{"id":"https://openalex.org/W4316652278","doi":"https://doi.org/10.1137/1.9781611977554.ch65","title":"Integrality Gaps for Random Integer Programs via Discrepancy","display_name":"Integrality Gaps for Random Integer Programs via Discrepancy","publication_year":2023,"publication_date":"2023-01-01","ids":{"openalex":"https://openalex.org/W4316652278","doi":"https://doi.org/10.1137/1.9781611977554.ch65"},"language":"en","primary_location":{"id":"doi:10.1137/1.9781611977554.ch65","is_oa":false,"landing_page_url":"https://doi.org/10.1137/1.9781611977554.ch65","pdf_url":null,"source":{"id":"https://openalex.org/S4306463922","display_name":"Society for Industrial and Applied Mathematics eBooks","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"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":"ebook platform"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2023 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA)","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/A5086943500","display_name":"Sander Borst","orcid":"https://orcid.org/0000-0003-4001-6675"},"institutions":[{"id":"https://openalex.org/I1341640284","display_name":"Centrum Wiskunde & Informatica","ror":"https://ror.org/00x7ekv49","country_code":"NL","type":"facility","lineage":["https://openalex.org/I1341640284","https://openalex.org/I2800991832","https://openalex.org/I4405262988"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Sander Borst","raw_affiliation_strings":["Centrum Wiskunde & Informatica (CWI), Amsterdam, The Netherlands,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Centrum Wiskunde & Informatica (CWI), Amsterdam, The Netherlands,","institution_ids":["https://openalex.org/I1341640284"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5044591096","display_name":"Daniel Dadush","orcid":"https://orcid.org/0000-0001-5577-5012"},"institutions":[{"id":"https://openalex.org/I1341640284","display_name":"Centrum Wiskunde & Informatica","ror":"https://ror.org/00x7ekv49","country_code":"NL","type":"facility","lineage":["https://openalex.org/I1341640284","https://openalex.org/I2800991832","https://openalex.org/I4405262988"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Daniel Dadush","raw_affiliation_strings":["Centrum Wiskunde & Informatica (CWI), Amsterdam, The Netherlands,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Centrum Wiskunde & Informatica (CWI), Amsterdam, The Netherlands,","institution_ids":["https://openalex.org/I1341640284"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5086897744","display_name":"Dan Mikulincer","orcid":"https://orcid.org/0000-0003-3597-3550"},"institutions":[{"id":"https://openalex.org/I4210110987","display_name":"IIT@MIT","ror":"https://ror.org/01wp8zh54","country_code":"US","type":"facility","lineage":["https://openalex.org/I30771326","https://openalex.org/I4210110987"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Dan Mikulincer","raw_affiliation_strings":["MIT, Cambridge, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"MIT, Cambridge, USA","institution_ids":["https://openalex.org/I4210110987"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.7436,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.91807494,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":null,"issue":null,"first_page":"1692","last_page":"1733"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9898999929428101,"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":0.9898999929428101,"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/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.9886000156402588,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/T12404","display_name":"Mathematical Approximation and Integration","score":0.9732000231742859,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7650856971740723},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6518930792808533},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.6007646322250366},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.5498587489128113},{"id":"https://openalex.org/keywords/distribution","display_name":"Distribution (mathematics)","score":0.5059952139854431},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.4927559196949005},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.49235403537750244},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.49226561188697815},{"id":"https://openalex.org/keywords/integer-programming","display_name":"Integer programming","score":0.48204144835472107},{"id":"https://openalex.org/keywords/probability-distribution","display_name":"Probability distribution","score":0.47985023260116577},{"id":"https://openalex.org/keywords/linear-programming-relaxation","display_name":"Linear programming relaxation","score":0.45972058176994324},{"id":"https://openalex.org/keywords/linear-programming","display_name":"Linear programming","score":0.427787721157074},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.1712060570716858},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.12501925230026245},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.11844879388809204},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.11123138666152954},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.08164167404174805}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7650856971740723},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6518930792808533},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.6007646322250366},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5498587489128113},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.5059952139854431},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.4927559196949005},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.49235403537750244},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.49226561188697815},{"id":"https://openalex.org/C56086750","wikidata":"https://www.wikidata.org/wiki/Q6042592","display_name":"Integer programming","level":2,"score":0.48204144835472107},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.47985023260116577},{"id":"https://openalex.org/C25360446","wikidata":"https://www.wikidata.org/wiki/Q1512771","display_name":"Linear programming relaxation","level":3,"score":0.45972058176994324},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.427787721157074},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.1712060570716858},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.12501925230026245},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.11844879388809204},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.11123138666152954},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.08164167404174805},{"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/1.9781611977554.ch65","is_oa":false,"landing_page_url":"https://doi.org/10.1137/1.9781611977554.ch65","pdf_url":null,"source":{"id":"https://openalex.org/S4306463922","display_name":"Society for Industrial and Applied Mathematics eBooks","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"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":"ebook platform"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2023 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA)","raw_type":"book-chapter"},{"id":"pmh:oai:cwi.nl:33769","is_oa":false,"landing_page_url":"https://ir.cwi.nl/pub/33769","pdf_url":null,"source":{"id":"https://openalex.org/S7407055335","display_name":"Centrum Wiskunde & Informatica (CWI), the national research institute for mathematics and computer science in the Netherlands","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/conferenceObject"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1773082376","display_name":"Towards a Quantitative Theory of Integer Programming","funder_award_id":"805241","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G2142617837","display_name":"Pathwise methods and stochastic calculus in the path towards understanding high-dimensional phenomena","funder_award_id":"803084","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G7842005466","display_name":null,"funder_award_id":"Horizon 2020","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"}],"funders":[{"id":"https://openalex.org/F4320309369","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44"},{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W144802579","https://openalex.org/W1559907478","https://openalex.org/W1560153690","https://openalex.org/W1910278602","https://openalex.org/W2035337703","https://openalex.org/W2049833095","https://openalex.org/W2052864894","https://openalex.org/W2106318612","https://openalex.org/W2483979206","https://openalex.org/W2499688774","https://openalex.org/W2732711529","https://openalex.org/W2787248994","https://openalex.org/W2808598845","https://openalex.org/W3142980271","https://openalex.org/W3159313784","https://openalex.org/W3160768711","https://openalex.org/W4206039841","https://openalex.org/W4252213128","https://openalex.org/W4294022794"],"related_works":["https://openalex.org/W134055995","https://openalex.org/W1963627056","https://openalex.org/W1973873435","https://openalex.org/W2124947072","https://openalex.org/W2773285351","https://openalex.org/W2161226285","https://openalex.org/W1981350060","https://openalex.org/W58208513","https://openalex.org/W2021079478","https://openalex.org/W2009127293"],"abstract_inverted_index":{"In":[0,135],"this":[1,136],"work,":[2],"we":[3,138,176],"prove":[4],"new":[5,251],"bounds":[6],"on":[7,43,111,153,194,299,331],"the":[8,12,50,64,97,108,114,118,143,146,163,179,197,225,242,246,279,316,332,348],"additive":[9,71],"gap":[10,120,202],"between":[11],"value":[13],"of":[14,32,41,52,66,99,148,165,227,278,281,297,334,350],"a":[15,38,60,250,265,275,282,293,326],"random":[16,91,256,283,351],"integer":[17,155],"program":[18],"max":[19],"cTx,":[20],"Ax":[21],"\u2264":[22],"b,":[23],"x":[24],"\u2208":[25],"{0,1}n":[26],"with":[27,126,214],"m":[28],"constraints":[29],"and":[30,55,75,79,93,161,241,303,305,336,340,342,354],"that":[31,88,205],"its":[33],"linear":[34,252],"programming":[35],"relaxation":[36],"for":[37,62,89,206,219,229,255],"wide":[39],"range":[40,296],"distributions":[42,298],"(A,b,c).":[44],"Our":[45,237,258,323],"investigation":[46],"is":[47,121,232,249,268],"motivated":[48],"by":[49,123],"work":[51,333],"Dey,":[53],"Dubey,":[54],"Molinaro":[56],"(SODA'21),":[57],"who":[58,346],"gave":[59],"framework":[61],"relating":[63],"size":[65,212],"Branch-and-Bound":[67],"(B&B)":[68],"trees":[69,210],"to":[70,106,142,170,182,187,199,234,244,270,274,287,311,315],"integrality":[72,119],"gaps.":[73],"Dyer":[74],"Frieze":[76],"(MOR":[77],"'89)":[78],"Borst":[80],"et":[81],"al.":[82],"(Mathematical":[83],"Programming":[84],"'22),":[85],"respectively,":[86],"showed":[87],"certain":[90],"packing":[92],"Gaussian":[94,115],"IPs,":[95],"where":[96,145,162],"entries":[98,147,158],"A,":[100,300],"c":[101],"are":[102,150,167],"independently":[103],"distributed":[104,152,168],"according":[105,169],"either":[107],"uniform":[109],"distribution":[110,116],"[0,1]":[112],"or":[113,271],"N(0,1),":[117],"bounded":[122],"Om(log2":[124],"n/n)":[125],"probability":[127,181,189,216,308,318],"at":[128],"least":[129],"1":[130,183],"\u2212":[131],"1/n":[132],"-":[133,184],"e\u2212\u03a9m(1).":[134],"paper,":[137],"generalize":[139],"these":[140,207],"results":[141,203,248],"cases":[144],"A":[149,166],"uniformly":[151],"an":[154,171],"interval":[156],"(e.g.,":[157],"in":[159,190,320],"{-1,0,1}),":[160],"columns":[164,280],"isotropic":[172],"logconcave":[173],"distribution.":[174],"Second,":[175],"substantially":[177],"improve":[178],"success":[180,307],"1/poly(n),":[185],"compared":[186],"constant":[188,317],"prior":[191,288],"works":[192],"(depending":[193],"m).":[195],"Leveraging":[196],"connection":[198],"Branch-and-Bound,":[200],"our":[201,290],"imply":[204],"IPs":[208,228],"B&B":[209,231],"have":[211],"npoly(m)":[213],"high":[215],"(i.e.,":[217],"polynomial":[218],"fixed":[220],"m),":[221],"which":[222,230,264],"significantly":[223],"extends":[224],"class":[226],"known":[233],"be":[235],"polynomial.":[236],"main":[238],"technical":[239],"contribution":[240],"key":[243],"achieving":[245],"above":[247],"discrepancy":[253,349],"theorem":[254,259,291],"matrices.":[257],"gives":[260],"general":[261],"conditions":[262],"under":[263],"target":[266],"vector":[267],"equal":[269],"very":[272],"close":[273,310],"{0,1}":[276],"combination":[277],"matrix":[284],"A.":[285],"Compared":[286],"results,":[289],"handles":[292],"much":[294],"wider":[295],"both":[301],"continuous":[302],"discrete,":[304],"achieves":[306],"exponentially":[309],"1,":[312],"as":[313],"opposed":[314],"shown":[319],"earlier":[321],"results.":[322],"proof":[324],"uses":[325],"Fourier":[327],"analytic":[328],"approach,":[329],"building":[330],"Hoberg":[335],"Rothvoss":[337],"(SODA":[338],"'19)":[339],"Franks":[341],"Saks":[343],"(RSA":[344],"'20)":[345],"studied":[347],"set":[352],"systems":[353],"matrices":[355],"respectively.":[356]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1}],"updated_date":"2026-07-08T08:33:18.762332","created_date":"2025-10-10T00:00:00"}
