{"id":"https://openalex.org/W2000444555","doi":"https://doi.org/10.1137/s0097539700382820","title":"A Polynomial Time Approximation Scheme for the Multiple Knapsack Problem","display_name":"A Polynomial Time Approximation Scheme for the Multiple Knapsack Problem","publication_year":2005,"publication_date":"2005-01-01","ids":{"openalex":"https://openalex.org/W2000444555","doi":"https://doi.org/10.1137/s0097539700382820","mag":"2000444555"},"language":"en","primary_location":{"id":"doi:10.1137/s0097539700382820","doi":"https://doi.org/10.1137/s0097539700382820","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0097539700382820","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,"listed_in":["ccf-a","cwts-core","dongbi-a","jufo-3","norway-2","poland-200","russia-white-list-1"],"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"},"parent_works":[],"lineage":["https://openalex.org/W2000444555"],"child_works_count":0,"type":"article","is_traditional":true,"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/A5036503505","display_name":"Chandra Chekuri","orcid":"https://orcid.org/0000-0003-3035-1699","observed_orcids":["https://orcid.org/0000-0003-3035-1699"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Chandra Chekuri","raw_affiliation_strings":["Lucent"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Lucent","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5039619350","display_name":"Sanjeev Khanna","orcid":"https://orcid.org/0009-0000-2601-1689","observed_orcids":["https://orcid.org/0009-0000-2601-1689"]},"institutions":[{"id":"https://openalex.org/I79576946","display_name":"University of Pennsylvania","ror":"https://ror.org/00b30xv10","country_code":"US","type":"education","lineage":["https://openalex.org/I79576946"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Sanjeev Khanna","raw_affiliation_strings":["#N#               * University of Pennsylvania"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"#N#               * University of Pennsylvania","institution_ids":["https://openalex.org/I79576946"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":14.4704,"has_fulltext":false,"cited_by_count":341,"citation_normalized_percentile":{"value":0.9867033,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":99,"max":100},"biblio":{"volume":"35","issue":"3","first_page":"713","last_page":"728"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12176","display_name":"Optimization and Packing Problems","score":0.9926999807357788,"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/T12176","display_name":"Optimization and Packing Problems","score":0.9926999807357788,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.00570000009611249,"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":9.999999747378752e-05,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"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/multiple-knapsack-problem","display_name":"multiple knapsack problem","score":1.0},{"id":"https://openalex.org/keywords/polynomial-time-approximation-scheme","display_name":"polynomial-time approximation scheme","score":0.9660000205039978},{"id":"https://openalex.org/keywords/generalized-assignment-problem","display_name":"generalized assignment problem","score":0.984000027179718},{"id":"https://openalex.org/keywords/apx-hardness","display_name":"APX-hardness","score":0.8420000076293945},{"id":"https://openalex.org/keywords/bin-packing-problem","display_name":"bin packing","score":0.7519999742507935},{"id":"https://openalex.org/keywords/knapsack-problem","display_name":"knapsack problem","score":0.8999999761581421},{"id":"https://openalex.org/keywords/approximation-algorithms","display_name":"approximation algorithms","score":0.6399999856948853}],"concepts":[{"id":"https://openalex.org/C113138325","wikidata":"https://www.wikidata.org/wiki/Q864457","display_name":"Knapsack problem","level":2,"score":0.9443851709365845},{"id":"https://openalex.org/C99140742","wikidata":"https://www.wikidata.org/wiki/Q843550","display_name":"Polynomial-time approximation scheme","level":3,"score":0.7778252363204956},{"id":"https://openalex.org/C87219788","wikidata":"https://www.wikidata.org/wiki/Q814581","display_name":"Bin packing problem","level":3,"score":0.7528743147850037},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6934980750083923},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.6386550664901733},{"id":"https://openalex.org/C156273044","wikidata":"https://www.wikidata.org/wiki/Q4913766","display_name":"Bin","level":2,"score":0.5673973560333252},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.5341747403144836},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.5021169185638428},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4909115433692932},{"id":"https://openalex.org/C130253271","wikidata":"https://www.wikidata.org/wiki/Q3851477","display_name":"Packing problems","level":2,"score":0.41322576999664307},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.38767382502555847},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.37689208984375},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.18347445130348206},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/s0097539700382820","doi":"https://doi.org/10.1137/s0097539700382820","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0097539700382820","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,"listed_in":["ccf-a","cwts-core","dongbi-a","jufo-3","norway-2","poland-200","russia-white-list-1"],"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:oai:repository.upenn.edu:20.500.14332/6276","doi":null,"is_oa":false,"landing_page_url":"https://repository.upenn.edu/handle/20.500.14332/6276","pdf_url":null,"source":{"id":"https://openalex.org/S4306402083","display_name":"ScholarlyCommons (University of Pennsylvania)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I79576946","host_organization_name":"University of Pennsylvania","host_organization_lineage":["https://openalex.org/I79576946"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"published","raw_type":"Article"},{"id":"pmh:oai:repository.upenn.edu:cis_papers-1255","doi":null,"is_oa":false,"landing_page_url":"https://repository.upenn.edu/cis_papers/238","pdf_url":null,"source":{"id":"https://openalex.org/S4306402083","display_name":"ScholarlyCommons (University of Pennsylvania)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I79576946","host_organization_name":"University of Pennsylvania","host_organization_lineage":["https://openalex.org/I79576946"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Departmental Papers (CIS)","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.226.3387","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.226.3387","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":31,"referenced_works":["https://openalex.org/W964861289","https://openalex.org/W1480006018","https://openalex.org/W1509898203","https://openalex.org/W1556368910","https://openalex.org/W1680189815","https://openalex.org/W1825072153","https://openalex.org/W1965966338","https://openalex.org/W1991407520","https://openalex.org/W1992527911","https://openalex.org/W2011039300","https://openalex.org/W2014071862","https://openalex.org/W2014369282","https://openalex.org/W2024427769","https://openalex.org/W2026891055","https://openalex.org/W2031376842","https://openalex.org/W2031595762","https://openalex.org/W2032522336","https://openalex.org/W2055037276","https://openalex.org/W2062761494","https://openalex.org/W2066671865","https://openalex.org/W2071016718","https://openalex.org/W2076481663","https://openalex.org/W2102201348","https://openalex.org/W2113195911","https://openalex.org/W2123068254","https://openalex.org/W2145028977","https://openalex.org/W2576116471","https://openalex.org/W2757107770","https://openalex.org/W2808376720","https://openalex.org/W2922809901","https://openalex.org/W4234897719"],"related_works":["https://openalex.org/W2013198217","https://openalex.org/W2085922444","https://openalex.org/W2167596143","https://openalex.org/W2095673391","https://openalex.org/W2166185745","https://openalex.org/W2108285089","https://openalex.org/W2024427769","https://openalex.org/W1981417680","https://openalex.org/W7095266495","https://openalex.org/W2005461483"],"abstract_inverted_index":{"The":[0,54,144],"multiple":[1],"knapsack":[2,14,172],"problem":[3,15,85],"(MKP)":[4],"is":[5,17,56,77,105,109,116,150,188,223],"a":[6,24,39,43,51,59,70,78,112,151,166,224],"natural":[7],"and":[8,16,29,42,46,90,111,123,132,173,241],"well-known":[9],"generalization":[10,168],"of":[11,26,61,63,81,93,121,147,169,185,199,213,220,231],"the":[12,74,82,88,91,100,119,138,170,181,208],"single":[13],"defined":[18],"as":[19,165],"follows.":[20],"We":[21,191],"are":[22,201],"given":[23],"set":[25],"n":[27],"items":[28,62],"m":[30],"bins":[31],"(knapsacks)":[32],"such":[33,66],"that":[34,67,103,187,196],"each":[35,47],"item":[36,95],"i":[37],"has":[38,50],"profit":[40,65,89],"$p(i)$":[41],"size":[44,92],"$s(i)$,":[45],"bin":[48,102,174],"j":[49],"capacity":[52],"$c(j)$.":[53],"goal":[55],"to":[57,179,233],"find":[58],"subset":[60],"maximum":[64],"they":[68],"have":[69],"feasible":[71],"packing":[72,175],"in":[73,118],"bins.":[75],"MKP":[76,200,232],"special":[79,183],"case":[80,184],"generalized":[83],"assignment":[84],"(GAP)":[86],"where":[87],"an":[94,228,234],"can":[96],"vary":[97],"based":[98],"on":[99],"specific":[101],"it":[104,115,177],"assigned":[106],"to.":[107],"GAP":[108,186,214],"APX-hard":[110],"2-approximation,":[113],"for":[114,142,157],"implicit":[117],"work":[120],"Shmoys":[122],"Tardos":[124],"[Math.":[125],"Program.":[126],"A,":[127],"62":[128],"(1993),":[129],"pp.":[130],"461-474],":[131],"thus":[133],"far,":[134],"this":[135,148,193],"was":[136],"also":[137],"best":[139],"known":[140],"approximation":[141,154],"MKP\\@.":[143,158],"main":[145],"result":[146],"paper":[149],"polynomial":[152],"time":[153],"scheme":[155],"(PTAS)":[156],"Apart":[159],"from":[160,227],"its":[161],"inherent":[162],"theoretical":[163],"interest":[164],"common":[167],"well-studied":[171],"problems,":[176],"appears":[178],"be":[180],"strongest":[182],"not":[189],"APX-hard.":[190,202,216],"substantiate":[192],"by":[194],"showing":[195],"slight":[197],"generalizations":[198],"Thus":[203],"our":[204,221],"results":[205],"help":[206],"demarcate":[207],"boundary":[209],"at":[210],"which":[211],"instances":[212],"become":[215],"An":[217],"interesting":[218],"aspect":[219],"approach":[222],"PTAS-preserving":[225],"reduction":[226],"arbitrary":[229],"instance":[230,235],"with":[236],"$O(\\log":[237],"n)$":[238],"distinct":[239],"sizes":[240],"profits.":[242]},"counts_by_year":[{"year":2026,"cited_by_count":17},{"year":2025,"cited_by_count":17},{"year":2024,"cited_by_count":27},{"year":2023,"cited_by_count":19},{"year":2022,"cited_by_count":25},{"year":2021,"cited_by_count":34},{"year":2020,"cited_by_count":17},{"year":2019,"cited_by_count":14},{"year":2018,"cited_by_count":25},{"year":2017,"cited_by_count":16},{"year":2016,"cited_by_count":14},{"year":2015,"cited_by_count":19},{"year":2014,"cited_by_count":19},{"year":2013,"cited_by_count":19},{"year":2012,"cited_by_count":10}],"updated_date":"2026-11-15T12:55:33.944570","created_date":"2016-06-24T00:00:00"}