{"id":"https://openalex.org/W1994736182","doi":"https://doi.org/10.1137/s0895480101396949","title":"On PreemptiveResource Constrained Scheduling: Polynomial-Time Approximation Schemes","display_name":"On PreemptiveResource Constrained Scheduling: Polynomial-Time Approximation Schemes","publication_year":2006,"publication_date":"2006-01-01","ids":{"openalex":"https://openalex.org/W1994736182","doi":"https://doi.org/10.1137/s0895480101396949","mag":"1994736182"},"language":"en","primary_location":{"id":"doi:10.1137/s0895480101396949","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895480101396949","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"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 Discrete Mathematics","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/A5071305115","display_name":"Klaus Jansen","orcid":"https://orcid.org/0000-0001-8358-6796"},"institutions":[{"id":"https://openalex.org/I32021983","display_name":"Kiel University","ror":"https://ror.org/04v76ef78","country_code":"DE","type":"education","lineage":["https://openalex.org/I32021983"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Klaus Jansen","raw_affiliation_strings":["Institut f\u00fcr Informatik und Praktische Mathematik Christian-Albrechts-Universit\u00e4t zu Kiel, Kiel, Germany"],"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Informatik und Praktische Mathematik Christian-Albrechts-Universit\u00e4t zu Kiel, Kiel, Germany","institution_ids":["https://openalex.org/I32021983"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5033762785","display_name":"Lorant Porkolab","orcid":null},"institutions":[{"id":"https://openalex.org/I4210133790","display_name":"PricewaterhouseCoopers (United Kingdom)","ror":"https://ror.org/041gev667","country_code":"GB","type":"company","lineage":["https://openalex.org/I4210133790"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Lorant Porkolab","raw_affiliation_strings":["Applied Decision Analysis, PricewaterhouseCoopers, London, UK"],"affiliations":[{"raw_affiliation_string":"Applied Decision Analysis, PricewaterhouseCoopers, London, UK","institution_ids":["https://openalex.org/I4210133790"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5071305115"],"corresponding_institution_ids":["https://openalex.org/I32021983"],"apc_list":null,"apc_paid":null,"fwci":7.99290256,"has_fulltext":false,"cited_by_count":33,"citation_normalized_percentile":{"value":0.96913546,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"20","issue":"3","first_page":"545","last_page":"563"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10551","display_name":"Scheduling and Optimization Algorithms","score":0.9995999932289124,"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":0.9995999932289124,"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/T12176","display_name":"Optimization and Packing Problems","score":0.9994999766349792,"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":0.998199999332428,"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/approximation-algorithm","display_name":"Approximation algorithm","score":0.6283303499221802},{"id":"https://openalex.org/keywords/knapsack-problem","display_name":"Knapsack problem","score":0.6074532866477966},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5720056891441345},{"id":"https://openalex.org/keywords/job-shop-scheduling","display_name":"Job shop scheduling","score":0.5500034093856812},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5389974117279053},{"id":"https://openalex.org/keywords/scheduling","display_name":"Scheduling (production processes)","score":0.5155580043792725},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.4898986220359802},{"id":"https://openalex.org/keywords/logarithm","display_name":"Logarithm","score":0.46928083896636963},{"id":"https://openalex.org/keywords/polynomial-time-approximation-scheme","display_name":"Polynomial-time approximation scheme","score":0.4594188332557678},{"id":"https://openalex.org/keywords/multiprocessor-scheduling","display_name":"Multiprocessor scheduling","score":0.4300568997859955},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.38145941495895386},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.36998772621154785},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.32011663913726807},{"id":"https://openalex.org/keywords/flow-shop-scheduling","display_name":"Flow shop scheduling","score":0.19118648767471313},{"id":"https://openalex.org/keywords/routing","display_name":"Routing (electronic design automation)","score":0.08477917313575745}],"concepts":[{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.6283303499221802},{"id":"https://openalex.org/C113138325","wikidata":"https://www.wikidata.org/wiki/Q864457","display_name":"Knapsack problem","level":2,"score":0.6074532866477966},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5720056891441345},{"id":"https://openalex.org/C55416958","wikidata":"https://www.wikidata.org/wiki/Q6206757","display_name":"Job shop scheduling","level":3,"score":0.5500034093856812},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5389974117279053},{"id":"https://openalex.org/C206729178","wikidata":"https://www.wikidata.org/wiki/Q2271896","display_name":"Scheduling (production processes)","level":2,"score":0.5155580043792725},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.4898986220359802},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.46928083896636963},{"id":"https://openalex.org/C99140742","wikidata":"https://www.wikidata.org/wiki/Q843550","display_name":"Polynomial-time approximation scheme","level":3,"score":0.4594188332557678},{"id":"https://openalex.org/C85924588","wikidata":"https://www.wikidata.org/wiki/Q107419135","display_name":"Multiprocessor scheduling","level":5,"score":0.4300568997859955},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.38145941495895386},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.36998772621154785},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.32011663913726807},{"id":"https://openalex.org/C158336966","wikidata":"https://www.wikidata.org/wiki/Q3074426","display_name":"Flow shop scheduling","level":4,"score":0.19118648767471313},{"id":"https://openalex.org/C74172769","wikidata":"https://www.wikidata.org/wiki/Q1446839","display_name":"Routing (electronic design automation)","level":2,"score":0.08477917313575745},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","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:10.1137/s0895480101396949","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895480101396949","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"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 Discrete Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.4399999976158142,"display_name":"Decent work and economic growth","id":"https://metadata.un.org/sdg/8"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":62,"referenced_works":["https://openalex.org/W320858859","https://openalex.org/W617577063","https://openalex.org/W1497640858","https://openalex.org/W1524700731","https://openalex.org/W1542883217","https://openalex.org/W1552313225","https://openalex.org/W1561272249","https://openalex.org/W1966815789","https://openalex.org/W1969310934","https://openalex.org/W1970118687","https://openalex.org/W1984383419","https://openalex.org/W1985211757","https://openalex.org/W1993119087","https://openalex.org/W1997959089","https://openalex.org/W1998948241","https://openalex.org/W2002272911","https://openalex.org/W2006860292","https://openalex.org/W2007087937","https://openalex.org/W2012329067","https://openalex.org/W2017949344","https://openalex.org/W2019318803","https://openalex.org/W2022191808","https://openalex.org/W2024427769","https://openalex.org/W2024742034","https://openalex.org/W2025787252","https://openalex.org/W2026891055","https://openalex.org/W2031666601","https://openalex.org/W2042017208","https://openalex.org/W2042276676","https://openalex.org/W2050328660","https://openalex.org/W2051020376","https://openalex.org/W2054094480","https://openalex.org/W2055037276","https://openalex.org/W2057913648","https://openalex.org/W2058422149","https://openalex.org/W2059422698","https://openalex.org/W2059453880","https://openalex.org/W2060963575","https://openalex.org/W2066883826","https://openalex.org/W2067500652","https://openalex.org/W2086190489","https://openalex.org/W2088961276","https://openalex.org/W2094179603","https://openalex.org/W2094511120","https://openalex.org/W2100172689","https://openalex.org/W2100440346","https://openalex.org/W2101848567","https://openalex.org/W2110526045","https://openalex.org/W2113195911","https://openalex.org/W2128957728","https://openalex.org/W2134422938","https://openalex.org/W2145028977","https://openalex.org/W2154305205","https://openalex.org/W2155341688","https://openalex.org/W2163085705","https://openalex.org/W2618183731","https://openalex.org/W2736018979","https://openalex.org/W3138484722","https://openalex.org/W4234119786","https://openalex.org/W4253698849","https://openalex.org/W4285719527","https://openalex.org/W4293860921"],"related_works":["https://openalex.org/W4288642040","https://openalex.org/W2908214350","https://openalex.org/W1556368910","https://openalex.org/W2799046353","https://openalex.org/W1984121220","https://openalex.org/W2900218461","https://openalex.org/W2098281589","https://openalex.org/W3155769677","https://openalex.org/W2962917430","https://openalex.org/W1903284337"],"abstract_inverted_index":{"We":[0,27],"study":[1],"resource":[2,69,101],"constrained":[3,70],"scheduling":[4,71],"problems":[5],"where":[6],"the":[7,16,38,41,47,80,88,99,105,127],"objective":[8],"is":[9],"to":[10,86,104],"compute":[11],"feasible":[12],"preemptive":[13],"schedules":[14],"minimizing":[15],"makespan":[17],"and":[18,64,72,75,134],"using":[19],"no":[20],"more":[21],"resources":[22],"than":[23],"what":[24],"are":[25,53],"available.":[26],"present":[28,124],"approximation":[29,120],"schemes":[30],"along":[31],"with":[32,60,107,113],"some":[33,65],"inapproximability":[34],"results":[35,52,89,129],"showing":[36],"how":[37],"approximability":[39],"of":[40,46,49,79,126],"problem":[42,103],"changes":[43],"in":[44,130],"terms":[45],"number":[48],"resources.":[50],"The":[51],"based":[54],"on":[55],"linear":[56],"programming":[57],"formulations":[58],"(though":[59],"exponentially":[61],"many":[62],"variables)":[63],"interesting":[66],"connections":[67],"between":[68],"(multidimensional,":[73],"multiple-choice,":[74],"cardinality":[76],"constrained)":[77],"variants":[78],"classical":[81],"knapsack":[82],"problem.":[83],"In":[84],"order":[85],"prove":[87],"we":[90,123],"generalize":[91],"a":[92],"method":[93],"by":[94],"Grigoriadis":[95],"et":[96],"al.":[97],"for":[98],"max-min":[100],"sharing":[102],"case":[106],"weak":[108],"approximate":[109],"block":[110],"solvers":[111],"(i.e.,":[112],"only":[114],"constant,":[115],"logarithmic,":[116],"or":[117],"even":[118],"worse":[119],"ratios).":[121],"Finally,":[122],"applications":[125],"above":[128],"fractional":[131],"graph":[132],"coloring":[133],"multiprocessor":[135],"task":[136],"scheduling.":[137]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}