{"id":"https://openalex.org/W2007123818","doi":"https://doi.org/10.1137/0218081","title":"On Relaxed Squashed Embedding of Graphs into a Hypercube","display_name":"On Relaxed Squashed Embedding of Graphs into a Hypercube","publication_year":1989,"publication_date":"1989-12-01","ids":{"openalex":"https://openalex.org/W2007123818","doi":"https://doi.org/10.1137/0218081","mag":"2007123818"},"language":"en","primary_location":{"id":"doi:10.1137/0218081","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0218081","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/A5036009069","display_name":"Ming-Syan Chen\u22c6","orcid":"https://orcid.org/0000-0002-0711-8197"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Ming-Syan Chen","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5053541912","display_name":"Kang G. Shin","orcid":"https://orcid.org/0000-0003-0086-8777"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Kang G. Shin","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5036009069"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":5.06381459,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.94041141,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":null,"biblio":{"volume":"18","issue":"6","first_page":"1226","last_page":"1244"},"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/T11522","display_name":"VLSI and FPGA Design Techniques","score":0.9990000128746033,"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/T10054","display_name":"Parallel Computing and Optimization Techniques","score":0.9988999962806702,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/hypercube","display_name":"Hypercube","score":0.772615909576416},{"id":"https://openalex.org/keywords/embedding","display_name":"Embedding","score":0.6874375939369202},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5809674263000488},{"id":"https://openalex.org/keywords/cube","display_name":"Cube (algebra)","score":0.5441885590553284},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5440163016319275},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.520414412021637},{"id":"https://openalex.org/keywords/heuristic","display_name":"Heuristic","score":0.4534469246864319},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.45326635241508484},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.42516839504241943},{"id":"https://openalex.org/keywords/graph-embedding","display_name":"Graph embedding","score":0.41695916652679443},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.41680267453193665},{"id":"https://openalex.org/keywords/node","display_name":"Node (physics)","score":0.41097235679626465},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3835432231426239},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3600696921348572},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3539876341819763},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.09964314103126526}],"concepts":[{"id":"https://openalex.org/C50820777","wikidata":"https://www.wikidata.org/wiki/Q213723","display_name":"Hypercube","level":2,"score":0.772615909576416},{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.6874375939369202},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5809674263000488},{"id":"https://openalex.org/C53051483","wikidata":"https://www.wikidata.org/wiki/Q861555","display_name":"Cube (algebra)","level":2,"score":0.5441885590553284},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5440163016319275},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.520414412021637},{"id":"https://openalex.org/C173801870","wikidata":"https://www.wikidata.org/wiki/Q201413","display_name":"Heuristic","level":2,"score":0.4534469246864319},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.45326635241508484},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.42516839504241943},{"id":"https://openalex.org/C75564084","wikidata":"https://www.wikidata.org/wiki/Q5597085","display_name":"Graph embedding","level":3,"score":0.41695916652679443},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.41680267453193665},{"id":"https://openalex.org/C62611344","wikidata":"https://www.wikidata.org/wiki/Q1062658","display_name":"Node (physics)","level":2,"score":0.41097235679626465},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3835432231426239},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3600696921348572},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3539876341819763},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.09964314103126526},{"id":"https://openalex.org/C66938386","wikidata":"https://www.wikidata.org/wiki/Q633538","display_name":"Structural engineering","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/0218081","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0218081","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":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W140456478","https://openalex.org/W183327403","https://openalex.org/W1964602554","https://openalex.org/W1968082675","https://openalex.org/W2009796613","https://openalex.org/W2028085583","https://openalex.org/W2051311803","https://openalex.org/W2067242805","https://openalex.org/W2068135225","https://openalex.org/W2068380082","https://openalex.org/W2090189305","https://openalex.org/W2093031243","https://openalex.org/W2107997203","https://openalex.org/W2143774478","https://openalex.org/W2164898082","https://openalex.org/W2785506964","https://openalex.org/W2977453201","https://openalex.org/W4213214460"],"related_works":["https://openalex.org/W2495029940","https://openalex.org/W195224515","https://openalex.org/W2135693030","https://openalex.org/W2157828285","https://openalex.org/W2361284192","https://openalex.org/W2007173733","https://openalex.org/W4250393251","https://openalex.org/W2087725382","https://openalex.org/W2392648935","https://openalex.org/W2279178133"],"abstract_inverted_index":{"Task":[0],"allocation":[1,38],"in":[2,71,90,107,134,141],"an":[3,7,26,72],"n-dimensional":[4],"hypercube":[5],"(or":[6],"n-cube)":[8],"multicomputer":[9],"consists":[10],"of":[11,17,20,30,33,39,45,69,114,123,158,165,179,185,194,226],"two":[12],"sequential":[13],"steps:":[14],"(i)":[15,52],"determination":[16],"the":[18,21,40,46,58,67,115,121,142,153,162,175,180,186,211,222],"size":[19],"cube":[22,44,167],"required":[23,168],"to":[24,42,66,80,131,202,220],"accommodate":[25],"incoming":[27,100],"task":[28,41,101,116,144,205],"composed":[29],"a":[31,43,105,112,132,136,159,166,170,227],"set":[32],"interacting":[34],"modules,":[35],"and":[36,64,117,161],"(ii)":[37,85],"dimension":[47,164,178,225],"determined":[48],"from":[49],"(i).":[50,83],"Step":[51,84],"is":[53,61,79,102,151,173,217],"usually":[54],"done":[55],"manually":[56],"by":[57,104],"users,":[59],"which":[60,108],"often":[62],"difficult":[63],"leads":[65],"underutilization":[68],"processors":[70],"n-cube":[73],"system.":[74],"The":[75],"main":[76],"objective":[77],"here":[78],"automate":[81],"step":[82],"has":[86],"already":[87],"been":[88],"addressed":[89],"[":[91],"IEEE":[92],"Trans.":[93],"Comput.,":[94],"36":[95],"(1987),":[96],"pp.":[97],"1396\u20131407].":[98],"Each":[99,126],"represented":[103],"graph":[106,145,172],"each":[109,118],"node":[110,139],"denotes":[111],"module":[113,127],"link":[119],"represents":[120],"need":[122],"intermodule":[124],"communication.":[125],"must":[128],"be":[129],"assigned":[130],"subcube":[133],"such":[135],"way":[137],"that":[138],"adjacencies":[140],"associated":[143],"are":[146,189,200],"preserved.":[147],"This":[148],"assignment":[149],"problem":[150],"called":[152],"relaxed":[154],"squashed":[155],"(RS)":[156],"embedding":[157,188],"graph,":[160],"minimal":[163],"for":[169,210],"given":[171],"termed":[174],"weak":[176,223],"cubical":[177,224],"graph.":[181,228],"Some":[182],"mathematical":[183,196],"properties":[184],"RS":[187,203],"derived":[190,219],"first.":[191],"In":[192],"light":[193],"these":[195],"properties,":[197],"fast":[198],"algorithms":[199],"developed":[201],"embed":[204],"graphs.":[206],"A":[207],"heuristic":[208],"function":[209],"$A^":[212],"*":[213],"$":[214],"search":[215],"algorithm":[216],"also":[218],"determine":[221]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}