{"id":"https://openalex.org/W2048904689","doi":"https://doi.org/10.1137/s0097539795295626","title":"Complexity Analysis of a Parallel Lattice Basis Reduction Algorithm","display_name":"Complexity Analysis of a Parallel Lattice Basis Reduction Algorithm","publication_year":1998,"publication_date":"1998-10-01","ids":{"openalex":"https://openalex.org/W2048904689","doi":"https://doi.org/10.1137/s0097539795295626","mag":"2048904689"},"language":"en","primary_location":{"id":"doi:10.1137/s0097539795295626","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0097539795295626","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"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 Computing","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/A5035915552","display_name":"Christian Heckler","orcid":null},"institutions":[{"id":"https://openalex.org/I206945453","display_name":"Paderborn University","ror":"https://ror.org/058kzsd48","country_code":"DE","type":"education","lineage":["https://openalex.org/I206945453"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"C. Heckler","raw_affiliation_strings":["Paderborn University:"],"affiliations":[{"raw_affiliation_string":"Paderborn University:","institution_ids":["https://openalex.org/I206945453"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5060999697","display_name":"Lothar Thiele","orcid":"https://orcid.org/0000-0001-6139-868X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"L. Thiele","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5035915552"],"corresponding_institution_ids":["https://openalex.org/I206945453"],"apc_list":null,"apc_paid":null,"fwci":0.5353,"has_fulltext":false,"cited_by_count":15,"citation_normalized_percentile":{"value":0.74839908,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"27","issue":"5","first_page":"1295","last_page":"1302"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10237","display_name":"Cryptography and Data Security","score":0.9997000098228455,"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/T10237","display_name":"Cryptography and Data Security","score":0.9997000098228455,"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":0.9991999864578247,"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/T11130","display_name":"Coding theory and cryptography","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/speedup","display_name":"Speedup","score":0.7065132856369019},{"id":"https://openalex.org/keywords/lattice-problem","display_name":"Lattice problem","score":0.6314975619316101},{"id":"https://openalex.org/keywords/lattice-reduction","display_name":"Lattice reduction","score":0.627474308013916},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6150463223457336},{"id":"https://openalex.org/keywords/lattice","display_name":"Lattice (music)","score":0.6138767004013062},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.5273329019546509},{"id":"https://openalex.org/keywords/basis","display_name":"Basis (linear algebra)","score":0.5063363313674927},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.5017437934875488},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5007565021514893},{"id":"https://openalex.org/keywords/binary-logarithm","display_name":"Binary logarithm","score":0.4864889979362488},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.44832462072372437},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.41988465189933777},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3986576795578003},{"id":"https://openalex.org/keywords/cryptography","display_name":"Cryptography","score":0.3337523639202118},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.21773621439933777},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.20520377159118652},{"id":"https://openalex.org/keywords/parallel-computing","display_name":"Parallel computing","score":0.12937834858894348}],"concepts":[{"id":"https://openalex.org/C68339613","wikidata":"https://www.wikidata.org/wiki/Q1549489","display_name":"Speedup","level":2,"score":0.7065132856369019},{"id":"https://openalex.org/C168482242","wikidata":"https://www.wikidata.org/wiki/Q6497128","display_name":"Lattice problem","level":3,"score":0.6314975619316101},{"id":"https://openalex.org/C44274781","wikidata":"https://www.wikidata.org/wiki/Q6497132","display_name":"Lattice reduction","level":4,"score":0.627474308013916},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6150463223457336},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.6138767004013062},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.5273329019546509},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.5063363313674927},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.5017437934875488},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5007565021514893},{"id":"https://openalex.org/C63553672","wikidata":"https://www.wikidata.org/wiki/Q581168","display_name":"Binary logarithm","level":2,"score":0.4864889979362488},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.44832462072372437},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.41988465189933777},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3986576795578003},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.3337523639202118},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.21773621439933777},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.20520377159118652},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.12937834858894348},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C54197355","wikidata":"https://www.wikidata.org/wiki/Q5782992","display_name":"Beamforming","level":2,"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/C207987634","wikidata":"https://www.wikidata.org/wiki/Q176862","display_name":"MIMO","level":3,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/s0097539795295626","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0097539795295626","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"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 Computing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W1508816856","https://openalex.org/W1549180787","https://openalex.org/W1576391039","https://openalex.org/W1963547452","https://openalex.org/W2023560340","https://openalex.org/W2067935912","https://openalex.org/W2114616381","https://openalex.org/W2126483728","https://openalex.org/W2141040012","https://openalex.org/W2156251728","https://openalex.org/W2175796176"],"related_works":["https://openalex.org/W3112306103","https://openalex.org/W2949749387","https://openalex.org/W1597211008","https://openalex.org/W1819927718","https://openalex.org/W3187275826","https://openalex.org/W4390571163","https://openalex.org/W4378220036","https://openalex.org/W2071893554","https://openalex.org/W2348168089","https://openalex.org/W166611642"],"abstract_inverted_index":{"Lattice":[0],"basis":[1,61],"reduction":[2],"is":[3,77,80,117],"an":[4,84,112],"important":[5],"problem":[6],"in":[7,13,29],"geometry":[8],"of":[9,48,58,69,73,115],"numbers":[10],"with":[11],"applications":[12],"combinatorial":[14],"optimization,":[15],"computer":[16],"algebra,":[17],"and":[18,51,75,109],"cryptography.":[19],"The":[20],"well-known":[21],"sequential":[22],"LLL":[23],"algorithm":[24,72],"finds":[25],"a":[26,66],"short":[27],"vector":[28],"O(n4":[30],"log":[31,41,92,102],"B)":[32,93],"arithmetic":[33,94],"operations":[34,95],"on":[35,83,96],"integers":[36,97],"having":[37,98],"binary":[38,99],"length":[39,100],"O(n":[40,101],"B),":[42],"where":[43],"n":[44,85,87],"denotes":[45,53],"the":[46,49,54,59,70,106],"dimension":[47],"lattice":[50],"B":[52],"maximum":[55],"L2":[56],"norm":[57],"initial":[60],"vectors.":[62],"In":[63],"this":[64],"paper":[65],"new":[67],"analysis":[68,108],"parallel":[71],"Roch":[74],"Villard":[76],"presented.":[78],"It":[79],"shown":[81],"that":[82,111],"x":[86],"mesh":[88],"it":[89],"needs":[90],"O(n2":[91],"B).":[103],"This":[104],"improves":[105],"previous":[107],"shows":[110],"asymptotical":[113],"speedup":[114],"n2":[116,120],"possible":[118],"using":[119],"processors.":[121]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}