{"id":"https://openalex.org/W2901053464","doi":"https://doi.org/10.1007/978-3-030-04618-7_22","title":"Approximation Algorithms and a Hardness Result for the Three-Machine Proportionate Mixed Shop","display_name":"Approximation Algorithms and a Hardness Result for the Three-Machine Proportionate Mixed Shop","publication_year":2018,"publication_date":"2018-01-01","ids":{"openalex":"https://openalex.org/W2901053464","doi":"https://doi.org/10.1007/978-3-030-04618-7_22","mag":"2901053464"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-030-04618-7_22","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-030-04618-7_22","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"type":"book-chapter","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/A5101848063","display_name":"Longcheng Liu","orcid":"https://orcid.org/0000-0003-2294-9340"},"institutions":[{"id":"https://openalex.org/I154425047","display_name":"University of Alberta","ror":"https://ror.org/0160cpw27","country_code":"CA","type":"education","lineage":["https://openalex.org/I154425047"]},{"id":"https://openalex.org/I191208505","display_name":"Xiamen University","ror":"https://ror.org/00mcjh785","country_code":"CN","type":"education","lineage":["https://openalex.org/I191208505"]}],"countries":["CA","CN"],"is_corresponding":false,"raw_author_name":"Longcheng Liu","raw_affiliation_strings":["Department of Computing Science, University of Alberta, Edmonton, AB, Canada","School of Mathematical Sciences, Xiamen University, Xiamen, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computing Science, University of Alberta, Edmonton, AB, Canada","institution_ids":["https://openalex.org/I154425047"]},{"raw_affiliation_string":"School of Mathematical Sciences, Xiamen University, Xiamen, China","institution_ids":["https://openalex.org/I191208505"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5071239144","display_name":"Guanqun Ni","orcid":"https://orcid.org/0000-0002-4565-4484"},"institutions":[{"id":"https://openalex.org/I154425047","display_name":"University of Alberta","ror":"https://ror.org/0160cpw27","country_code":"CA","type":"education","lineage":["https://openalex.org/I154425047"]},{"id":"https://openalex.org/I61057504","display_name":"Fujian Agriculture and Forestry University","ror":"https://ror.org/04kx2sy84","country_code":"CN","type":"education","lineage":["https://openalex.org/I61057504"]}],"countries":["CA","CN"],"is_corresponding":false,"raw_author_name":"Guanqun Ni","raw_affiliation_strings":["College of Management, Fujian Agriculture and Forestry University, Fuzhou, China","Department of Computing Science, University of Alberta, Edmonton, AB, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Management, Fujian Agriculture and Forestry University, Fuzhou, China","institution_ids":["https://openalex.org/I61057504"]},{"raw_affiliation_string":"Department of Computing Science, University of Alberta, Edmonton, AB, Canada","institution_ids":["https://openalex.org/I154425047"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102006459","display_name":"Yong Chen","orcid":"https://orcid.org/0000-0003-0264-5200"},"institutions":[{"id":"https://openalex.org/I154425047","display_name":"University of Alberta","ror":"https://ror.org/0160cpw27","country_code":"CA","type":"education","lineage":["https://openalex.org/I154425047"]},{"id":"https://openalex.org/I50760025","display_name":"Hangzhou Dianzi University","ror":"https://ror.org/0576gt767","country_code":"CN","type":"education","lineage":["https://openalex.org/I50760025"]}],"countries":["CA","CN"],"is_corresponding":false,"raw_author_name":"Yong Chen","raw_affiliation_strings":["Department of Computing Science, University of Alberta, Edmonton, AB, Canada","Department of Mathematics, Hangzhou Dianzi University, Hangzhou, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computing Science, University of Alberta, Edmonton, AB, Canada","institution_ids":["https://openalex.org/I154425047"]},{"raw_affiliation_string":"Department of Mathematics, Hangzhou Dianzi University, Hangzhou, China","institution_ids":["https://openalex.org/I50760025"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5091866119","display_name":"Randy Goebel","orcid":"https://orcid.org/0000-0002-0739-2946"},"institutions":[{"id":"https://openalex.org/I154425047","display_name":"University of Alberta","ror":"https://ror.org/0160cpw27","country_code":"CA","type":"education","lineage":["https://openalex.org/I154425047"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Randy Goebel","raw_affiliation_strings":["Department of Computing Science, University of Alberta, Edmonton, AB, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computing Science, University of Alberta, Edmonton, AB, Canada","institution_ids":["https://openalex.org/I154425047"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5032087542","display_name":"Yue Luo","orcid":"https://orcid.org/0000-0002-9934-5839"},"institutions":[{"id":"https://openalex.org/I191208505","display_name":"Xiamen University","ror":"https://ror.org/00mcjh785","country_code":"CN","type":"education","lineage":["https://openalex.org/I191208505"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yue Luo","raw_affiliation_strings":["School of Mathematical Sciences, Xiamen University, Xiamen, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Xiamen University, Xiamen, China","institution_ids":["https://openalex.org/I191208505"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100601642","display_name":"An Zhang","orcid":"https://orcid.org/0000-0002-6085-9402"},"institutions":[{"id":"https://openalex.org/I154425047","display_name":"University of Alberta","ror":"https://ror.org/0160cpw27","country_code":"CA","type":"education","lineage":["https://openalex.org/I154425047"]},{"id":"https://openalex.org/I50760025","display_name":"Hangzhou Dianzi University","ror":"https://ror.org/0576gt767","country_code":"CN","type":"education","lineage":["https://openalex.org/I50760025"]}],"countries":["CA","CN"],"is_corresponding":false,"raw_author_name":"An Zhang","raw_affiliation_strings":["Department of Computing Science, University of Alberta, Edmonton, AB, Canada","Department of Mathematics, Hangzhou Dianzi University, Hangzhou, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computing Science, University of Alberta, Edmonton, AB, Canada","institution_ids":["https://openalex.org/I154425047"]},{"raw_affiliation_string":"Department of Mathematics, Hangzhou Dianzi University, Hangzhou, China","institution_ids":["https://openalex.org/I50760025"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5089344475","display_name":"Guohui Lin","orcid":"https://orcid.org/0000-0003-4283-3396"},"institutions":[{"id":"https://openalex.org/I154425047","display_name":"University of Alberta","ror":"https://ror.org/0160cpw27","country_code":"CA","type":"education","lineage":["https://openalex.org/I154425047"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Guohui Lin","raw_affiliation_strings":["Department of Computing Science, University of Alberta, Edmonton, AB, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computing Science, University of Alberta, Edmonton, AB, Canada","institution_ids":["https://openalex.org/I154425047"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":7,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.16659637,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"268","last_page":"280"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10551","display_name":"Scheduling and Optimization Algorithms","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9959999918937683,"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/T12176","display_name":"Optimization and Packing Problems","score":0.9925000071525574,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/flow-shop-scheduling","display_name":"Flow shop scheduling","score":0.6853311061859131},{"id":"https://openalex.org/keywords/job-shop","display_name":"Job shop","score":0.6311408281326294},{"id":"https://openalex.org/keywords/open-shop","display_name":"Open shop","score":0.541071891784668},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5346668362617493},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.48284488916397095},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.48063698410987854},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4774501919746399},{"id":"https://openalex.org/keywords/flow","display_name":"Flow (mathematics)","score":0.47738975286483765},{"id":"https://openalex.org/keywords/approximation-algorithm","display_name":"Approximation algorithm","score":0.46757107973098755},{"id":"https://openalex.org/keywords/job-shop-scheduling","display_name":"Job shop scheduling","score":0.4409913420677185},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.390094131231308},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.38227319717407227},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3762235641479492},{"id":"https://openalex.org/keywords/schedule","display_name":"Schedule","score":0.07371711730957031}],"concepts":[{"id":"https://openalex.org/C158336966","wikidata":"https://www.wikidata.org/wiki/Q3074426","display_name":"Flow shop scheduling","level":4,"score":0.6853311061859131},{"id":"https://openalex.org/C2777243215","wikidata":"https://www.wikidata.org/wiki/Q1493226","display_name":"Job shop","level":5,"score":0.6311408281326294},{"id":"https://openalex.org/C2776484797","wikidata":"https://www.wikidata.org/wiki/Q7096412","display_name":"Open shop","level":5,"score":0.541071891784668},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5346668362617493},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.48284488916397095},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.48063698410987854},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4774501919746399},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.47738975286483765},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.46757107973098755},{"id":"https://openalex.org/C55416958","wikidata":"https://www.wikidata.org/wiki/Q6206757","display_name":"Job shop scheduling","level":3,"score":0.4409913420677185},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.390094131231308},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.38227319717407227},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3762235641479492},{"id":"https://openalex.org/C68387754","wikidata":"https://www.wikidata.org/wiki/Q7271585","display_name":"Schedule","level":2,"score":0.07371711730957031},{"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/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/978-3-030-04618-7_22","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-030-04618-7_22","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Decent work and economic growth","id":"https://metadata.un.org/sdg/8","score":0.6700000166893005}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W198859738","https://openalex.org/W1488422606","https://openalex.org/W1607976652","https://openalex.org/W2011039300","https://openalex.org/W2022026355","https://openalex.org/W2037726054","https://openalex.org/W2040889502","https://openalex.org/W2045096187","https://openalex.org/W2048153410","https://openalex.org/W2065331050","https://openalex.org/W2073967547","https://openalex.org/W2077168140","https://openalex.org/W2081136687","https://openalex.org/W2341350247","https://openalex.org/W2890063554","https://openalex.org/W2953662409","https://openalex.org/W4236127247","https://openalex.org/W4240119221"],"related_works":["https://openalex.org/W3094194260","https://openalex.org/W2050053691","https://openalex.org/W2025157869","https://openalex.org/W2074650926","https://openalex.org/W2974687000","https://openalex.org/W2087693503","https://openalex.org/W2070373866","https://openalex.org/W82886544","https://openalex.org/W4230463050","https://openalex.org/W2023809033"],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}