{"id":"https://openalex.org/W4224229783","doi":"https://doi.org/10.1137/21m1435288","title":"Anticoncentration and the Exact Gap-Hamming Problem","display_name":"Anticoncentration and the Exact Gap-Hamming Problem","publication_year":2022,"publication_date":"2022-04-21","ids":{"openalex":"https://openalex.org/W4224229783","doi":"https://doi.org/10.1137/21m1435288"},"language":"en","primary_location":{"id":"doi:10.1137/21m1435288","is_oa":false,"landing_page_url":"https://doi.org/10.1137/21m1435288","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/A5035012558","display_name":"Anup Rao","orcid":"https://orcid.org/0000-0002-6449-9547"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Anup Rao","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5041051779","display_name":"Amir Yehudayoff","orcid":"https://orcid.org/0000-0002-0177-1814"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Amir Yehudayoff","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5035012558"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.1461,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.45204859,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"36","issue":"2","first_page":"1071","last_page":"1092"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9998999834060669,"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":0.9998999834060669,"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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/T10237","display_name":"Cryptography and Data Security","score":0.998199999332428,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/combinatorics","display_name":"Combinatorics","score":0.8070536255836487},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.778294563293457},{"id":"https://openalex.org/keywords/hamming-distance","display_name":"Hamming distance","score":0.6102643013000488},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.5701520442962646},{"id":"https://openalex.org/keywords/product","display_name":"Product (mathematics)","score":0.5335476994514465},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4194398522377014},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.08530336618423462}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8070536255836487},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.778294563293457},{"id":"https://openalex.org/C193319292","wikidata":"https://www.wikidata.org/wiki/Q272172","display_name":"Hamming distance","level":2,"score":0.6102643013000488},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.5701520442962646},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.5335476994514465},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4194398522377014},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.08530336618423462}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/21m1435288","is_oa":false,"landing_page_url":"https://doi.org/10.1137/21m1435288","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":[],"awards":[{"id":"https://openalex.org/G6840542549","display_name":null,"funder_award_id":"1162/15","funder_id":"https://openalex.org/F4320322252","funder_display_name":"Israel Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320322252","display_name":"Israel Science Foundation","ror":"https://ror.org/04sazxf24"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W996473569","https://openalex.org/W1012441002","https://openalex.org/W1968319543","https://openalex.org/W1973286131","https://openalex.org/W1981696777","https://openalex.org/W1985526537","https://openalex.org/W1989751882","https://openalex.org/W1994786975","https://openalex.org/W2014485295","https://openalex.org/W2047705353","https://openalex.org/W2062669257","https://openalex.org/W2104635635","https://openalex.org/W2122058331","https://openalex.org/W2162317237","https://openalex.org/W2170168647","https://openalex.org/W3083309575","https://openalex.org/W3208399317"],"related_works":["https://openalex.org/W2980963558","https://openalex.org/W2002282073","https://openalex.org/W2167635576","https://openalex.org/W1882246857","https://openalex.org/W3103304230","https://openalex.org/W2185360082","https://openalex.org/W1992365905","https://openalex.org/W2067417168","https://openalex.org/W4287664878","https://openalex.org/W3212023493"],"abstract_inverted_index":{"We":[0,24,93,114],"prove":[1,18,74,98],"anticoncentration":[2,117],"bounds":[3,16,20],"for":[4,118],"the":[5,32,57,75,100],"inner":[6,58],"product":[7,59],"of":[8,31,141,143],"two":[9],"independent":[10],"random":[11],"vectors":[12],"and":[13,43,47,54,132],"use":[14,94],"these":[15,95],"to":[17,97,138],"lower":[19],"in":[21,111],"communication":[22,112],"complexity.":[23,113],"show":[25],"that":[26,99],"if":[27],"$A,B$":[28],"are":[29,51],"subsets":[30],"cube":[33],"$\\{\\pm":[34],"1\\}^n$":[35,136],"with":[36,66,121],"$|A|":[37],"\\cdot":[38],"|B|":[39],"\\geq":[40],"2^{1.01":[41],"n}$,":[42],"$X":[44],"\\in":[45,49,126],"A$":[46],"$Y":[48],"B$":[50],"sampled":[52],"independently":[53],"uniformly,":[55],"then":[56,146],"$\\langle{X},{Y}\\rangle$":[60],"takes":[61],"on":[62],"any":[63],"fixed":[64],"value":[65],"probability":[67],"at":[68],"most":[69],"$O(1/\\sqrt{n})$.":[70],"In":[71],"fact,":[72],"we":[73],"following":[76],"stronger":[77],"\u201csmoothness\"":[78],"statement:":[79],"$":[80],"\\max_{k":[81],"}":[82],"\\big|":[83],"\\Pr[\\langle{X},{Y}\\rangle":[84,88],"=":[85,89,149],"k]":[86,150],"-":[87],"k+4]\\big|":[90],"\\leq":[91,151],"O(1/n).$":[92],"results":[96],"exact":[101],"gap-hamming":[102],"problem":[103,110],"requires":[104],"linear":[105],"communication,":[106],"resolving":[107],"an":[108],"open":[109],"also":[115],"conclude":[116],"structured":[119],"distributions":[120],"low":[122],"entropy.":[123],"If":[124],"$x":[125],"\\mathbb{Z}^n$":[127],"has":[128],"no":[129],"zero":[130],"coordinates,":[131],"$B":[133],"\\subseteq":[134],"\\{\\pm":[135],"corresponds":[137],"a":[139],"subspace":[140],"$\\mathbb{F}_2^n$":[142],"dimension":[144],"$0.51n$,":[145],"$\\max_k":[147],"\\Pr[\\langle{x},{Y}\\rangle":[148],"O(\\sqrt{\\ln":[152],"(n)/n})$.":[153]},"counts_by_year":[{"year":2023,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}