{"id":"https://openalex.org/W2115435070","doi":"https://doi.org/10.1137/080735503","title":"On the Approximability of Budgeted Allocations and Improved Lower Bounds for Submodular Welfare Maximization and GAP","display_name":"On the Approximability of Budgeted Allocations and Improved Lower Bounds for Submodular Welfare Maximization and GAP","publication_year":2010,"publication_date":"2010-01-01","ids":{"openalex":"https://openalex.org/W2115435070","doi":"https://doi.org/10.1137/080735503","mag":"2115435070"},"language":"en","primary_location":{"id":"doi:10.1137/080735503","is_oa":false,"landing_page_url":"https://doi.org/10.1137/080735503","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/A5069364300","display_name":"Deeparnab Chakrabarty","orcid":"https://orcid.org/0000-0001-7596-6035"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Deeparnab Chakrabarty","raw_affiliation_strings":["deepc@math.uwaterloo.ca#TAB#"],"affiliations":[{"raw_affiliation_string":"deepc@math.uwaterloo.ca#TAB#","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5008057846","display_name":"Gagan Goel","orcid":"https://orcid.org/0000-0001-9035-0917"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Gagan Goel","raw_affiliation_strings":["gagang@cc.gatech.edu#TAB#"],"affiliations":[{"raw_affiliation_string":"gagang@cc.gatech.edu#TAB#","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5069364300"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.1003,"has_fulltext":false,"cited_by_count":63,"citation_normalized_percentile":{"value":0.94018864,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"39","issue":"6","first_page":"2189","last_page":"2211"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9994999766349792,"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"}},"topics":[{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9994999766349792,"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/T11182","display_name":"Auction Theory and Applications","score":0.9988999962806702,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T12288","display_name":"Optimization and Search Problems","score":0.9977999925613403,"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/common-value-auction","display_name":"Common value auction","score":0.7163470983505249},{"id":"https://openalex.org/keywords/submodular-set-function","display_name":"Submodular set function","score":0.6643578410148621},{"id":"https://openalex.org/keywords/combinatorial-auction","display_name":"Combinatorial auction","score":0.628475546836853},{"id":"https://openalex.org/keywords/revenue","display_name":"Revenue","score":0.6220822930335999},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.6202858686447144},{"id":"https://openalex.org/keywords/maximization","display_name":"Maximization","score":0.5682373046875},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5458233952522278},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.48962074518203735},{"id":"https://openalex.org/keywords/approximation-algorithm","display_name":"Approximation algorithm","score":0.48670604825019836},{"id":"https://openalex.org/keywords/relaxation","display_name":"Relaxation (psychology)","score":0.425525039434433},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.39015495777130127},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.37177854776382446},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3245382606983185},{"id":"https://openalex.org/keywords/economics","display_name":"Economics","score":0.28049492835998535},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.09733235836029053}],"concepts":[{"id":"https://openalex.org/C163239763","wikidata":"https://www.wikidata.org/wiki/Q5153637","display_name":"Common value auction","level":2,"score":0.7163470983505249},{"id":"https://openalex.org/C178621042","wikidata":"https://www.wikidata.org/wiki/Q7631710","display_name":"Submodular set function","level":2,"score":0.6643578410148621},{"id":"https://openalex.org/C59919655","wikidata":"https://www.wikidata.org/wiki/Q5150821","display_name":"Combinatorial auction","level":3,"score":0.628475546836853},{"id":"https://openalex.org/C195487862","wikidata":"https://www.wikidata.org/wiki/Q850210","display_name":"Revenue","level":2,"score":0.6220822930335999},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.6202858686447144},{"id":"https://openalex.org/C2776330181","wikidata":"https://www.wikidata.org/wiki/Q18358244","display_name":"Maximization","level":2,"score":0.5682373046875},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5458233952522278},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.48962074518203735},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.48670604825019836},{"id":"https://openalex.org/C2776029896","wikidata":"https://www.wikidata.org/wiki/Q3935810","display_name":"Relaxation (psychology)","level":2,"score":0.425525039434433},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.39015495777130127},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.37177854776382446},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3245382606983185},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.28049492835998535},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.09733235836029053},{"id":"https://openalex.org/C121955636","wikidata":"https://www.wikidata.org/wiki/Q4116214","display_name":"Accounting","level":1,"score":0.0},{"id":"https://openalex.org/C77805123","wikidata":"https://www.wikidata.org/wiki/Q161272","display_name":"Social psychology","level":1,"score":0.0},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/080735503","is_oa":false,"landing_page_url":"https://doi.org/10.1137/080735503","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:oai:CiteSeerX.psu:10.1.1.164.2272","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.164.2272","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www-static.cc.gatech.edu/grads/g/gagang/MBA.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.182.386","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.182.386","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cc.gatech.edu/%7Emihail/D.7520reading/7520goel.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.46000000834465027,"id":"https://metadata.un.org/sdg/17","display_name":"Partnerships for the goals"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":28,"referenced_works":["https://openalex.org/W1496647032","https://openalex.org/W1518985150","https://openalex.org/W1519520700","https://openalex.org/W1525162419","https://openalex.org/W1569146567","https://openalex.org/W1579522749","https://openalex.org/W1704721253","https://openalex.org/W1769120835","https://openalex.org/W1966079129","https://openalex.org/W1968220721","https://openalex.org/W1989453388","https://openalex.org/W1999032440","https://openalex.org/W2004045061","https://openalex.org/W2013198217","https://openalex.org/W2014369282","https://openalex.org/W2031691288","https://openalex.org/W2053881531","https://openalex.org/W2055155874","https://openalex.org/W2102201348","https://openalex.org/W2113207452","https://openalex.org/W2126307323","https://openalex.org/W2131951207","https://openalex.org/W2133372967","https://openalex.org/W2153014861","https://openalex.org/W2291236298","https://openalex.org/W2611804663","https://openalex.org/W2912794399","https://openalex.org/W3100899548"],"related_works":["https://openalex.org/W2164943659","https://openalex.org/W187768306","https://openalex.org/W2293269701","https://openalex.org/W1775068182","https://openalex.org/W2896347948","https://openalex.org/W1594147293","https://openalex.org/W2184491186","https://openalex.org/W2950500962","https://openalex.org/W1495402553","https://openalex.org/W2963545891"],"abstract_inverted_index":{"In":[0],"this":[1],"paper":[2],"we":[3],"consider":[4],"the":[5,40,64,93,105,120,126,137,147,177,182,186,229,261,274,302,316,327,346,367,372,382],"following":[6],"maximum":[7,36,247],"budgeted":[8],"allocation":[9],"(MBA)":[10],"problem:":[11],"Given":[12],"a":[13,35,86,165,254,362,377],"set":[14],"of":[15,38,73,96,104,119,128,139,146,153,169,185,228,245,265,273,280,319,326,345,366],"m":[16],"indivisible":[17],"items":[18,45],"and":[19,33,62,100,142,171,210,224,269,322,341],"n":[20],"agents,":[21],"with":[22,34,250],"each":[23],"agent":[24],"i":[25],"willing":[26],"to":[27,43,46,48,194,197,253,294,300,307,370],"pay":[28],"$b_{ij}$":[29],"on":[30,109,125,151,164,233,278,332,350,361,381],"item":[31],"j":[32],"budget":[37],"$B_i$,":[39],"goal":[41],"is":[42,174,192,298],"allocate":[44],"agents":[47,74],"maximize":[49],"revenue.":[50],"The":[51],"problem":[52,67,305,369],"naturally":[53],"arises":[54],"as":[55,63,81],"auctioneer":[56],"revenue":[57],"maximization":[58],"in":[59,68,176,387],"budget-constrained":[60],"auctions":[61,70],"winner":[65],"determination":[66],"combinatorial":[69],"when":[71],"utilities":[72],"are":[75,80,162],"budgeted-additive.":[76],"Our":[77,160,240,288],"main":[78],"results":[79],"follows:":[82],"(i)":[83],"We":[84,189,357,374],"give":[85,376],"$3/4$-approximation":[87],"algorithm":[88,379],"for":[89,390],"MBA":[90,196,368],"improving":[91,259],"upon":[92,260,315],"previous":[94],"best":[95,262],"$\\simeq0.632$":[97],"[N.":[98],"Andelman":[99],"Y.":[101],"Mansour,":[102],"Proceedings":[103,118,145,227,272,325,344],"9th":[106],"Scandinavian":[107,348],"Workshop":[108,349],"Algorithm":[110,351],"Theory":[111,127,352],"(SWAT),":[112,353],"2004,":[113],"pp.":[114,132,158,218,238,285,337,355],"26\u201338],":[115],"[J.":[116],"Vondr\u00e1k,":[117,144,271],"40th":[121],"Annual":[122,329],"ACM":[123,231],"Symposium":[124,150,277,331],"Computing":[129],"(STOC),":[130],"2008,":[131],"67\u201374]":[133],"(also":[134],"implied":[135],"by":[136],"result":[138,241],"[U.":[140,267],"Feige":[141,268],"J.":[143,270,342],"47th":[148,275],"IEEE":[149,276],"Foundations":[152,279],"Computer":[154,281],"Science":[155,282],"(FOCS),":[156,283],"2006,":[157,284],"667\u2013676]).":[159],"techniques":[161,290],"based":[163,380],"natural":[166,363],"LP":[167,364],"relaxation":[168,365],"MBA,":[170],"our":[172],"factor":[173,199,255,309],"optimal":[175],"sense":[178],"that":[179,296],"it":[180,191,297],"matches":[181],"integrality":[183],"gap":[184],"LP.":[187],"(ii)":[188],"prove":[190,295],"NP-hard":[193,299],"approximate":[195,301],"any":[198,308,391],"better":[200,256,310],"than":[201,257,311],"$15/16$;":[202],"previously":[203],"only":[204],"NP-hardness":[205,244],"was":[206],"known":[207,263],"[T.":[208],"Sandholm":[209],"S.":[211,323],"Suri,":[212],"Games":[213],"Econom.":[214],"Behav.,":[215],"55":[216],"(2006),":[217],"321\u2013330],":[219],"[B.":[220],"Lehmann,":[221,223],"D.":[222],"N.":[225],"Nisan,":[226],"3rd":[230],"Conference":[232],"Electronic":[234],"Commerce":[235],"(EC),":[236],"2001,":[237],"18\u201328].":[239],"also":[242,375],"implies":[243],"approximating":[246],"submodular":[248],"welfare":[249],"demand":[251],"oracle":[252],"$15/16$,":[258],"hardness":[264,289,318],"$275/276$":[266],"667\u2013676].":[286],"(iii)":[287],"can":[291],"be":[292],"modified":[293],"generalized":[303],"assignment":[304],"(GAP)":[306],"$10/11$.":[312],"This":[313],"improves":[314],"$422/423$":[317],"[C.":[320],"Chekuri":[321],"Khanna,":[324],"11th":[328],"ACM-SIAM":[330],"Discrete":[333],"Algorithms":[334],"(SODA),":[335],"2000,":[336],"213\u2013222],":[338],"[M.":[339],"Chleb\u00edk":[340],"Chleb\u00edkov\u00e1,":[343],"8th":[347],"2002,":[354],"170\u2013179].":[356],"use":[358],"iterative":[359],"rounding":[360],"obtain":[371],"$3/4$-approximation.":[373],"$(3/4-\\epsilon)$-factor":[378],"primal-dual":[383],"schema":[384],"which":[385],"runs":[386],"$\\tilde{O}(nm)$":[388],"time,":[389],"constant":[392],"$\\epsilon>0$.":[393]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":10},{"year":2015,"cited_by_count":8},{"year":2014,"cited_by_count":6},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":3}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}