{"id":"https://openalex.org/W2102419291","doi":"https://doi.org/10.1109/iscas.2005.1464847","title":"Small Congestion Embedding of Separable Graphs into Grids of the Same Size","display_name":"Small Congestion Embedding of Separable Graphs into Grids of the Same Size","publication_year":2005,"publication_date":"2005-07-27","ids":{"openalex":"https://openalex.org/W2102419291","doi":"https://doi.org/10.1109/iscas.2005.1464847","mag":"2102419291"},"language":"en","primary_location":{"id":"doi:10.1109/iscas.2005.1464847","is_oa":false,"landing_page_url":"https://doi.org/10.1109/iscas.2005.1464847","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2005 IEEE International Symposium on Circuits and Systems","raw_type":"proceedings-article"},"type":"conference-paper","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/A5052292825","display_name":"Akira Matsubayashi","orcid":"https://orcid.org/0000-0002-7861-4876"},"institutions":[{"id":"https://openalex.org/I10091056","display_name":"Kanazawa University","ror":"https://ror.org/02hwp6a56","country_code":"JP","type":"education","lineage":["https://openalex.org/I10091056"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"A. Matsubayashi","raw_affiliation_strings":["Division of Electrical Engineering and Computer Science, Kanazawa University, Kanazawa, Japan","Div. of Electr. Eng. & Comput. Sci., Kanazawa Univ., Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Division of Electrical Engineering and Computer Science, Kanazawa University, Kanazawa, Japan","institution_ids":["https://openalex.org/I10091056"]},{"raw_affiliation_string":"Div. of Electr. Eng. & Comput. Sci., Kanazawa Univ., Japan","institution_ids":["https://openalex.org/I10091056"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5052292825"],"corresponding_institution_ids":["https://openalex.org/I10091056"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":"9","issue":null,"first_page":"1354","last_page":"1357"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10829","display_name":"Interconnection Networks and Systems","score":0.9997000098228455,"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":0.9997000098228455,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9986000061035156,"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/T11181","display_name":"Advanced Data Storage Technologies","score":0.9962000250816345,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6241075992584229},{"id":"https://openalex.org/keywords/grid","display_name":"Grid","score":0.5641645789146423},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.526232898235321},{"id":"https://openalex.org/keywords/embedding","display_name":"Embedding","score":0.5214859247207642},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.501533031463623},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.471798837184906},{"id":"https://openalex.org/keywords/separable-space","display_name":"Separable space","score":0.4669298529624939},{"id":"https://openalex.org/keywords/planar-graph","display_name":"Planar graph","score":0.44363996386528015},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.42565256357192993},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3759990930557251},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.0621165931224823}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6241075992584229},{"id":"https://openalex.org/C187691185","wikidata":"https://www.wikidata.org/wiki/Q2020720","display_name":"Grid","level":2,"score":0.5641645789146423},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.526232898235321},{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.5214859247207642},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.501533031463623},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.471798837184906},{"id":"https://openalex.org/C70710897","wikidata":"https://www.wikidata.org/wiki/Q680081","display_name":"Separable space","level":2,"score":0.4669298529624939},{"id":"https://openalex.org/C101837359","wikidata":"https://www.wikidata.org/wiki/Q547823","display_name":"Planar graph","level":3,"score":0.44363996386528015},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.42565256357192993},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3759990930557251},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0621165931224823},{"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/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/iscas.2005.1464847","is_oa":false,"landing_page_url":"https://doi.org/10.1109/iscas.2005.1464847","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2005 IEEE International Symposium on Circuits and Systems","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W224664467","https://openalex.org/W1545790954","https://openalex.org/W1549935796","https://openalex.org/W1989650529","https://openalex.org/W2029282358","https://openalex.org/W2038643780","https://openalex.org/W2079966248","https://openalex.org/W2085091875","https://openalex.org/W2109562758","https://openalex.org/W2143314829","https://openalex.org/W2150148016","https://openalex.org/W2157211828","https://openalex.org/W4205403515","https://openalex.org/W6608838215","https://openalex.org/W6996387589"],"related_works":["https://openalex.org/W2081900870","https://openalex.org/W2009525028","https://openalex.org/W4321064619","https://openalex.org/W2037549926","https://openalex.org/W2076561698","https://openalex.org/W2053599029","https://openalex.org/W2082479932","https://openalex.org/W4302177579","https://openalex.org/W1798304401","https://openalex.org/W2476624396"],"abstract_inverted_index":{"In":[0],"this":[1],"paper":[2],"we":[3],"consider":[4],"the":[5,16,24,49,86,115],"problem":[6],"of":[7,19,23,48],"embedding":[8],"a":[9,13,34,46,89,111],"(guest)":[10],"graph":[11,26,35,62,87],"into":[12,45,72,96],"grid":[14,47,75,99],"with":[15,27,52,63,76,100],"same":[17,50],"number":[18],"nodes":[20],"as":[21],"those":[22],"guest":[25],"minimum":[28],"edge":[29],"congestion.":[30,54],"We":[31],"show":[32],"that":[33,58],"which":[36],"has":[37],"some":[38],"efficient":[39],"recursive":[40],"separators":[41],"can":[42,69,93],"be":[43,70,94],"embedded":[44,71,95],"size":[51],"small":[53],"Our":[55],"results":[56],"imply":[57],"an":[59,73,97,123],"N-node":[60,74,98],"planar":[61,118],"maximum":[64],"vertex":[65],"degree":[66],"/spl":[67,127,130],"Delta/":[68,131],"congestion":[77,101,105,116],"O":[78],"(/spl":[79],"Delta//sup":[80,125],"2/":[81,126],"log":[82,132],"N),":[83],"and":[84,114],"if":[85],"is":[88,108,120],"tree,":[90],"then":[91],"it":[92],"O(/spl":[102],"Delta/).":[103],"The":[104],"for":[106,117],"trees":[107],"optimal":[109,121],"within":[110,122],"constant":[112],"factor,":[113],"graphs":[119],"O(min{/spl":[124],"radic/log":[128],"N,":[129],"N})":[133],"factor.":[134]},"counts_by_year":[],"updated_date":"2026-07-14T23:27:15.235271","created_date":"2025-10-10T00:00:00"}