{"id":"https://openalex.org/W1611248441","doi":"https://doi.org/10.4086/toc.2014.v010a010","title":"","display_name":"","publication_year":2014,"publication_date":"2014-01-01","ids":{"openalex":"https://openalex.org/W1611248441","doi":"https://doi.org/10.4086/toc.2014.v010a010","mag":"1611248441"},"language":"en","primary_location":{"id":"doi:10.4086/toc.2014.v010a010","is_oa":true,"landing_page_url":"https://doi.org/10.4086/toc.2014.v010a010","pdf_url":"https://theoryofcomputing.org/articles/v010a010/v010a010.pdf","source":{"id":"https://openalex.org/S142665794","display_name":"Theory of Computing","issn_l":"1557-2862","issn":["1557-2862"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310315690","host_organization_name":"University of Chicago","host_organization_lineage":["https://openalex.org/P4310315690"],"host_organization_lineage_names":["University of Chicago"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Theory of Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://theoryofcomputing.org/articles/v010a010/v010a010.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5082676353","display_name":"Tobias Brunsch","orcid":null},"institutions":[{"id":"https://openalex.org/I4210164937","display_name":"Microsoft Research (United Kingdom)","ror":"https://ror.org/05k87vq12","country_code":"GB","type":"company","lineage":["https://openalex.org/I1290206253","https://openalex.org/I4210164937"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Tobias Brunsch","raw_affiliation_strings":["Microsoft"],"affiliations":[{"raw_affiliation_string":"Microsoft","institution_ids":["https://openalex.org/I4210164937"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5029531416","display_name":"Navin Goyal","orcid":"https://orcid.org/0000-0002-8521-0108"},"institutions":[{"id":"https://openalex.org/I4210164937","display_name":"Microsoft Research (United Kingdom)","ror":"https://ror.org/05k87vq12","country_code":"GB","type":"company","lineage":["https://openalex.org/I1290206253","https://openalex.org/I4210164937"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Navin Goyal","raw_affiliation_strings":["Microsoft"],"affiliations":[{"raw_affiliation_string":"Microsoft","institution_ids":["https://openalex.org/I4210164937"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5090342129","display_name":"Luis Rademacher","orcid":"https://orcid.org/0000-0001-8708-2755"},"institutions":[{"id":"https://openalex.org/I52357470","display_name":"The Ohio State University","ror":"https://ror.org/00rs6vg23","country_code":"US","type":"education","lineage":["https://openalex.org/I52357470"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Luis Rademacher","raw_affiliation_strings":["Ohio State University"],"affiliations":[{"raw_affiliation_string":"Ohio State University","institution_ids":["https://openalex.org/I52357470"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5111471766","display_name":"Heiko Roeglin","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Heiko Roeglin","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5082676353"],"corresponding_institution_ids":["https://openalex.org/I4210164937"],"apc_list":null,"apc_paid":null,"fwci":2.7798,"has_fulltext":true,"cited_by_count":12,"citation_normalized_percentile":{"value":0.88240942,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"10","issue":"1","first_page":"237","last_page":"256"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11830","display_name":"Point processes and geometric inequalities","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11830","display_name":"Point processes and geometric inequalities","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9994000196456909,"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"}},{"id":"https://openalex.org/T12176","display_name":"Optimization and Packing Problems","score":0.9977999925613403,"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/mathematics","display_name":"Mathematics","score":0.7357788681983948},{"id":"https://openalex.org/keywords/knapsack-problem","display_name":"Knapsack problem","score":0.7319505214691162},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.5955203771591187},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5895882844924927},{"id":"https://openalex.org/keywords/pareto-principle","display_name":"Pareto principle","score":0.5296772718429565},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.49037671089172363},{"id":"https://openalex.org/keywords/hyperplane","display_name":"Hyperplane","score":0.46437305212020874},{"id":"https://openalex.org/keywords/multi-objective-optimization","display_name":"Multi-objective optimization","score":0.41622811555862427},{"id":"https://openalex.org/keywords/omega","display_name":"Omega","score":0.4155097007751465},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3691343069076538}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7357788681983948},{"id":"https://openalex.org/C113138325","wikidata":"https://www.wikidata.org/wiki/Q864457","display_name":"Knapsack problem","level":2,"score":0.7319505214691162},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5955203771591187},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5895882844924927},{"id":"https://openalex.org/C137635306","wikidata":"https://www.wikidata.org/wiki/Q182667","display_name":"Pareto principle","level":2,"score":0.5296772718429565},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.49037671089172363},{"id":"https://openalex.org/C68693459","wikidata":"https://www.wikidata.org/wiki/Q657586","display_name":"Hyperplane","level":2,"score":0.46437305212020874},{"id":"https://openalex.org/C68781425","wikidata":"https://www.wikidata.org/wiki/Q2052203","display_name":"Multi-objective optimization","level":2,"score":0.41622811555862427},{"id":"https://openalex.org/C2779557605","wikidata":"https://www.wikidata.org/wiki/Q9890","display_name":"Omega","level":2,"score":0.4155097007751465},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3691343069076538},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","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},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.4086/toc.2014.v010a010","is_oa":true,"landing_page_url":"https://doi.org/10.4086/toc.2014.v010a010","pdf_url":"https://theoryofcomputing.org/articles/v010a010/v010a010.pdf","source":{"id":"https://openalex.org/S142665794","display_name":"Theory of Computing","issn_l":"1557-2862","issn":["1557-2862"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310315690","host_organization_name":"University of Chicago","host_organization_lineage":["https://openalex.org/P4310315690"],"host_organization_lineage_names":["University of Chicago"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Theory of Computing","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.4086/toc.2014.v010a010","is_oa":true,"landing_page_url":"https://doi.org/10.4086/toc.2014.v010a010","pdf_url":"https://theoryofcomputing.org/articles/v010a010/v010a010.pdf","source":{"id":"https://openalex.org/S142665794","display_name":"Theory of Computing","issn_l":"1557-2862","issn":["1557-2862"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310315690","host_organization_name":"University of Chicago","host_organization_lineage":["https://openalex.org/P4310315690"],"host_organization_lineage_names":["University of Chicago"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Theory of Computing","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.4300000071525574,"id":"https://metadata.un.org/sdg/17","display_name":"Partnerships for the goals"}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1611248441.pdf","grobid_xml":"https://content.openalex.org/works/W1611248441.grobid-xml"},"referenced_works_count":29,"referenced_works":["https://openalex.org/W87904750","https://openalex.org/W97263645","https://openalex.org/W565214016","https://openalex.org/W1480622933","https://openalex.org/W1572529050","https://openalex.org/W1799626923","https://openalex.org/W1817061570","https://openalex.org/W1964402547","https://openalex.org/W1968246336","https://openalex.org/W1981507127","https://openalex.org/W1992963068","https://openalex.org/W2007458506","https://openalex.org/W2019110169","https://openalex.org/W2034053794","https://openalex.org/W2075100187","https://openalex.org/W2098712873","https://openalex.org/W2101837693","https://openalex.org/W2107843968","https://openalex.org/W2139230981","https://openalex.org/W2400908863","https://openalex.org/W2568203473","https://openalex.org/W2573642654","https://openalex.org/W2911302472","https://openalex.org/W3022013732","https://openalex.org/W3022308742","https://openalex.org/W3029201735","https://openalex.org/W4226347946","https://openalex.org/W4252017042","https://openalex.org/W4302557773"],"related_works":["https://openalex.org/W2090178682","https://openalex.org/W4241467429","https://openalex.org/W2001591765","https://openalex.org/W2073147994","https://openalex.org/W2384474142","https://openalex.org/W3083133203","https://openalex.org/W1588199609","https://openalex.org/W2744462909","https://openalex.org/W1971520370","https://openalex.org/W1550055091"],"abstract_inverted_index":{"Smoothed":[0],"analysis":[1],"of":[2,21,65,75,96,105,112,125,196,210],"multiobjective":[3,50,147,186],"0-1":[4,212],"linear":[5,98],"optimization":[6,51,81,148],"has":[7],"drawn":[8],"considerable":[9],"attention":[10],"recently.":[11],"The":[12],"goal":[13],"is":[14,34,71,166],"to":[15,115,132,169],"give":[16],"bounds":[17,60,108,173],"for":[18,49,61,80,109,145,175,207],"the":[19,28,41,62,94,97,103,110,134,141,154,211],"number":[20,64,111],"Pareto-optimal":[22],"solutions":[23,26],"(i.":[24],"e.,":[25],"with":[27,83,159,215],"property":[29],"that":[30],"no":[31],"other":[32,176],"solution":[33],"at":[35,46],"least":[36,47],"as":[37,185],"good":[38],"in":[39,45,117,181],"all":[40],"coordinates":[42],"and":[43,86,120],"better":[44],"one)":[48],"problems.":[52,149],"In":[53],"this":[54,152,182],"article":[55],"we":[56],"prove":[57],"several":[58],"lower":[59,73,107,143,172,194],"expected":[63],"Pareto":[66,113],"optima.":[67],"Our":[68,100,164],"basic":[69,130],"result":[70,131],"a":[72],"bound":[74,144,195],"d":[76,84,198,201,204,216],"(n":[77,199],"d-1":[78],")":[79],"problems":[82],"objectives":[85],"n":[87],"variables":[88],"under":[89],"fairly":[90],"general":[91],"conditions":[92],"on":[93,153],"distributions":[95],"objectives.":[99],"proof":[101],"relates":[102],"problem":[104,158,214],"finding":[106],"optima":[114],"results":[116],"discrete":[118],"geometry":[119],"geometric":[121],"probability":[122],"about":[123],"arrangements":[124],"hyperplanes.":[126],"We":[127,150],"use":[128],"our":[129,139],"derive":[133],"following":[135],"results:":[136],"(1)":[137],"To":[138],"knowledge,":[140],"first":[142],"natural":[146],"illustrate":[151],"maximum":[155],"spanning":[156],"tree":[157],"randomly":[160],"chosen":[161],"edge":[162],"weights.":[163],"technique":[165],"sufficiently":[167],"flexible":[168],"yield":[170],"such":[171],"also":[174],"standard":[177],"objective":[178],"functions":[179],"studied":[180],"setting":[183],"(such":[184],"shortest":[187],"path,":[188],"TSP,":[189],"matching).":[190],"(2)":[191],"A":[192],"smoothed":[193],"min{":[197],"d-1.5":[200],"),":[202],"2":[203],"(n)":[205],"}":[206],"-smooth":[208],"instances":[209],"knapsack":[213],"profits.":[217]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":1}],"updated_date":"2025-12-17T22:08:43.090829","created_date":"2016-06-24T00:00:00"}