{"id":"https://openalex.org/W2966915191","doi":"https://doi.org/10.1145/3328731","title":"Tree Partitioning Reduction","display_name":"Tree Partitioning Reduction","publication_year":2019,"publication_date":"2019-08-08","ids":{"openalex":"https://openalex.org/W2966915191","doi":"https://doi.org/10.1145/3328731","mag":"2966915191"},"language":"en","primary_location":{"id":"doi:10.1145/3328731","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3328731","pdf_url":null,"source":{"id":"https://openalex.org/S163326656","display_name":"ACM Transactions on Mathematical Software","issn_l":"0098-3500","issn":["0098-3500","1557-7295"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Mathematical Software","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/A5049023670","display_name":"Adri\u00e1n Perez Di\u00e9guez","orcid":"https://orcid.org/0000-0001-7168-9050"},"institutions":[{"id":"https://openalex.org/I11019714","display_name":"Universidade da Coru\u00f1a","ror":"https://ror.org/01qckj285","country_code":"ES","type":"education","lineage":["https://openalex.org/I11019714"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Adri\u00e1n P. Di\u00e9guez","raw_affiliation_strings":["University of A Coru\u00f1a, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of A Coru\u00f1a, Spain","institution_ids":["https://openalex.org/I11019714"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5068836759","display_name":"Margarita Amor","orcid":"https://orcid.org/0000-0003-4641-7891"},"institutions":[{"id":"https://openalex.org/I11019714","display_name":"Universidade da Coru\u00f1a","ror":"https://ror.org/01qckj285","country_code":"ES","type":"education","lineage":["https://openalex.org/I11019714"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Margarita Amor","raw_affiliation_strings":["University of A Coru\u00f1a, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of A Coru\u00f1a, Spain","institution_ids":["https://openalex.org/I11019714"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5070686724","display_name":"Ram\u00f3n Doallo","orcid":"https://orcid.org/0000-0002-6011-3387"},"institutions":[{"id":"https://openalex.org/I11019714","display_name":"Universidade da Coru\u00f1a","ror":"https://ror.org/01qckj285","country_code":"ES","type":"education","lineage":["https://openalex.org/I11019714"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Ram\u00f3n Doallo","raw_affiliation_strings":["University of A Coru\u00f1a, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of A Coru\u00f1a, Spain","institution_ids":["https://openalex.org/I11019714"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I11019714"],"apc_list":null,"apc_paid":null,"fwci":0.7402,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.69237589,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"45","issue":"3","first_page":"1","last_page":"26"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10054","display_name":"Parallel Computing and Optimization Techniques","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1708","display_name":"Hardware and Architecture"},"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/T10054","display_name":"Parallel Computing and Optimization Techniques","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1708","display_name":"Hardware and Architecture"},"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/T10904","display_name":"Embedded Systems Design Techniques","score":0.9980999827384949,"subfield":{"id":"https://openalex.org/subfields/1708","display_name":"Hardware and Architecture"},"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/T10829","display_name":"Interconnection Networks and Systems","score":0.9980000257492065,"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":0.7735973596572876},{"id":"https://openalex.org/keywords/parallel-computing","display_name":"Parallel computing","score":0.7020459175109863},{"id":"https://openalex.org/keywords/shared-memory","display_name":"Shared memory","score":0.5688427090644836},{"id":"https://openalex.org/keywords/partition","display_name":"Partition (number theory)","score":0.5619940757751465},{"id":"https://openalex.org/keywords/tridiagonal-matrix","display_name":"Tridiagonal matrix","score":0.5605122447013855},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.5353057384490967},{"id":"https://openalex.org/keywords/cuda","display_name":"CUDA","score":0.5167731046676636},{"id":"https://openalex.org/keywords/distributed-memory","display_name":"Distributed memory","score":0.5079115033149719},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.4983251094818115},{"id":"https://openalex.org/keywords/tree","display_name":"Tree (set theory)","score":0.4375165104866028},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.39712414145469666},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.35598084330558777},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.21943730115890503}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.7735973596572876},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.7020459175109863},{"id":"https://openalex.org/C133875982","wikidata":"https://www.wikidata.org/wiki/Q764810","display_name":"Shared memory","level":2,"score":0.5688427090644836},{"id":"https://openalex.org/C42812","wikidata":"https://www.wikidata.org/wiki/Q1082910","display_name":"Partition (number theory)","level":2,"score":0.5619940757751465},{"id":"https://openalex.org/C51647924","wikidata":"https://www.wikidata.org/wiki/Q1755277","display_name":"Tridiagonal matrix","level":3,"score":0.5605122447013855},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.5353057384490967},{"id":"https://openalex.org/C2778119891","wikidata":"https://www.wikidata.org/wiki/Q477690","display_name":"CUDA","level":2,"score":0.5167731046676636},{"id":"https://openalex.org/C91481028","wikidata":"https://www.wikidata.org/wiki/Q1054686","display_name":"Distributed memory","level":3,"score":0.5079115033149719},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.4983251094818115},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.4375165104866028},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.39712414145469666},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.35598084330558777},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.21943730115890503},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","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/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.0},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.0},{"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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1145/3328731","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3328731","pdf_url":null,"source":{"id":"https://openalex.org/S163326656","display_name":"ACM Transactions on Mathematical Software","issn_l":"0098-3500","issn":["0098-3500","1557-7295"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Mathematical Software","raw_type":"journal-article"},{"id":"pmh:oai:ruc.udc.es:2183/34520","is_oa":false,"landing_page_url":"http://hdl.handle.net/2183/34520","pdf_url":null,"source":{"id":"https://openalex.org/S4306402204","display_name":"RUC (Universidade Da Coru\u00f1a)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G153833309","display_name":null,"funder_award_id":"ED7431G/01","funder_id":"https://openalex.org/F4320335322","funder_display_name":"European Regional Development Fund"}],"funders":[{"id":"https://openalex.org/F4320326655","display_name":"Xunta de Galicia","ror":"https://ror.org/0181xnw06"},{"id":"https://openalex.org/F4320335322","display_name":"European Regional Development Fund","ror":"https://ror.org/00k4n6c32"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W189428928","https://openalex.org/W1480666649","https://openalex.org/W1512833653","https://openalex.org/W1762731526","https://openalex.org/W1990523337","https://openalex.org/W1997659541","https://openalex.org/W2008110907","https://openalex.org/W2013855928","https://openalex.org/W2017838066","https://openalex.org/W2045992017","https://openalex.org/W2047610878","https://openalex.org/W2089309544","https://openalex.org/W2102512593","https://openalex.org/W2112185810","https://openalex.org/W2141524575","https://openalex.org/W2160406723","https://openalex.org/W2161456019","https://openalex.org/W2278832816","https://openalex.org/W2323164726","https://openalex.org/W2568222782","https://openalex.org/W2731702594"],"related_works":["https://openalex.org/W2026512611","https://openalex.org/W1985165680","https://openalex.org/W4245497162","https://openalex.org/W2353146130","https://openalex.org/W1990817968","https://openalex.org/W2150064838","https://openalex.org/W1933089384","https://openalex.org/W2185094550","https://openalex.org/W2088823210","https://openalex.org/W2135766592"],"abstract_inverted_index":{"Solving":[0],"tridiagonal":[1],"linear-equation":[2],"systems":[3],"is":[4,60,83,174],"a":[5,10,40,73,127],"fundamental":[6],"computing":[7],"kernel":[8],"in":[9,39,50,67,105,117,149,170],"wide":[11],"range":[12],"of":[13,76,103],"scientific":[14],"and":[15,18,72,165],"engineering":[16],"applications,":[17],"its":[19],"computation":[20,52,104],"can":[21,145,159],"be":[22,64,116,146,160],"modeled":[23],"with":[24,190],"parallel":[25,28,96,150,164],"algorithms.":[26],"These":[27],"solvers":[29],"are":[30,79],"typically":[31],"designed":[32],"to":[33,84,180,192],"compute":[34],"problems":[35],"whose":[36],"data":[37,62],"fit":[38],"common":[41,69,153],"shared-memory":[42,70,154],"space":[43],"where":[44],"all":[45],"the":[46,51,57,68,86,101,131,139],"cores":[47],"taking":[48],"part":[49],"have":[53],"access.":[54],"However,":[55],"when":[56],"problem":[58,87,140],"size":[59,183],"large,":[61],"cannot":[63],"entirely":[65],"stored":[66],"space,":[71],"high":[74],"number":[75],"high-latency":[77],"communications":[78],"performed.":[80],"One":[81],"alternative":[82],"partition":[85,102],"among":[88],"different":[89,118,152],"memory":[90],"spaces.":[91,155],"At":[92],"this":[93,171],"point,":[94],"conventional":[95],"algorithms":[97],"do":[98],"not":[99],"facilitate":[100],"independent":[106,142],"tiles,":[107],"since":[108],"each":[109],"reduction":[110],"depends":[111],"on":[112,126,196],"equations":[113],"that":[114,144],"may":[115],"tiles.":[119],"This":[120],"article":[121],"proposes":[122],"an":[123],"algorithm":[124],"based":[125],"tree":[128],"reduction,":[129],"called":[130],"Tree":[132],"Partitioning":[133],"Reduction":[134],"(TPR)":[135],"method,":[136],"which":[137],"partitions":[138],"into":[141],"slices":[143],"partially":[147],"computed":[148],"within":[151],"The":[156],"TPR":[157,173],"method":[158],"implemented":[161,176],"for":[162,177],"any":[163],"distributed":[166],"programming":[167],"paradigm.":[168],"Furthermore,":[169],"work,":[172],"efficiently":[175],"CUDA":[178],"GPUs":[179],"solve":[181],"large":[182],"problems,":[184],"providing":[185],"highly":[186],"competitive":[187],"performance":[188],"results":[189],"respect":[191],"existing":[193],"packages,":[194],"being,":[195],"average,":[197],"22.03\u00d7":[198],"faster":[199],"than":[200],"CUSPARSE.":[201]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1}],"updated_date":"2026-06-26T08:34:08.712188","created_date":"2025-10-10T00:00:00"}
