{"id":"https://openalex.org/W2895464064","doi":"https://doi.org/10.1109/tpds.2018.2873354","title":"Solving Linear Diophantine Systems on Parallel Architectures","display_name":"Solving Linear Diophantine Systems on Parallel Architectures","publication_year":2018,"publication_date":"2018-10-05","ids":{"openalex":"https://openalex.org/W2895464064","doi":"https://doi.org/10.1109/tpds.2018.2873354","mag":"2895464064"},"language":"en","primary_location":{"id":"doi:10.1109/tpds.2018.2873354","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tpds.2018.2873354","pdf_url":null,"source":{"id":"https://openalex.org/S97130795","display_name":"IEEE Transactions on Parallel and Distributed Systems","issn_l":"1045-9219","issn":["1045-9219","1558-2183","2161-9883"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Parallel and Distributed Systems","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/A5033228887","display_name":"Dmitry A. Zaitsev","orcid":"https://orcid.org/0000-0001-5698-7324"},"institutions":[{"id":"https://openalex.org/I4210094535","display_name":"International Humanitarian University","ror":"https://ror.org/00811aj93","country_code":"UA","type":"education","lineage":["https://openalex.org/I4210094535"]}],"countries":["UA"],"is_corresponding":false,"raw_author_name":"Dmitry Zaitsev","raw_affiliation_strings":["Department of Computer Engineering and Innovative Technology, International Humanitarian University, Fontanskaya Doroga 33, Odessa, Ukraine","[Department of Computer Engineering and Innovative Technology, International Humanitarian University, Fontanskaya Doroga 33, Odessa, Ukraine]"],"raw_orcid":"https://orcid.org/0000-0001-5698-7324","affiliations":[{"raw_affiliation_string":"Department of Computer Engineering and Innovative Technology, International Humanitarian University, Fontanskaya Doroga 33, Odessa, Ukraine","institution_ids":["https://openalex.org/I4210094535"]},{"raw_affiliation_string":"[Department of Computer Engineering and Innovative Technology, International Humanitarian University, Fontanskaya Doroga 33, Odessa, Ukraine]","institution_ids":["https://openalex.org/I4210094535"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5083604741","display_name":"Stanimire Tomov","orcid":"https://orcid.org/0000-0002-5937-7959"},"institutions":[{"id":"https://openalex.org/I75027704","display_name":"University of Tennessee at Knoxville","ror":"https://ror.org/020f3ap87","country_code":"US","type":"education","lineage":["https://openalex.org/I75027704"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Stanimire Tomov","raw_affiliation_strings":["Innovative Computing Laboratory, The University of Tennessee, Knoxville, TN, USA","[Innovative Computing Laboratory, The University of Tennessee, Knoxville, TN, USA]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Innovative Computing Laboratory, The University of Tennessee, Knoxville, TN, USA","institution_ids":["https://openalex.org/I75027704"]},{"raw_affiliation_string":"[Innovative Computing Laboratory, The University of Tennessee, Knoxville, TN, USA]","institution_ids":["https://openalex.org/I75027704"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5075517045","display_name":"Jack Dongarra","orcid":"https://orcid.org/0000-0003-3247-1782"},"institutions":[{"id":"https://openalex.org/I75027704","display_name":"University of Tennessee at Knoxville","ror":"https://ror.org/020f3ap87","country_code":"US","type":"education","lineage":["https://openalex.org/I75027704"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jack Dongarra","raw_affiliation_strings":["Innovative Computing Laboratory, The University of Tennessee, Knoxville, TN, USA","[Innovative Computing Laboratory, The University of Tennessee, Knoxville, TN, USA]"],"raw_orcid":"https://orcid.org/0000-0003-3247-1782","affiliations":[{"raw_affiliation_string":"Innovative Computing Laboratory, The University of Tennessee, Knoxville, TN, USA","institution_ids":["https://openalex.org/I75027704"]},{"raw_affiliation_string":"[Innovative Computing Laboratory, The University of Tennessee, Knoxville, TN, USA]","institution_ids":["https://openalex.org/I75027704"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":2645,"currency":"USD","value_usd":2645},"apc_paid":null,"fwci":1.7652,"has_fulltext":false,"cited_by_count":17,"citation_normalized_percentile":{"value":0.86923389,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"30","issue":"5","first_page":"1158","last_page":"1169"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11125","display_name":"Petri Nets in System Modeling","score":0.9994000196456909,"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/T11125","display_name":"Petri Nets in System Modeling","score":0.9994000196456909,"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/T10142","display_name":"Formal Methods in Verification","score":0.9983999729156494,"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/T10772","display_name":"Distributed systems and fault tolerance","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/computer-science","display_name":"Computer science","score":0.8004534244537354},{"id":"https://openalex.org/keywords/parallel-computing","display_name":"Parallel computing","score":0.6288597583770752},{"id":"https://openalex.org/keywords/speedup","display_name":"Speedup","score":0.6164368987083435},{"id":"https://openalex.org/keywords/diophantine-equation","display_name":"Diophantine equation","score":0.5425084829330444},{"id":"https://openalex.org/keywords/solver","display_name":"Solver","score":0.5380188226699829},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.3988490700721741},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3406696319580078},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.1468355655670166},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.11721667647361755}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.8004534244537354},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.6288597583770752},{"id":"https://openalex.org/C68339613","wikidata":"https://www.wikidata.org/wiki/Q1549489","display_name":"Speedup","level":2,"score":0.6164368987083435},{"id":"https://openalex.org/C206530611","wikidata":"https://www.wikidata.org/wiki/Q905896","display_name":"Diophantine equation","level":2,"score":0.5425084829330444},{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.5380188226699829},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3988490700721741},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3406696319580078},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.1468355655670166},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.11721667647361755},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/tpds.2018.2873354","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tpds.2018.2873354","pdf_url":null,"source":{"id":"https://openalex.org/S97130795","display_name":"IEEE Transactions on Parallel and Distributed Systems","issn_l":"1045-9219","issn":["1045-9219","1558-2183","2161-9883"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Parallel and Distributed Systems","raw_type":"journal-article"},{"id":"pmh:oai:pure.atira.dk:openaire_cris_publications/f70764bd-a0e4-433f-929d-0a04e192b8ec","is_oa":false,"landing_page_url":"https://research.manchester.ac.uk/en/publications/f70764bd-a0e4-433f-929d-0a04e192b8ec","pdf_url":null,"source":{"id":"https://openalex.org/S4306400662","display_name":"Research Explorer (The University of Manchester)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I28407311","host_organization_name":"University of Manchester","host_organization_lineage":["https://openalex.org/I28407311"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Zaitsev, D, Tomov, S & Dongarra, J 2018, 'Solving Linear Diophantine Systems on Parallel Architectures', IEEE Transactions on Parallel and Distributed Systems. https://doi.org/10.1109/TPDS.2018.2873354","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:pure.atira.dk:publications/f70764bd-a0e4-433f-929d-0a04e192b8ec","is_oa":false,"landing_page_url":"https://www.research.manchester.ac.uk/portal/en/publications/solving-linear-diophantine-systems-on-parallel-architectures(f70764bd-a0e4-433f-929d-0a04e192b8ec).html","pdf_url":null,"source":{"id":"https://openalex.org/S4306400662","display_name":"Research Explorer (The University of Manchester)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I28407311","host_organization_name":"University of Manchester","host_organization_lineage":["https://openalex.org/I28407311"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Zaitsev, D, Tomov, S & Dongarra, J 2018, 'Solving Linear Diophantine Systems on Parallel Architectures', IEEE Transactions on Parallel and Distributed Systems. https://doi.org/10.1109/TPDS.2018.2873354","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G8055921353","display_name":null,"funder_award_id":"Fulbright Schollarship,Dmitry Zaitsev,Sep-Nov,2017","funder_id":"https://openalex.org/F4320312210","funder_display_name":"Fulbright Association"}],"funders":[{"id":"https://openalex.org/F4320312210","display_name":"Fulbright Association","ror":"https://ror.org/00300j256"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W31923072","https://openalex.org/W1493186690","https://openalex.org/W1503001724","https://openalex.org/W1510543252","https://openalex.org/W1520511539","https://openalex.org/W1555374034","https://openalex.org/W1589918049","https://openalex.org/W1600301286","https://openalex.org/W1996109622","https://openalex.org/W2003854010","https://openalex.org/W2061854932","https://openalex.org/W2070996046","https://openalex.org/W2105294563","https://openalex.org/W2112979757","https://openalex.org/W2118861911","https://openalex.org/W2150468831","https://openalex.org/W2156934291","https://openalex.org/W2162322364","https://openalex.org/W2167435639","https://openalex.org/W2255347072","https://openalex.org/W2712815726","https://openalex.org/W2799004609","https://openalex.org/W6629506945","https://openalex.org/W6677391886"],"related_works":["https://openalex.org/W2317245370","https://openalex.org/W4249323025","https://openalex.org/W198851386","https://openalex.org/W1980160788","https://openalex.org/W2030310580","https://openalex.org/W947442053","https://openalex.org/W2148915962","https://openalex.org/W2283866686","https://openalex.org/W27867058","https://openalex.org/W2948365806"],"abstract_inverted_index":{"Solving":[0],"linear":[1,68],"Diophantine":[2,69],"systems":[3,28,70,129,165],"of":[4,51,67,76,115,121,171,181],"equations":[5],"is":[6,38,56,82,104,125,142,161],"applied":[7,126,143],"in":[8,34,144,168],"discrete-event":[9],"systems,":[10],"model":[11],"checking,":[12],"formal":[13],"languages":[14],"and":[15,23,84,99],"automata,":[16],"logic":[17],"programming,":[18],"cryptography,":[19],"networking,":[20],"signal":[21],"processing,":[22],"chemistry.":[24],"For":[25,45],"modeling":[26],"discrete":[27],"with":[29,53,200],"Petri":[30],"nets,":[31],"a":[32,64,92,108,111,133,146,151,179],"solution":[33],"non-negative":[35],"integer":[36],"numbers":[37],"required,":[39],"which":[40],"represents":[41],"an":[42],"intractable":[43],"problem.":[44],"this":[46,60],"reason,":[47],"solving":[48,128,145],"such":[49],"kinds":[50],"tasks":[52],"significant":[54],"speedup":[55,195],"highly":[57],"appreciated.":[58],"In":[59],"paper":[61],"we":[62],"design":[63],"new":[65],"solver":[66,81],"based":[71,96],"on":[72,88,97,136,150,166,178,197],"the":[73,77,116,119,122,169,187],"parallel-sequential":[74,134],"composition":[75,135],"system":[78,103,149],"clans.":[79],"The":[80],"studied":[83],"implemented":[85],"to":[86,192],"run":[87],"parallel":[89],"architectures":[90],"using":[91,132,154],"two-level":[93],"parallelization":[94],"concept":[95],"MPI":[98,124],"OpenMP.":[100],"A":[101,157],"decomposable":[102],"usually":[105],"represented":[106],"by":[107],"sparse":[109],"matrix;":[110],"minimal":[112],"clan":[113],"size":[114],"decomposition":[117],"restricts":[118],"granulation":[120],"technique.":[123],"for":[127,130,163],"clans":[131],"distributed-memory":[137],"computing":[138],"nodes,":[139],"while":[140],"OpenMP":[141],"single":[147,152],"indecomposable":[148],"node":[153],"multiple":[155],"cores.":[156],"dynamic":[158],"task-dispatching":[159],"subsystem":[160],"developed":[162],"distributing":[164],"nodes":[167,199],"process":[170],"compositional":[172],"solution.":[173],"Computational":[174],"speedups":[175],"are":[176],"obtained":[177,196],"series":[180],"test":[182],"examples,":[183],"e.g.,":[184],"illustrating":[185],"that":[186],"best":[188],"value":[189],"constitutes":[190],"up":[191],"45":[193],"times":[194],"5":[198],"20":[201],"cores":[202],"each.":[203]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":2}],"updated_date":"2026-08-26T07:47:46.906454","created_date":"2025-10-10T00:00:00"}
