{"id":"https://openalex.org/W2067945058","doi":"https://doi.org/10.1137/0205005","title":"Scheduling Graphs on Two Processors","display_name":"Scheduling Graphs on Two Processors","publication_year":1976,"publication_date":"1976-03-01","ids":{"openalex":"https://openalex.org/W2067945058","doi":"https://doi.org/10.1137/0205005","mag":"2067945058"},"language":"en","primary_location":{"id":"doi:10.1137/0205005","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0205005","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/A5004544151","display_name":"Ravi Sethi","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Ravi Sethi","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5004544151"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":10.1786,"has_fulltext":false,"cited_by_count":75,"citation_normalized_percentile":{"value":0.9849505,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"5","issue":"1","first_page":"73","last_page":"82"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10551","display_name":"Scheduling and Optimization Algorithms","score":0.9994000196456909,"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":0.9994000196456909,"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/T12288","display_name":"Optimization and Search Problems","score":0.9988999962806702,"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/T10829","display_name":"Interconnection Networks and Systems","score":0.9939000010490417,"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/computer-science","display_name":"Computer science","score":0.6513247489929199},{"id":"https://openalex.org/keywords/directed-acyclic-graph","display_name":"Directed acyclic graph","score":0.6242678165435791},{"id":"https://openalex.org/keywords/directed-graph","display_name":"Directed graph","score":0.6059085726737976},{"id":"https://openalex.org/keywords/schedule","display_name":"Schedule","score":0.5737259984016418},{"id":"https://openalex.org/keywords/scheduling","display_name":"Scheduling (production processes)","score":0.5729416608810425},{"id":"https://openalex.org/keywords/construct","display_name":"Construct (python library)","score":0.5118200182914734},{"id":"https://openalex.org/keywords/task","display_name":"Task (project management)","score":0.469463974237442},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.4622132182121277},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4620032012462616},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.44623711705207825},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.41765230894088745},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.41487085819244385},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.34459054470062256},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.3444283604621887},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3239341676235199},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.17251655459403992}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6513247489929199},{"id":"https://openalex.org/C74197172","wikidata":"https://www.wikidata.org/wiki/Q1195339","display_name":"Directed acyclic graph","level":2,"score":0.6242678165435791},{"id":"https://openalex.org/C146380142","wikidata":"https://www.wikidata.org/wiki/Q1137726","display_name":"Directed graph","level":2,"score":0.6059085726737976},{"id":"https://openalex.org/C68387754","wikidata":"https://www.wikidata.org/wiki/Q7271585","display_name":"Schedule","level":2,"score":0.5737259984016418},{"id":"https://openalex.org/C206729178","wikidata":"https://www.wikidata.org/wiki/Q2271896","display_name":"Scheduling (production processes)","level":2,"score":0.5729416608810425},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.5118200182914734},{"id":"https://openalex.org/C2780451532","wikidata":"https://www.wikidata.org/wiki/Q759676","display_name":"Task (project management)","level":2,"score":0.469463974237442},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.4622132182121277},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4620032012462616},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.44623711705207825},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.41765230894088745},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.41487085819244385},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.34459054470062256},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3444283604621887},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3239341676235199},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.17251655459403992},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","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},{"id":"https://openalex.org/C187736073","wikidata":"https://www.wikidata.org/wiki/Q2920921","display_name":"Management","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/0205005","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0205005","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/W1487184349","https://openalex.org/W1969148345","https://openalex.org/W1973310391","https://openalex.org/W1973538756","https://openalex.org/W1978452004","https://openalex.org/W1986022261","https://openalex.org/W1987374783","https://openalex.org/W2086119402","https://openalex.org/W2089269509","https://openalex.org/W2092333800","https://openalex.org/W2104680817","https://openalex.org/W2118382442"],"related_works":["https://openalex.org/W2146569528","https://openalex.org/W4287028074","https://openalex.org/W2106828717","https://openalex.org/W3191289342","https://openalex.org/W1998712144","https://openalex.org/W4300165677","https://openalex.org/W4297817344","https://openalex.org/W4292730466","https://openalex.org/W2372211403","https://openalex.org/W3164774158"],"abstract_inverted_index":{"Consider":[0],"a":[1,15,18,22,91,135,140],"directed":[2],"acyclic":[3],"graph":[4],"(dag)":[5],"D":[6,13],"with":[7],"n":[8],"nodes":[9],"and":[10,24,57],"e":[11],"edges.":[12],"represents":[14],"task":[16,30,36],"system;":[17],"node":[19],"corresponds":[20],"to":[21,45,81,89,112,127,138],"task,":[23],"an":[25,60,110,154],"edge":[26],"$(x,y)$":[27],"means":[28],"that":[29],"x":[31],"must":[32],"be":[33,39],"finished":[34],"before":[35],"y":[37],"can":[38],"started.":[40],"We":[41,108,133],"shall":[42],"restrict":[43],"attention":[44],"systems":[46],"in":[47,116,145],"which":[48],"all":[49],"tasks":[50],"require":[51],"the":[52,95,114,143],"same":[53],"processing":[54],"time.":[55],"Coffman":[56],"Graham":[58],"give":[59,109,134],"algorithm":[61,77,111,137],"for":[62,69,102,131],"determining":[63],"nonpreemptive":[64],"schedules":[65],"on":[66],"two":[67],"processors":[68],"such":[70],"systems.":[71],"The":[72,83,99],"first":[73],"part":[74,85,104],"of":[75,97,158],"their":[76],"assigns":[78],"unique":[79],"labels":[80,88],"nodes.":[82],"second":[84,136],"uses":[86],"these":[87],"construct":[90,139],"list":[92],"schedule":[93,141],"(in":[94],"sense":[96],"Graham).":[98],"time":[100],"taken":[101],"each":[103],"is":[105,153],"$O(n^2":[106],")$.":[107],"determine":[113],"labeling":[115,144],"$O(n":[117],"+":[118,148],"e)$":[119,149],"steps.":[120,150],"Similar":[121],"algorithms":[122],"have":[123],"independently":[124],"been":[125],"devised":[126],"test":[128],"undirected":[129],"graphs":[130],"chordality.":[132],"from":[142],"$O(n\\alpha":[146],"(n)":[147],"$\\alpha":[151],"(n)$":[152],"almost":[155],"constant":[156],"function":[157],"n.":[159]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
