970491116","https://openalex.org/W4387006201","https://openalex.org/W2040050870","https://openalex.org/W3089811425","https://openalex.org/W2801279942","https://openalex.org/W1966261337"],"abstract_inverted_index":{"Suppose":[0],"that":[1,104],"n":[2],"independent":[3],"tasks":[4],"are":[5,107,115],"to":[6,69,91],"be":[7],"scheduled":[8],"without":[9],"preemption":[10],"on":[11,35,45,73],"an":[12],"unlimited":[13],"number":[14],"of":[15,18,65,96],"parallel":[16],"machines":[17,23],"two":[19,51],"types:":[20],"inexpensive":[21],"slow":[22,37,75],"and":[24],"expensive":[25],"fast":[26,47],"machines.":[27],"Each":[28],"task":[29,57,79],"requires":[30],"a":[31,36,40,46,59,74,81,93],"given":[32,41],"processing":[33,43,61,71],"time":[34,44,72],"machine":[38,99],"or":[39],"smaller":[42],"machine.":[48],"We":[49],"make":[50],"different":[52],"feasibility":[53],"assumptions:":[54],"(a)":[55],"each":[56,78],"has":[58,80],"specified":[60,82],"interval,":[62],"the":[63,70,110],"length":[64],"which":[66],"is":[67,102],"equal":[68],"machine;":[76],"(b)":[77],"starting":[83],"time.":[84],"For":[85],"either":[86],"problem":[87],"type,":[88],"we":[89],"wish":[90],"find":[92],"feasible":[94],"schedule":[95],"minimum":[97],"total":[98],"cost.":[100],"It":[101],"shown":[103],"both":[105],"problems":[106],"NP-hard":[108],"in":[109],"strong":[111],"sense.":[112],"These":[113],"results":[114],"complemented":[116],"by":[117],"polynomial":[118],"algorithms":[119],"for":[120],"some":[121],"special":[122],"cases.":[123]},"counts_by_year":[{"year":2017,"cited_by_count":1}],"updated_date":"2026-04-21T08:09:41.155169","created_date":"2025-10-10T00:00:00"}