{"id":"https://openalex.org/W2056986113","doi":"https://doi.org/10.1137/0221039","title":"Dynamic Tree Embeddings in Butterflies and Hypercubes","display_name":"Dynamic Tree Embeddings in Butterflies and Hypercubes","publication_year":1992,"publication_date":"1992-08-01","ids":{"openalex":"https://openalex.org/W2056986113","doi":"https://doi.org/10.1137/0221039","mag":"2056986113"},"language":"en","primary_location":{"id":"doi:10.1137/0221039","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0221039","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"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 Computing","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/A5110453378","display_name":"Frank Thomson Leighton","orcid":null},"institutions":[{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"F. T. Leighton","raw_affiliation_strings":["[Massachusetts Inst. of Technol., Cambridge]"],"affiliations":[{"raw_affiliation_string":"[Massachusetts Inst. of Technol., Cambridge]","institution_ids":["https://openalex.org/I63966007"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5075414122","display_name":"Mark Newman","orcid":"https://orcid.org/0000-0002-9924-7120"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Mark J. Newman","raw_affiliation_strings":["Temple Barker and Sloane Inc., Lexington, MA"],"affiliations":[{"raw_affiliation_string":"Temple Barker and Sloane Inc., Lexington, MA","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5023011448","display_name":"Abhiram Ranade","orcid":"https://orcid.org/0000-0001-8350-0438"},"institutions":[{"id":"https://openalex.org/I95457486","display_name":"University of California, Berkeley","ror":"https://ror.org/01an7q238","country_code":"US","type":"education","lineage":["https://openalex.org/I95457486"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Abhiram G. Ranade","raw_affiliation_strings":["University of California, Berkeley"],"affiliations":[{"raw_affiliation_string":"University of California, Berkeley","institution_ids":["https://openalex.org/I95457486"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5056928345","display_name":"Eric J. Schwabe","orcid":null},"institutions":[{"id":"https://openalex.org/I74973139","display_name":"Carnegie Mellon University","ror":"https://ror.org/05x2bcf33","country_code":"US","type":"education","lineage":["https://openalex.org/I74973139"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Eric J. Schwabe","raw_affiliation_strings":["Carnegie-Mellon University, Pittsburgh, PA"],"affiliations":[{"raw_affiliation_string":"Carnegie-Mellon University, Pittsburgh, PA","institution_ids":["https://openalex.org/I74973139"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5110453378"],"corresponding_institution_ids":["https://openalex.org/I63966007"],"apc_list":null,"apc_paid":null,"fwci":0.4711,"has_fulltext":false,"cited_by_count":49,"citation_normalized_percentile":{"value":0.69820359,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"21","issue":"4","first_page":"639","last_page":"654"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10829","display_name":"Interconnection Networks and Systems","score":0.9998999834060669,"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":0.9998999834060669,"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/T11522","display_name":"VLSI and FPGA Design Techniques","score":0.996999979019165,"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"}},{"id":"https://openalex.org/T10847","display_name":"Advanced Optical Network Technologies","score":0.9958999752998352,"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/hypercube","display_name":"Hypercube","score":0.8350690603256226},{"id":"https://openalex.org/keywords/dilation","display_name":"Dilation (metric space)","score":0.8047305345535278},{"id":"https://openalex.org/keywords/embedding","display_name":"Embedding","score":0.7588976621627808},{"id":"https://openalex.org/keywords/binary-tree","display_name":"Binary tree","score":0.5946046113967896},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.554033637046814},{"id":"https://openalex.org/keywords/parallel-computing","display_name":"Parallel computing","score":0.529839038848877},{"id":"https://openalex.org/keywords/binary-logarithm","display_name":"Binary logarithm","score":0.4731156527996063},{"id":"https://openalex.org/keywords/tree","display_name":"Tree (set theory)","score":0.4631504416465759},{"id":"https://openalex.org/keywords/parallel-algorithm","display_name":"Parallel algorithm","score":0.4617043137550354},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.45986035466194153},{"id":"https://openalex.org/keywords/load-balancing","display_name":"Load balancing (electrical power)","score":0.43547573685646057},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4206588864326477},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4087618589401245},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.38993826508522034},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3802776634693146},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.32242512702941895}],"concepts":[{"id":"https://openalex.org/C50820777","wikidata":"https://www.wikidata.org/wiki/Q213723","display_name":"Hypercube","level":2,"score":0.8350690603256226},{"id":"https://openalex.org/C2780757906","wikidata":"https://www.wikidata.org/wiki/Q5276676","display_name":"Dilation (metric space)","level":2,"score":0.8047305345535278},{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.7588976621627808},{"id":"https://openalex.org/C197855036","wikidata":"https://www.wikidata.org/wiki/Q380172","display_name":"Binary tree","level":2,"score":0.5946046113967896},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.554033637046814},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.529839038848877},{"id":"https://openalex.org/C63553672","wikidata":"https://www.wikidata.org/wiki/Q581168","display_name":"Binary logarithm","level":2,"score":0.4731156527996063},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.4631504416465759},{"id":"https://openalex.org/C120373497","wikidata":"https://www.wikidata.org/wiki/Q1087987","display_name":"Parallel algorithm","level":2,"score":0.4617043137550354},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.45986035466194153},{"id":"https://openalex.org/C138959212","wikidata":"https://www.wikidata.org/wiki/Q1806783","display_name":"Load balancing (electrical power)","level":3,"score":0.43547573685646057},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4206588864326477},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4087618589401245},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.38993826508522034},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3802776634693146},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.32242512702941895},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","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},{"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/C187691185","wikidata":"https://www.wikidata.org/wiki/Q2020720","display_name":"Grid","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/0221039","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0221039","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"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 Computing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":2,"referenced_works":["https://openalex.org/W2004759812","https://openalex.org/W2094434349"],"related_works":["https://openalex.org/W2495029940","https://openalex.org/W2401906798","https://openalex.org/W2134058137","https://openalex.org/W1989441170","https://openalex.org/W2264338648","https://openalex.org/W1487268105","https://openalex.org/W1596300000","https://openalex.org/W1560383649","https://openalex.org/W2105195194","https://openalex.org/W2125532959"],"abstract_inverted_index":{"This":[0],"paper":[1,78,118,258],"presents":[2],"simple":[3,123],"randomized":[4],"algorithms":[5,24,273],"for":[6,62,126,147,168,189,270],"dynamically":[7,44,127],"embedding":[8,128,145,166,187,212,272,285],"M-node":[9],"binary":[10],"trees":[11,129],"in":[12,27,69,103,130],"either":[13],"a":[14,17,122,131,260],"butterfly":[15,132,170],"or":[16],"hypercube":[18,149,191],"network":[19,101],"of":[20,87,92,109,263],"N":[21],"processors.":[22],"These":[23],"are":[25,49,54,141,234],"dynamic":[26,64],"the":[28,31,57,75,77,82,85,88,90,93,97,100,107,148,169,190,242],"sense":[29],"that":[30,150,171,192,274,283,287],"tree":[32,65,94,243],"to":[33,80,105,218,237,244],"be":[34,245,294],"embedded":[35,51,246],"may":[36],"start":[37],"as":[38,52,224],"one":[39],"node":[40],"and":[41,71,96,114,134,204,216,291],"grow":[42],"by":[43,120,135],"spawning":[45],"children.":[46],"The":[47,117,138,210,230],"nodes":[48],"incrementally":[50],"they":[53],"spawned.":[55],"Thus,":[56],"algorithm":[58,146,167,188,286],"is":[59,247],"especially":[60],"suited":[61],"maintaining":[63],"structures":[66],"like":[67],"those":[68],"divide-and-conquer":[70],"branch-and-bound":[72],"algorithms.":[73],"In":[74,255],"embeddings,":[76],"seeks":[79],"optimize":[81],"load":[83,110,158,179,200,215,276,290],"on":[84,99],"processors":[86],"network,":[89,133],"dilation":[91,152,173,194,217,269,292],"edges,":[95,102],"congestion":[98,205,223],"order":[104],"satisfy":[106],"demands":[108],"balancing,":[111],"process":[112],"locality,":[113],"communication":[115],"efficiency.":[116],"begins":[119],"presenting":[121],"level-by-level":[124],"scheme":[125],"successive":[136],"modifications.":[137],"following":[139],"results":[140],"obtained:":[142],"1.":[143],"An":[144,165,186],"achieves":[151,172,193],"1":[153],"and,":[154,175,196],"with":[155,176,197],"high":[156,177,198],"probability,":[157,178,199],"$O((M":[159],"/N)":[160],"+":[161,182,202,208,279],"\\log":[162,183],"N)$.":[163,184,254],"2.":[164],"2":[174],"$O((M/":[180,206,277],"N)":[181,207,278],"3.":[185],"$O(1)$":[195],"$O((M/N)":[201],"1)$":[203],"1)$.":[209],"third":[211],"simultaneously":[213,288],"optimizes":[214,289],"within":[219,238],"constant":[220,239],"factors,":[221],"optimizing":[222],"well":[225],"when":[226,241],"$M":[227,250],"=":[228,251],"O(N)$.":[229],"first":[231],"two":[232],"embeddings":[233],"also":[235],"optimal":[236],"factors":[240],"large":[248],"(i.e.,":[249],"\\Omega":[252],"(N\\log":[253],"addition,":[256],"this":[257],"proves":[259],"lower":[261],"bound":[262],"$\\Omega":[264],"(\\sqrt":[265],"{\\log":[266],"N}":[267],")$":[268],"deterministic":[271],"achieve":[275],"1)$,":[280],"which":[281],"implies":[282],"any":[284],"must":[293],"randomized.":[295]},"counts_by_year":[{"year":2013,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}