{"id":"https://openalex.org/W4317787787","doi":"https://doi.org/10.1137/22m1510443","title":"Communication Lower Bounds and Optimal Algorithms for Multiple Tensor-Times-Matrix Computation","display_name":"Communication Lower Bounds and Optimal Algorithms for Multiple Tensor-Times-Matrix Computation","publication_year":2024,"publication_date":"2024-02-06","ids":{"openalex":"https://openalex.org/W4317787787","doi":"https://doi.org/10.1137/22m1510443"},"language":"en","primary_location":{"id":"doi:10.1137/22m1510443","is_oa":false,"landing_page_url":"https://doi.org/10.1137/22m1510443","pdf_url":null,"source":{"id":"https://openalex.org/S16958353","display_name":"SIAM Journal on Matrix Analysis and Applications","issn_l":"0895-4798","issn":["0895-4798","1095-7162"],"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 Matrix Analysis and Applications","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://inria.hal.science/hal-03950359v1/document","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5028202081","display_name":"Hussam Al Daas","orcid":"https://orcid.org/0000-0001-9355-4042"},"institutions":[{"id":"https://openalex.org/I162524378","display_name":"Science and Technology Facilities Council","ror":"https://ror.org/057g20z61","country_code":"GB","type":"government","lineage":["https://openalex.org/I162524378","https://openalex.org/I4210087105"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Hussam Al Daas","raw_affiliation_strings":["Science and Technology Facilities Council, Rutherford Appleton Laboratory, Didcot, Oxfordshire, OX11 0QX, UK"],"raw_orcid":"https://orcid.org/0000-0001-9355-4042","affiliations":[{"raw_affiliation_string":"Science and Technology Facilities Council, Rutherford Appleton Laboratory, Didcot, Oxfordshire, OX11 0QX, UK","institution_ids":["https://openalex.org/I162524378"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5064243391","display_name":"Grey Ballard","orcid":"https://orcid.org/0000-0003-1557-8027"},"institutions":[{"id":"https://openalex.org/I47251452","display_name":"Wake Forest University","ror":"https://ror.org/0207ad724","country_code":"US","type":"education","lineage":["https://openalex.org/I47251452"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Grey Ballard","raw_affiliation_strings":["Computer Science, Wake Forest University, Winston-Salem, NC 27106 USA"],"raw_orcid":"https://orcid.org/0000-0003-1557-8027","affiliations":[{"raw_affiliation_string":"Computer Science, Wake Forest University, Winston-Salem, NC 27106 USA","institution_ids":["https://openalex.org/I47251452"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5040521001","display_name":"Laura Grigori","orcid":"https://orcid.org/0000-0002-5880-1076"},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I142476485","display_name":"\u00c9cole Polytechnique","ror":"https://ror.org/05hy3tk52","country_code":"FR","type":"education","lineage":["https://openalex.org/I142476485","https://openalex.org/I4210145102"]},{"id":"https://openalex.org/I2802229908","display_name":"Paul Scherrer Institute","ror":"https://ror.org/03eh3y714","country_code":"CH","type":"facility","lineage":["https://openalex.org/I2799323385","https://openalex.org/I2802229908"]},{"id":"https://openalex.org/I39804081","display_name":"Sorbonne Universit\u00e9","ror":"https://ror.org/02en5vm52","country_code":"FR","type":"education","lineage":["https://openalex.org/I39804081"]},{"id":"https://openalex.org/I4210158291","display_name":"Laboratoire Jacques-Louis Lions","ror":"https://ror.org/04xmteb38","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I204730241","https://openalex.org/I39804081","https://openalex.org/I4210141950","https://openalex.org/I4210158291"]}],"countries":["CH","FR"],"is_corresponding":false,"raw_author_name":"Laura Grigori","raw_affiliation_strings":["Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne PFL Institute of Mathematics, 1015 Lausanne and Paul Scherrer Institute, Laboratory for Simulation and Modelling, 5232 PSI Villigen, Switzerland; Significant part of the work performed while at Sorbonne Universit\u00e9, Inria, CNRS, Universit\u00e9 de Paris, Laboratoire Jacques-Louis Lions, Paris, France"],"raw_orcid":"https://orcid.org/0000-0002-5880-1076","affiliations":[{"raw_affiliation_string":"Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne PFL Institute of Mathematics, 1015 Lausanne and Paul Scherrer Institute, Laboratory for Simulation and Modelling, 5232 PSI Villigen, Switzerland; Significant part of the work performed while at Sorbonne Universit\u00e9, Inria, CNRS, Universit\u00e9 de Paris, Laboratoire Jacques-Louis Lions, Paris, France","institution_ids":["https://openalex.org/I39804081","https://openalex.org/I2802229908","https://openalex.org/I142476485","https://openalex.org/I1294671590","https://openalex.org/I4210158291"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100669083","display_name":"Suraj Kumar","orcid":"https://orcid.org/0009-0001-1449-0165"},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I39804081","display_name":"Sorbonne Universit\u00e9","ror":"https://ror.org/02en5vm52","country_code":"FR","type":"education","lineage":["https://openalex.org/I39804081"]},{"id":"https://openalex.org/I4210158291","display_name":"Laboratoire Jacques-Louis Lions","ror":"https://ror.org/04xmteb38","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I204730241","https://openalex.org/I39804081","https://openalex.org/I4210141950","https://openalex.org/I4210158291"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Suraj Kumar","raw_affiliation_strings":["Inria Lyon Centre, France; Significant part of the work performed while at Sorbonne Universit\u00e9, Inria, CNRS, Universit\u00e9 de Paris, Laboratoire Jacques-Louis Lions, Paris, France"],"raw_orcid":"https://orcid.org/0009-0001-1449-0165","affiliations":[{"raw_affiliation_string":"Inria Lyon Centre, France; Significant part of the work performed while at Sorbonne Universit\u00e9, Inria, CNRS, Universit\u00e9 de Paris, Laboratoire Jacques-Louis Lions, Paris, France","institution_ids":["https://openalex.org/I39804081","https://openalex.org/I4210158291","https://openalex.org/I1294671590"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5102860683","display_name":"Kathryn Rouse","orcid":"https://orcid.org/0009-0001-4045-0423"},"institutions":[{"id":"https://openalex.org/I188405335","display_name":"Winston-Salem State University","ror":"https://ror.org/049yc0897","country_code":"US","type":"education","lineage":["https://openalex.org/I188405335"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Kathryn Rouse","raw_affiliation_strings":["Inmar Intelligence, Winston-Salem, NC 27101 USA"],"raw_orcid":"https://orcid.org/0009-0001-4045-0423","affiliations":[{"raw_affiliation_string":"Inmar Intelligence, Winston-Salem, NC 27101 USA","institution_ids":["https://openalex.org/I188405335"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":5,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.5804,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.52906977,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":95},"biblio":{"volume":"45","issue":"1","first_page":"450","last_page":"477"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12303","display_name":"Tensor decomposition and applications","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2605","display_name":"Computational Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12303","display_name":"Tensor decomposition and applications","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2605","display_name":"Computational Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.6423161029815674},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5942597389221191},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5380027294158936},{"id":"https://openalex.org/keywords/tensor","display_name":"Tensor (intrinsic definition)","score":0.49522653222084045},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4584888815879822},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.38424810767173767},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.10353371500968933}],"concepts":[{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.6423161029815674},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5942597389221191},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5380027294158936},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.49522653222084045},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4584888815879822},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.38424810767173767},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.10353371500968933},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.1137/22m1510443","is_oa":false,"landing_page_url":"https://doi.org/10.1137/22m1510443","pdf_url":null,"source":{"id":"https://openalex.org/S16958353","display_name":"SIAM Journal on Matrix Analysis and Applications","issn_l":"0895-4798","issn":["0895-4798","1095-7162"],"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 Matrix Analysis and Applications","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-03950359v1","is_oa":true,"landing_page_url":"https://inria.hal.science/hal-03950359","pdf_url":"https://inria.hal.science/hal-03950359v1/document","source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Journal on Matrix Analysis and Applications, 2024, 45 (1), pp.450-477. &#x27E8;10.1137/22M1510443&#x27E9;","raw_type":"Journal articles"},{"id":"pmh:oai:dora:psi_63406","is_oa":false,"landing_page_url":"https://www.dora.lib4ri.ch/psi/islandora/object/psi%3A63406","pdf_url":null,"source":{"id":"https://openalex.org/S4306402574","display_name":"DORA PSI (Paul Scherrer Institute)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2802229908","host_organization_name":"Paul Scherrer Institute","host_organization_lineage":["https://openalex.org/I2802229908"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Journal Article"},{"id":"pmh:oai:infoscience.epfl.ch:310165","is_oa":true,"landing_page_url":"http://infoscience.epfl.ch/record/310165","pdf_url":null,"source":{"id":"https://openalex.org/S4306400487","display_name":"Infoscience (Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"WoS","raw_type":"research article"},{"id":"pmh:oai:purl.org/net/epubs:work/57704627","is_oa":false,"landing_page_url":"https://epubs.stfc.ac.uk/work/57704627","pdf_url":null,"source":{"id":"https://openalex.org/S4306400600","display_name":"ePubs (Science and Technology Facilities Council, Research Councils UK)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I162524378","host_organization_name":"Science and Technology Facilities Council","host_organization_lineage":["https://openalex.org/I162524378"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},{"id":"pmh:oai:purl.org/net/epubs:work/58098614","is_oa":false,"landing_page_url":"https://epubs.stfc.ac.uk/work/58098614","pdf_url":null,"source":{"id":"https://openalex.org/S4306400600","display_name":"ePubs (Science and Technology Facilities Council, Research Councils UK)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I162524378","host_organization_name":"Science and Technology Facilities Council","host_organization_lineage":["https://openalex.org/I162524378"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"}],"best_oa_location":{"id":"pmh:oai:HAL:hal-03950359v1","is_oa":true,"landing_page_url":"https://inria.hal.science/hal-03950359","pdf_url":"https://inria.hal.science/hal-03950359v1/document","source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Journal on Matrix Analysis and Applications, 2024, 45 (1), pp.450-477. &#x27E8;10.1137/22M1510443&#x27E9;","raw_type":"Journal articles"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3342840589","display_name":null,"funder_award_id":"CCF-1942892","funder_id":"https://openalex.org/F4320337387","funder_display_name":"Division of Computing and Communication Foundations"},{"id":"https://openalex.org/G3903888952","display_name":null,"funder_award_id":"2106920","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G422536779","display_name":null,"funder_award_id":"CCF-1942892","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G4332098366","display_name":null,"funder_award_id":"1942892","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6440695960","display_name":null,"funder_award_id":"OAC-2106920","funder_id":"https://openalex.org/F4320337377","funder_display_name":"Office of Advanced Cyberinfrastructure"},{"id":"https://openalex.org/G7683707404","display_name":null,"funder_award_id":"810367","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G7831147273","display_name":"Extreme-scale Mathematically-based Computational Chemistry","funder_award_id":"810367","funder_id":"https://openalex.org/F4320338335","funder_display_name":"H2020 European Research Council"},{"id":"https://openalex.org/G8529981498","display_name":null,"funder_award_id":"EP/Y008200/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"},{"id":"https://openalex.org/F4320337377","display_name":"Office of Advanced Cyberinfrastructure","ror":"https://ror.org/04nh1dc89"},{"id":"https://openalex.org/F4320337387","display_name":"Division of Computing and Communication Foundations","ror":"https://ror.org/01mng8331"},{"id":"https://openalex.org/F4320338335","display_name":"H2020 European Research Council","ror":"https://ror.org/0472cxd90"}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4317787787.pdf"},"referenced_works_count":23,"referenced_works":["https://openalex.org/W49160414","https://openalex.org/W1823244711","https://openalex.org/W1963826206","https://openalex.org/W2010747199","https://openalex.org/W2013912476","https://openalex.org/W2024165284","https://openalex.org/W2065495631","https://openalex.org/W2090322880","https://openalex.org/W2099611016","https://openalex.org/W2131613942","https://openalex.org/W2168748809","https://openalex.org/W2170796499","https://openalex.org/W2892981087","https://openalex.org/W2901487162","https://openalex.org/W2910202643","https://openalex.org/W2962976813","https://openalex.org/W3002017272","https://openalex.org/W3008842210","https://openalex.org/W3034140865","https://openalex.org/W3102489672","https://openalex.org/W3199939468","https://openalex.org/W4231545661","https://openalex.org/W4254160523"],"related_works":["https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W4225152035","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W1587224694","https://openalex.org/W2911598644","https://openalex.org/W2042127053"],"abstract_inverted_index":{"Multiple":[0],"tensor-times-matrix":[1,137],"(Multi-TTM)":[2],"is":[3,19,37,110],"a":[4,58,66,78,134],"key":[5],"computation":[6,46,72,132],"in":[7,22,47,147],"algorithms":[8],"for":[9],"computing":[10],"and":[11,109,142],"operating":[12],"with":[13,81,93],"the":[14,44,52,75,87,99,103,106,126,131,140],"Tucker":[15],"tensor":[16],"decomposition,":[17],"which":[18],"frequently":[20],"used":[21],"multidimensional":[23],"data":[24,35],"analysis.":[25],"We":[26,63,90],"establish":[27],"communication":[28,100,112,123],"lower":[29,107],"bounds":[30,108],"that":[31,73,117],"determine":[32],"how":[33],"much":[34],"movement":[36],"required":[38],"(under":[39],"mild":[40],"conditions)":[41],"to":[42,69,125],"perform":[43,70],"Multi-TTM":[45],"parallel.":[48],"The":[49],"crux":[50],"of":[51,96,102,129,136],"proof":[53],"relies":[54],"on":[55],"analytically":[56],"solving":[57],"constrained,":[59],"nonlinear":[60],"optimization":[61],"problem.":[62],"also":[64],"present":[65],"parallel":[67],"algorithm":[68,104,119],"this":[71],"organizes":[74],"processors":[76],"into":[77],"logical":[79],"grid":[80,97],"twice":[82],"as":[83,86,133],"many":[84],"modes":[85],"input":[88,141],"tensor.":[89],"show":[91,116],"that,":[92],"correct":[94],"choices":[95],"dimensions,":[98],"cost":[101],"attains":[105],"therefore":[111],"optimal.":[113],"Finally,":[114],"we":[115],"our":[118],"can":[120],"significantly":[121],"reduce":[122],"compared":[124],"straightforward":[127],"approach":[128],"expressing":[130],"sequence":[135],"operations":[138],"when":[139],"output":[143],"tensors":[144],"vary":[145],"greatly":[146],"size.":[148]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1}],"updated_date":"2026-06-19T17:40:00.097472","created_date":"2023-01-24T00:00:00"}
