{"id":"https://openalex.org/W2900885752","doi":"https://doi.org/10.3390/s18113912","title":"Torus Pairwise Disjoint-Path Routing","display_name":"Torus Pairwise Disjoint-Path Routing","publication_year":2018,"publication_date":"2018-11-13","ids":{"openalex":"https://openalex.org/W2900885752","doi":"https://doi.org/10.3390/s18113912","mag":"2900885752","pmid":"https://pubmed.ncbi.nlm.nih.gov/30428614"},"language":"en","primary_location":{"id":"doi:10.3390/s18113912","is_oa":true,"landing_page_url":"https://doi.org/10.3390/s18113912","pdf_url":"https://www.mdpi.com/1424-8220/18/11/3912/pdf?version=1542116953","source":{"id":"https://openalex.org/S101949793","display_name":"Sensors","issn_l":"1424-8220","issn":["1424-8220"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Sensors","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj","pubmed"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1424-8220/18/11/3912/pdf?version=1542116953","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5058447810","display_name":"Antoine Bossard","orcid":"https://orcid.org/0000-0001-9381-9346"},"institutions":[{"id":"https://openalex.org/I41802502","display_name":"Kanagawa University","ror":"https://ror.org/02j6c0d67","country_code":"JP","type":"education","lineage":["https://openalex.org/I41802502"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Antoine Bossard","raw_affiliation_strings":["Graduate School of Science, Kanagawa University, Kanagawa 259-1293, Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Graduate School of Science, Kanagawa University, Kanagawa 259-1293, Japan","institution_ids":["https://openalex.org/I41802502"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5014838749","display_name":"Keiichi Kaneko","orcid":"https://orcid.org/0000-0003-1790-4615"},"institutions":[{"id":"https://openalex.org/I92614990","display_name":"Tokyo University of Agriculture and Technology","ror":"https://ror.org/00qg0kr10","country_code":"JP","type":"education","lineage":["https://openalex.org/I92614990"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Keiichi Kaneko","raw_affiliation_strings":["Graduate School of Engineering, Tokyo University of Agriculture and Technology, Tokyo 184-8588, Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Graduate School of Engineering, Tokyo University of Agriculture and Technology, Tokyo 184-8588, Japan","institution_ids":["https://openalex.org/I92614990"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5058447810"],"corresponding_institution_ids":["https://openalex.org/I41802502"],"apc_list":{"value":2400,"currency":"CHF","value_usd":2673},"apc_paid":{"value":2400,"currency":"CHF","value_usd":2673},"fwci":0.5141,"has_fulltext":true,"cited_by_count":6,"citation_normalized_percentile":{"value":0.73666121,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"18","issue":"11","first_page":"3912","last_page":"3912"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10829","display_name":"Interconnection Networks and Systems","score":1.0,"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"}},"topics":[{"id":"https://openalex.org/T10829","display_name":"Interconnection Networks and Systems","score":1.0,"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"}},{"id":"https://openalex.org/T10714","display_name":"Software-Defined Networks and 5G","score":0.9936000108718872,"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"}},{"id":"https://openalex.org/T10083","display_name":"Graphene research and applications","score":0.9919000267982483,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials 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":0.7079793810844421},{"id":"https://openalex.org/keywords/disjoint-sets","display_name":"Disjoint sets","score":0.58673095703125},{"id":"https://openalex.org/keywords/torus","display_name":"Torus","score":0.5576488971710205},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.5462148189544678},{"id":"https://openalex.org/keywords/correctness","display_name":"Correctness","score":0.4751960039138794},{"id":"https://openalex.org/keywords/shortest-path-problem","display_name":"Shortest path problem","score":0.47269323468208313},{"id":"https://openalex.org/keywords/dijkstras-algorithm","display_name":"Dijkstra's algorithm","score":0.42455458641052246},{"id":"https://openalex.org/keywords/network-topology","display_name":"Network topology","score":0.420663982629776},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.42027080059051514},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.4056690037250519},{"id":"https://openalex.org/keywords/distributed-computing","display_name":"Distributed computing","score":0.3906070590019226},{"id":"https://openalex.org/keywords/parallel-computing","display_name":"Parallel computing","score":0.37683138251304626},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.33383357524871826},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.3189865052700043},{"id":"https://openalex.org/keywords/computer-network","display_name":"Computer network","score":0.3179110288619995},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.2562848627567291},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.2141023874282837},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.20597150921821594}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.7079793810844421},{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.58673095703125},{"id":"https://openalex.org/C9767117","wikidata":"https://www.wikidata.org/wiki/Q12510","display_name":"Torus","level":2,"score":0.5576488971710205},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.5462148189544678},{"id":"https://openalex.org/C55439883","wikidata":"https://www.wikidata.org/wiki/Q360812","display_name":"Correctness","level":2,"score":0.4751960039138794},{"id":"https://openalex.org/C22590252","wikidata":"https://www.wikidata.org/wiki/Q1058754","display_name":"Shortest path problem","level":3,"score":0.47269323468208313},{"id":"https://openalex.org/C173870130","wikidata":"https://www.wikidata.org/wiki/Q8548","display_name":"Dijkstra's algorithm","level":4,"score":0.42455458641052246},{"id":"https://openalex.org/C199845137","wikidata":"https://www.wikidata.org/wiki/Q145490","display_name":"Network topology","level":2,"score":0.420663982629776},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.42027080059051514},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.4056690037250519},{"id":"https://openalex.org/C120314980","wikidata":"https://www.wikidata.org/wiki/Q180634","display_name":"Distributed computing","level":1,"score":0.3906070590019226},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.37683138251304626},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.33383357524871826},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.3189865052700043},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.3179110288619995},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2562848627567291},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2141023874282837},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.20597150921821594},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.3390/s18113912","is_oa":true,"landing_page_url":"https://doi.org/10.3390/s18113912","pdf_url":"https://www.mdpi.com/1424-8220/18/11/3912/pdf?version=1542116953","source":{"id":"https://openalex.org/S101949793","display_name":"Sensors","issn_l":"1424-8220","issn":["1424-8220"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Sensors","raw_type":"journal-article"},{"id":"pmid:30428614","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/30428614","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Sensors (Basel, Switzerland)","raw_type":null},{"id":"pmh:oai:doaj.org/article:93b5ba40d3fd4b23817ce527dbb7ede5","is_oa":true,"landing_page_url":"https://doaj.org/article/93b5ba40d3fd4b23817ce527dbb7ede5","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","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":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Sensors, Vol 18, Iss 11, p 3912 (2018)","raw_type":"article"},{"id":"pmh:oai:europepmc.org:5258019","is_oa":true,"landing_page_url":"http://europepmc.org/pmc/articles/PMC6264114","pdf_url":null,"source":{"id":"https://openalex.org/S4306400806","display_name":"Europe PMC (PubMed Central)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1303153112","host_organization_name":"European Bioinformatics Institute","host_organization_lineage":["https://openalex.org/I1303153112"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},{"id":"pmh:oai:mdpi.com:/1424-8220/18/11/3912/","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/s18113912","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"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":"Sensors","raw_type":"Text"},{"id":"pmh:oai:pubmedcentral.nih.gov:6264114","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/6264114","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"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":"Sensors (Basel)","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/s18113912","is_oa":true,"landing_page_url":"https://doi.org/10.3390/s18113912","pdf_url":"https://www.mdpi.com/1424-8220/18/11/3912/pdf?version=1542116953","source":{"id":"https://openalex.org/S101949793","display_name":"Sensors","issn_l":"1424-8220","issn":["1424-8220"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Sensors","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1717090015","display_name":"A Stochastic Link-fault-tolerant Routing Method in Torus Networks","funder_award_id":"17K00093","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G3903820703","display_name":null,"funder_award_id":"17K00093","funder_id":"https://openalex.org/F4320320912","funder_display_name":"Ministry of Education, Culture, Sports, Science and Technology"}],"funders":[{"id":"https://openalex.org/F4320320912","display_name":"Ministry of Education, Culture, Sports, Science and Technology","ror":"https://ror.org/048rj2z13"},{"id":"https://openalex.org/F4320334764","display_name":"Japan Society for the Promotion of Science","ror":"https://ror.org/00hhkn466"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2900885752.pdf","grobid_xml":"https://content.openalex.org/works/W2900885752.grobid-xml"},"referenced_works_count":26,"referenced_works":["https://openalex.org/W100926944","https://openalex.org/W282449985","https://openalex.org/W976211528","https://openalex.org/W1964602554","https://openalex.org/W1968025843","https://openalex.org/W1973518576","https://openalex.org/W1975422095","https://openalex.org/W2005079828","https://openalex.org/W2022794676","https://openalex.org/W2062826522","https://openalex.org/W2071014122","https://openalex.org/W2082154292","https://openalex.org/W2104852618","https://openalex.org/W2143448425","https://openalex.org/W2144245981","https://openalex.org/W2145625823","https://openalex.org/W2148482347","https://openalex.org/W2172760123","https://openalex.org/W2737473534","https://openalex.org/W2804035460","https://openalex.org/W2804126755","https://openalex.org/W2900885752","https://openalex.org/W4200017195","https://openalex.org/W4254367428","https://openalex.org/W6681854182","https://openalex.org/W6741014872"],"related_works":["https://openalex.org/W3209137076","https://openalex.org/W2374560440","https://openalex.org/W1490490684","https://openalex.org/W4221129498","https://openalex.org/W2887026015","https://openalex.org/W2361442013","https://openalex.org/W2373384475","https://openalex.org/W4310124294","https://openalex.org/W143403600","https://openalex.org/W2761711678"],"abstract_inverted_index":{"Modern":[0],"supercomputers":[1,54],"include":[2],"hundreds":[3],"of":[4,6,18,24,78,81,113,130,138,177,201,215],"thousands":[5],"processors":[7],"and":[8,51,104,109,115,123,136,196],"they":[9],"are":[10,143],"thus":[11],"massively":[12],"parallel":[13],"systems.":[14],"The":[15,60],"interconnection":[16,37],"network":[17,38,68],"a":[19,34,66,91],"system":[20,102],"is":[21,69,204,219],"in":[22,65,71,147,221],"charge":[23],"mutually":[25,82,174],"connecting":[26],"these":[27],"processors.":[28],"Recently,":[29],"the":[30,42,79,128,134,139,161,197,202,216],"torus":[31,67,151],"has":[32,96],"become":[33],"very":[35],"popular":[36],"topology.":[39,59],"For":[40],"example,":[41],"Fujitsu":[43],"K,":[44],"IBM":[45,48],"Blue":[46,49],"Gene/L,":[47],"Gene/P,":[50],"Cray":[52],"Titan":[53],"all":[55],"rely":[56],"on":[57],"this":[58,72,94],"pairwise":[61],"disjoint-path":[62],"routing":[63,141],"problem":[64,76,95],"addressed":[70],"paper.":[73],"This":[74],"fundamental":[75],"consists":[77],"selection":[80],"vertex":[83,88,171],"disjoint":[84],"paths":[85,176],"between":[86],"given":[87],"pairs.":[89],"Proposing":[90],"solution":[92],"to":[93,223],"critical":[97],"implications,":[98],"such":[99],"as":[100,118,120],"increased":[101],"dependability":[103],"more":[105],"efficient":[106],"data":[107],"transfers,":[108],"provides":[110],"concrete":[111],"implementation":[112],"green":[114],"sustainable":[116],"computing":[117],"well":[119],"security,":[121],"privacy,":[122],"trust,":[124],"for":[125,127],"instance,":[126],"Internet":[129],"Things":[131],"(IoT).":[132],"Then,":[133],"correctness":[135],"complexities":[137],"proposed":[140,162,217],"algorithm":[142,163,203,218],"formally":[144],"established.":[145],"Precisely,":[146],"an":[148],"n-dimensional":[149],"k-ary":[150],"(":[152,166,183,206],"n":[153,169,189,207],"<":[154],"k":[155,157,182,191],",":[156,195],"\u2265":[158],"5":[159],"),":[160],"connects":[164],"c":[165,167,184,208],"\u2264":[168],")":[170,187,210],"pairs":[172],"with":[173],"vertex-disjoint":[175],"lengths":[178],"at":[179],"most":[180],"2":[181,193],"\u2212":[185],"1":[186],"+":[188],"\u230a":[190],"/":[192],"\u230b":[194],"worst-case":[198],"time":[199],"complexity":[200],"O":[205],"4":[209],".":[211],"Finally,":[212],"empirical":[213],"evaluation":[214],"conducted":[220],"order":[222],"inspect":[224],"its":[225],"practical":[226],"behavior.":[227]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2020,"cited_by_count":2},{"year":2018,"cited_by_count":1}],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2025-10-10T00:00:00"}