{"id":"https://openalex.org/W2807135138","doi":"https://doi.org/10.1137/17m1110353","title":"Local Testing of Lattices","display_name":"Local Testing of Lattices","publication_year":2018,"publication_date":"2018-01-01","ids":{"openalex":"https://openalex.org/W2807135138","doi":"https://doi.org/10.1137/17m1110353","mag":"2807135138"},"language":"en","primary_location":{"id":"doi:10.1137/17m1110353","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1110353","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/A5011591780","display_name":"Karthekeyan Chandrasekaran","orcid":"https://orcid.org/0000-0002-3421-7238"},"institutions":[{"id":"https://openalex.org/I157725225","display_name":"University of Illinois Urbana-Champaign","ror":"https://ror.org/047426m28","country_code":"US","type":"education","lineage":["https://openalex.org/I157725225"]},{"id":"https://openalex.org/I219193219","display_name":"Purdue University West Lafayette","ror":"https://ror.org/02dqehb95","country_code":"US","type":"education","lineage":["https://openalex.org/I219193219"]},{"id":"https://openalex.org/I74973139","display_name":"Carnegie Mellon University","ror":"https://ror.org/05x2bcf33","country_code":"US","type":"education","lineage":["https://openalex.org/I74973139"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Karthekeyan Chandrasekaran","raw_affiliation_strings":["Computer Science Department, Carnegie Mellon University, Pittsburgh, PA 15213","Computer Science, Purdue University, West Lafayette, IN 47906","Department of Industrial and Enterprise Systems Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Computer Science Department, Carnegie Mellon University, Pittsburgh, PA 15213","institution_ids":["https://openalex.org/I74973139"]},{"raw_affiliation_string":"Computer Science, Purdue University, West Lafayette, IN 47906","institution_ids":["https://openalex.org/I219193219"]},{"raw_affiliation_string":"Department of Industrial and Enterprise Systems Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801","institution_ids":["https://openalex.org/I157725225"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5002790246","display_name":"Mahdi Cheraghchi","orcid":"https://orcid.org/0000-0001-8957-0306"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Mahdi Cheraghchi","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5089321118","display_name":"Venkata Gandikota","orcid":"https://orcid.org/0000-0003-2381-7788"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Venkata Gandikota","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5090091569","display_name":"Elena Grigorescu","orcid":"https://orcid.org/0000-0001-9673-4313"},"institutions":[{"id":"https://openalex.org/I219193219","display_name":"Purdue University West Lafayette","ror":"https://ror.org/02dqehb95","country_code":"US","type":"education","lineage":["https://openalex.org/I219193219"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Elena Grigorescu","raw_affiliation_strings":["Computer Science, Purdue University, West Lafayette, IN 47906"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Computer Science, Purdue University, West Lafayette, IN 47906","institution_ids":["https://openalex.org/I219193219"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.09885541,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":95},"biblio":{"volume":"32","issue":"2","first_page":"1265","last_page":"1295"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9997000098228455,"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":0.9997000098228455,"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/T10237","display_name":"Cryptography and Data Security","score":0.9987000226974487,"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"}},{"id":"https://openalex.org/T12288","display_name":"Optimization and Search Problems","score":0.9976999759674072,"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/mathematics","display_name":"Mathematics","score":0.722651481628418},{"id":"https://openalex.org/keywords/lattice","display_name":"Lattice (music)","score":0.6114814281463623},{"id":"https://openalex.org/keywords/knapsack-problem","display_name":"Knapsack problem","score":0.6046510934829712},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5203063488006592},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.479593425989151},{"id":"https://openalex.org/keywords/matching","display_name":"Matching (statistics)","score":0.4449126124382019},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.43213874101638794},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.42874929308891296},{"id":"https://openalex.org/keywords/communication-complexity","display_name":"Communication complexity","score":0.42560499906539917},{"id":"https://openalex.org/keywords/cryptography","display_name":"Cryptography","score":0.42162463068962097},{"id":"https://openalex.org/keywords/group-testing","display_name":"Group testing","score":0.4172661602497101},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2500948905944824}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.722651481628418},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.6114814281463623},{"id":"https://openalex.org/C113138325","wikidata":"https://www.wikidata.org/wiki/Q864457","display_name":"Knapsack problem","level":2,"score":0.6046510934829712},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5203063488006592},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.479593425989151},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.4449126124382019},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.43213874101638794},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.42874929308891296},{"id":"https://openalex.org/C179145077","wikidata":"https://www.wikidata.org/wiki/Q5154130","display_name":"Communication complexity","level":2,"score":0.42560499906539917},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.42162463068962097},{"id":"https://openalex.org/C177580056","wikidata":"https://www.wikidata.org/wiki/Q5611272","display_name":"Group testing","level":2,"score":0.4172661602497101},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2500948905944824},{"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},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/17m1110353","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1110353","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"},{"id":"pmh:oai:spiral.imperial.ac.uk:10044/1/63227","is_oa":false,"landing_page_url":"http://hdl.handle.net/10044/1/63227","pdf_url":null,"source":{"id":"https://openalex.org/S4306401396","display_name":"Spiral (Imperial College London)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I47508984","host_organization_name":"Imperial College London","host_organization_lineage":["https://openalex.org/I47508984"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"1295","raw_type":"Journal Article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G80611279","display_name":null,"funder_award_id":"CCF-1649515","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320309667","display_name":"Purdue Research Foundation","ror":"https://ror.org/007n03h88"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W41804080","https://openalex.org/W112021158","https://openalex.org/W189554415","https://openalex.org/W1761303171","https://openalex.org/W2012632515","https://openalex.org/W2018925011","https://openalex.org/W2019578639","https://openalex.org/W2026129593","https://openalex.org/W2051880745","https://openalex.org/W2073966617","https://openalex.org/W2077388449","https://openalex.org/W2106287110","https://openalex.org/W2111809688","https://openalex.org/W2114616381","https://openalex.org/W2122621581","https://openalex.org/W2136370860","https://openalex.org/W2146453677","https://openalex.org/W2148352980","https://openalex.org/W2165406488","https://openalex.org/W2294062807","https://openalex.org/W2316593342","https://openalex.org/W2963757067","https://openalex.org/W3004537778","https://openalex.org/W4205426033"],"related_works":["https://openalex.org/W241127407","https://openalex.org/W1513451900","https://openalex.org/W4288641573","https://openalex.org/W2907393545","https://openalex.org/W2962784854","https://openalex.org/W2949083013","https://openalex.org/W2328371232","https://openalex.org/W3021623345","https://openalex.org/W1481287275","https://openalex.org/W3100257087"],"abstract_inverted_index":{"Testing":[0],"membership":[1,32,129,193],"in":[2,15,33,68,130,194,221],"lattices":[3,59,141,207],"is":[4,76,86],"of":[5,28,42,55,125,158,178,191,224],"practical":[6],"relevance,":[7],"with":[8,208],"applications":[9],"to":[10,70,78,99,146,167,219],"integer":[11],"programming,":[12],"error":[13],"detection":[14],"lattice-based":[16],"communication,":[17],"and":[18,36,60,89,104,118,151],"cryptography.":[19],"In":[20,48],"this":[21],"work,":[22],"we":[23,50,203],"initiate":[24],"a":[25],"systematic":[26],"study":[27],"local":[29,56,126],"testing":[30,127,159,166,169,179,192],"for":[31,58,95,128,138],"lattices,":[34],"complementing":[35],"building":[37],"upon":[38],"the":[39,53,62,122,155,175,188,195,200,215,222,225],"extensive":[40],"body":[41],"work":[43],"on":[44,121,154,174,187],"locally":[45],"testable":[46],"codes.":[47],"particular,":[49],"formally":[51],"define":[52],"notion":[54],"tests":[57],"present":[61],"following:":[63],"1.":[64],"We":[65,115,134,163],"show":[66,204],"that":[67,205],"order":[69],"achieve":[71],"low":[72],"query":[73,123,156,176,189],"complexity,":[74],"it":[75],"sufficient":[77],"design":[79],"$1$-sided":[80],"nonadaptive":[81],"canonical":[82],"tests.":[83],"This":[84,182],"result":[85,94],"akin":[87],"to,":[88],"based":[90],"on,":[91],"an":[92],"analogous":[93],"error-correcting":[96],"codes":[97,145],"due":[98],"[E.":[100],"Ben-Sasson,":[101],"P.":[102],"Harsha,":[103],"S.":[105],"Raskhodnikova,":[106],"SIAM":[107],"J.":[108],"Comput.,":[109],"35":[110],"(2005),":[111],"pp.":[112],"1--21].":[113],"2.":[114],"demonstrate":[116],"upper":[117,150],"lower":[119,152,172,185],"bounds":[120,153,173,186],"complexity":[124,157,177,190],"code":[131,139,168],"formula":[132,140],"lattices.":[133,161,181,198],"instantiate":[135],"our":[136],"results":[137],"constructed":[142],"from":[143],"Reed--Muller":[144],"obtain":[147],"nearly":[148],"matching":[149],"such":[160],"3.":[162],"contrast":[164],"lattice":[165],"by":[170],"showing":[171],"low-dimensional":[180],"illustrates":[183],"large":[184],"well-known":[196],"knapsack":[197,206],"On":[199],"other":[201],"hand,":[202],"bounded":[209],"coefficients":[210],"have":[211],"low-query":[212],"testers":[213],"if":[214],"inputs":[216],"are":[217],"promised":[218],"lie":[220],"span":[223],"lattice.":[226]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1}],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2025-10-10T00:00:00"}