{"id":"https://openalex.org/W2132302072","doi":"https://doi.org/10.1109/sfcs.1993.366815","title":"The hardness of approximate optima in lattices, codes, and systems of linear equations","display_name":"The hardness of approximate optima in lattices, codes, and systems of linear equations","publication_year":2002,"publication_date":"2002-12-30","ids":{"openalex":"https://openalex.org/W2132302072","doi":"https://doi.org/10.1109/sfcs.1993.366815","mag":"2132302072"},"language":"en","primary_location":{"is_oa":false,"landing_page_url":"https://doi.org/10.1109/sfcs.1993.366815","pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false},"type":"article","type_crossref":"proceedings-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/A5103209777","display_name":"Sanjeev Arora","orcid":"https://orcid.org/0000-0003-4852-691X"},"institutions":[{"id":"https://openalex.org/I95457486","display_name":"University of California, Berkeley","ror":"https://ror.org/01an7q238","country_code":"US","type":"education","lineage":["https://openalex.org/I95457486"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"S. Arora","raw_affiliation_strings":["Div. of Comput. Sci., California Univ., Berkeley, CA, USA#TAB#"],"affiliations":[{"raw_affiliation_string":"Div. of Comput. Sci., California Univ., Berkeley, CA, USA#TAB#","institution_ids":["https://openalex.org/I95457486"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5014978503","display_name":"L\u00e1szl\u00f3 Babai","orcid":"https://orcid.org/0000-0002-2058-685X"},"institutions":[{"id":"https://openalex.org/I20089843","display_name":"Princeton University","ror":"https://ror.org/00hx57361","country_code":"US","type":"education","lineage":["https://openalex.org/I20089843"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"L. Babai","raw_affiliation_strings":["Computer Science, Princeton University#TAB#"],"affiliations":[{"raw_affiliation_string":"Computer Science, Princeton University#TAB#","institution_ids":["https://openalex.org/I20089843"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5108393186","display_name":"Jacques Stern","orcid":null},"institutions":[{"id":"https://openalex.org/I20089843","display_name":"Princeton University","ror":"https://ror.org/00hx57361","country_code":"US","type":"education","lineage":["https://openalex.org/I20089843"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"J. Stern","raw_affiliation_strings":["Computer Science, Princeton University#TAB#"],"affiliations":[{"raw_affiliation_string":"Computer Science, Princeton University#TAB#","institution_ids":["https://openalex.org/I20089843"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5062516367","display_name":"Z. Sweedyk","orcid":null},"institutions":[{"id":"https://openalex.org/I20089843","display_name":"Princeton University","ror":"https://ror.org/00hx57361","country_code":"US","type":"education","lineage":["https://openalex.org/I20089843"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Z. Sweedyk","raw_affiliation_strings":["Computer Science, Princeton University#TAB#"],"affiliations":[{"raw_affiliation_string":"Computer Science, Princeton University#TAB#","institution_ids":["https://openalex.org/I20089843"]}]}],"institution_assertions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":7.285,"has_fulltext":true,"fulltext_origin":"ngrams","cited_by_count":188,"citation_normalized_percentile":{"value":0.966763,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":98,"max":99},"biblio":{"volume":null,"issue":null,"first_page":"724","last_page":"733"},"is_retracted":false,"is_paratext":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9999,"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"}},"topics":[{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9999,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9997,"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/T11797","display_name":"graph theory and CDMA systems","score":0.9993,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.39801383},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3711422},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.36364824},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.35573798}],"mesh":[],"locations_count":1,"locations":[{"is_oa":false,"landing_page_url":"https://doi.org/10.1109/sfcs.1993.366815","pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false}],"best_oa_location":null,"sustainable_development_goals":[],"grants":[],"datasets":[],"versions":[],"referenced_works_count":35,"referenced_works":["https://openalex.org/W1505918075","https://openalex.org/W1511716344","https://openalex.org/W1592882366","https://openalex.org/W1973270757","https://openalex.org/W1984424319","https://openalex.org/W1989510734","https://openalex.org/W2002032317","https://openalex.org/W2011039300","https://openalex.org/W2016232593","https://openalex.org/W2026129593","https://openalex.org/W2033361557","https://openalex.org/W2035929826","https://openalex.org/W2038225707","https://openalex.org/W2040579873","https://openalex.org/W2046751564","https://openalex.org/W2053086236","https://openalex.org/W2053113791","https://openalex.org/W2055767422","https://openalex.org/W2059453880","https://openalex.org/W2066356146","https://openalex.org/W2079473728","https://openalex.org/W2080578129","https://openalex.org/W2097206148","https://openalex.org/W2111416661","https://openalex.org/W2132258126","https://openalex.org/W2132605415","https://openalex.org/W2141040012","https://openalex.org/W2141815340","https://openalex.org/W2150780437","https://openalex.org/W2171712712","https://openalex.org/W2401610261","https://openalex.org/W3004537778","https://openalex.org/W3217775779","https://openalex.org/W4256317935","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W4238204885","https://openalex.org/W3002753104","https://openalex.org/W2748952813","https://openalex.org/W2600246793","https://openalex.org/W2142036596","https://openalex.org/W2077600819","https://openalex.org/W2072657027","https://openalex.org/W2061531152","https://openalex.org/W2007980826","https://openalex.org/W1979597421"],"abstract_inverted_index":{"We":[0],"prove":[1],"the":[2,5,15,22,29,39,61,93,99,105,118,123,126],"following":[3],"about":[4],"Nearest":[6,16],"Lattice":[7,95],"Vector":[8,96,128],"Problem":[9,18,97,129],"(in":[10],"any":[11,42],"l/sub":[12,100,131],"p/":[13],"norm),":[14],"Code-word":[17],"for":[19,49,92,115],"binary":[20],"codes,":[21],"problem":[23],"of":[24,31,66,117,125],"learning":[25],"a":[26,55,64,152],"halfspace":[27],"in":[28,75,98,130],"presence":[30],"errors,":[32],"and":[33],"some":[34,50],"other":[35],"problems.":[36],"1.":[37],"Approximating":[38],"optimum":[40,62],"within":[41,63],"constant":[43],"factor":[44,65,106],"is":[45,74],"NP-hard.":[46],"2.":[47],"If":[48],"/spl":[51,101,113],"epsiv/>0":[52],"there":[53],"exists":[54],"polynomial":[56],"time":[57],"algorithm":[58],"that":[59,87],"approximates":[60],"2/sup":[67,107],"log(0.5-/spl":[68,108],"epsiv/)/":[69,109],"/sup":[70,82,110],"n/":[71,111],"then":[72],"NP":[73],"quasi-polynomial":[76],"deterministic":[77],"time:":[78],"NP/spl":[79],"sube/DTIME(n/sup":[80],"poly(log/":[81],"n)/).":[83],"Moreover,":[84],"we":[85],"show":[86],"result":[88],"2":[89],"also":[90],"holds":[91],"Shortest":[94,127],"infin//":[102],"norm.":[103],"Improving":[104],"to":[112],"radic/(dim)":[114],"either":[116,148],"lattice":[119],"problems":[120],"would":[121],"imply":[122],"hardness":[124],"2/":[132],"norm;":[133],"an":[134],"old":[135],"open":[136],"problem.":[137],"Our":[138],"proofs":[139],"use":[140],"reductions":[141],"from":[142],"few-prover,":[143],"one-round":[144],"interactive":[145],"proof":[146],"systems,":[147],"directly,":[149],"or":[150],"through":[151],"set-cover":[153],"problem.<":[154],">":[157]},"cited_by_api_url":"https://api.openalex.org/works?filter=cites:W2132302072","counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":8},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":17},{"year":2014,"cited_by_count":13},{"year":2013,"cited_by_count":11},{"year":2012,"cited_by_count":4}],"updated_date":"2025-01-21T09:28:23.463472","created_date":"2016-06-24"}