{"id":"https://openalex.org/W2137647587","doi":"https://doi.org/10.1109/tpds.2005.151","title":"Optimal path embedding in crossed cubes","display_name":"Optimal path embedding in crossed cubes","publication_year":2005,"publication_date":"2005-11-01","ids":{"openalex":"https://openalex.org/W2137647587","doi":"https://doi.org/10.1109/tpds.2005.151","mag":"2137647587"},"language":"en","primary_location":{"id":"doi:10.1109/tpds.2005.151","doi":"https://doi.org/10.1109/tpds.2005.151","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tpds.2005.151","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,"listed_in":["ccf-a","cwts-core","dongbi-a","jufo-2","norway-2","poland-140","russia-white-list-1","vabb-shw"],"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"},"volume":null,"type":"article","is_traditional":true,"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/A5022101610","display_name":"Jianxi Fan","orcid":"https://orcid.org/0000-0002-7055-5891","observed_orcids":["https://orcid.org/0000-0002-7055-5891"]},"institutions":[{"id":"https://openalex.org/I168719708","display_name":"City University of Hong Kong","ror":"https://ror.org/03q8dnn23","country_code":"HK","type":"education","lineage":["https://openalex.org/I168719708"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"J. Fan","raw_affiliation_strings":["Department of Computer Science, City University of Hong Kong, Kowloon, Hong Kong, China","Dept. of Computer Science, City University of Hong Kong, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, City University of Hong Kong, Kowloon, Hong Kong, China","institution_ids":["https://openalex.org/I168719708"]},{"raw_affiliation_string":"Dept. of Computer Science, City University of Hong Kong, China","institution_ids":["https://openalex.org/I168719708"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5024050806","display_name":"Xiaola Lin","orcid":"https://orcid.org/0000-0002-7665-8349","observed_orcids":["https://orcid.org/0000-0002-7665-8349"]},"institutions":[{"id":"https://openalex.org/I157773358","display_name":"Sun Yat-sen University","ror":"https://ror.org/0064kty71","country_code":"CN","type":"education","lineage":["https://openalex.org/I157773358"]},{"id":"https://openalex.org/I168719708","display_name":"City University of Hong Kong","ror":"https://ror.org/03q8dnn23","country_code":"HK","type":"education","lineage":["https://openalex.org/I168719708"]}],"countries":["CN","HK"],"is_corresponding":false,"raw_author_name":"X. Lin","raw_affiliation_strings":["College of Information Science and Technology, Sun Yat-Sen University, Guangzhou, China","Dept. of Computer Science, City University of Hong Kong, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Information Science and Technology, Sun Yat-Sen University, Guangzhou, China","institution_ids":["https://openalex.org/I157773358"]},{"raw_affiliation_string":"Dept. of Computer Science, City University of Hong Kong, China","institution_ids":["https://openalex.org/I168719708"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5013643572","display_name":"Xiaohua Jia","orcid":"https://orcid.org/0000-0001-8702-8302","observed_orcids":["https://orcid.org/0000-0001-8702-8302"]},"institutions":[{"id":"https://openalex.org/I168719708","display_name":"City University of Hong Kong","ror":"https://ror.org/03q8dnn23","country_code":"HK","type":"education","lineage":["https://openalex.org/I168719708"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"X. Jia","raw_affiliation_strings":["Department of Computer Science, City University of Hong Kong, Kowloon, Hong Kong, China","Dept. of Computer Science, City University of Hong Kong, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, City University of Hong Kong, Kowloon, Hong Kong, China","institution_ids":["https://openalex.org/I168719708"]},{"raw_affiliation_string":"Dept. of Computer Science, City University of Hong Kong, China","institution_ids":["https://openalex.org/I168719708"]}]}],"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":8.4018,"has_fulltext":false,"cited_by_count":106,"citation_normalized_percentile":{"value":0.97405821,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":88,"max":99},"biblio":{"volume":"16","issue":"12","first_page":"1190","last_page":"1200"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10829","display_name":"Interconnection Networks and Systems","score":0.9994999766349792,"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":0.9994999766349792,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.00019999999494757503,"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/T11522","display_name":"VLSI and FPGA Design Techniques","score":9.999999747378752e-05,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/crossed-cubes","display_name":"crossed cubes","score":0.8999999761581421},{"id":"https://openalex.org/keywords/path-embedding","display_name":"path embedding","score":0.8370000123977661},{"id":"https://openalex.org/keywords/dilation","display_name":"dilation","score":0.5979999899864197},{"id":"https://openalex.org/keywords/interconnection-networks","display_name":"interconnection networks","score":0.7319999933242798},{"id":"https://openalex.org/keywords/shortest-path","display_name":"shortest path","score":0.6620000004768372},{"id":"https://openalex.org/keywords/hamiltonian-paths","display_name":"Hamiltonian paths","score":0.7590000033378601},{"id":"https://openalex.org/keywords/fault-diameter","display_name":"fault diameter","score":0.4620000123977661},{"id":"https://openalex.org/keywords/optimal-embeddings","display_name":"optimal embeddings","score":0.3610000014305115}],"concepts":[{"id":"https://openalex.org/C50820777","wikidata":"https://www.wikidata.org/wiki/Q213723","display_name":"Hypercube","level":2,"score":0.9083621501922607},{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.8406299352645874},{"id":"https://openalex.org/C53051483","wikidata":"https://www.wikidata.org/wiki/Q861555","display_name":"Cube (algebra)","level":2,"score":0.7694549560546875},{"id":"https://openalex.org/C2780757906","wikidata":"https://www.wikidata.org/wiki/Q5276676","display_name":"Dilation (metric space)","level":2,"score":0.720161497592926},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6745861768722534},{"id":"https://openalex.org/C22590252","wikidata":"https://www.wikidata.org/wiki/Q1058754","display_name":"Shortest path problem","level":3,"score":0.6349204778671265},{"id":"https://openalex.org/C86524685","wikidata":"https://www.wikidata.org/wiki/Q273037","display_name":"Hamiltonian path","level":3,"score":0.5292633771896362},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4959443509578705},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3980455696582794},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.35913586616516113},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.055253565311431885},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tpds.2005.151","doi":"https://doi.org/10.1109/tpds.2005.151","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tpds.2005.151","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,"listed_in":["ccf-a","cwts-core","dongbi-a","jufo-2","norway-2","poland-140","russia-white-list-1","vabb-shw"],"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"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":38,"referenced_works":["https://openalex.org/W127371434","https://openalex.org/W224664467","https://openalex.org/W1488698111","https://openalex.org/W1528853579","https://openalex.org/W1983569347","https://openalex.org/W1983901430","https://openalex.org/W1984188070","https://openalex.org/W1985051597","https://openalex.org/W1990269643","https://openalex.org/W2032312374","https://openalex.org/W2047760643","https://openalex.org/W2051916444","https://openalex.org/W2056357964","https://openalex.org/W2064672441","https://openalex.org/W2069657003","https://openalex.org/W2085091875","https://openalex.org/W2095983440","https://openalex.org/W2100783053","https://openalex.org/W2100864244","https://openalex.org/W2103504495","https://openalex.org/W2105629997","https://openalex.org/W2108904169","https://openalex.org/W2114119464","https://openalex.org/W2121839513","https://openalex.org/W2124147496","https://openalex.org/W2130401388","https://openalex.org/W2137164589","https://openalex.org/W2137422654","https://openalex.org/W2138131200","https://openalex.org/W2142730954","https://openalex.org/W2149025218","https://openalex.org/W2153605009","https://openalex.org/W2155950798","https://openalex.org/W2157828285","https://openalex.org/W2157953482","https://openalex.org/W2159687416","https://openalex.org/W2218968469","https://openalex.org/W4250393251"],"related_works":["https://openalex.org/W7099831967","https://openalex.org/W2079184636","https://openalex.org/W2144072206","https://openalex.org/W2613990757","https://openalex.org/W2134854336","https://openalex.org/W2383020210","https://openalex.org/W2139941930","https://openalex.org/W2122373889","https://openalex.org/W2581481049","https://openalex.org/W2076455679"],"abstract_inverted_index":{"The":[0,10,115],"crossed":[1,12,40,64,83,113,157],"cube":[2,13],"is":[3,119,130,137],"an":[4],"important":[5],"variant":[6],"of":[7,24,26,31,55,73,75,89,108,117,127],"the":[8,27,53,111,122,125,128,138,155],"hypercube.":[9,29],"n-dimensional":[11,28,112,156],"has":[14,49],"only":[15],"about":[16],"half":[17],"diameter,":[18,20],"wide":[19],"and":[21,36,60,94],"fault":[22],"diameter":[23],"those":[25],"Embeddings":[30],"trees,":[32],"cycles,":[33],"shortest":[34,58,139],"paths,":[35,59],"Hamiltonian":[37,61],"paths":[38,56,62,74,88,118],"in":[39,45,63,82,110,121,154],"cubes":[41],"have":[42],"been":[43,50],"studied":[44],"literature.":[46],"Little":[47],"work":[48],"done":[51],"on":[52],"embedding":[54,72,116,129],"except":[57],"cubes.":[65,84],"In":[66],"this":[67],"paper,":[68],"we":[69],"study":[70],"optimal":[71,120],"different":[76],"lengths":[77,91],"between":[78,92,100,146],"any":[79,101],"two":[80,102,148],"nodes":[81,104,150],"We":[85,132],"prove":[86,134],"that":[87,124,135,142],"all":[90],"[(n+1)/2]":[93],"2/sup":[95],"n/-1":[96],"can":[97,143],"be":[98,144],"embedded":[99,145],"distinct":[103,149],"with":[105,151],"a":[106],"dilation":[107,126,152],"1":[109,153],"cube.":[114,158],"sense":[123],"1.":[131],"also":[133],"[(n+1)/2]+1":[136],"possible":[140],"length":[141],"arbitrary":[147]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":6},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":7},{"year":2017,"cited_by_count":7},{"year":2016,"cited_by_count":5},{"year":2015,"cited_by_count":5},{"year":2014,"cited_by_count":5},{"year":2013,"cited_by_count":7},{"year":2012,"cited_by_count":5}],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2016-06-24T00:00:00"}
