{"id":"https://openalex.org/W1988738304","doi":"https://doi.org/10.1137/s0097539794270881","title":"An Optimal Algorithm for Scanning All Spanning Trees of Undirected Graphs","display_name":"An Optimal Algorithm for Scanning All Spanning Trees of Undirected Graphs","publication_year":1997,"publication_date":"1997-06-01","ids":{"openalex":"https://openalex.org/W1988738304","doi":"https://doi.org/10.1137/s0097539794270881","mag":"1988738304"},"language":"en","primary_location":{"id":"doi:10.1137/s0097539794270881","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0097539794270881","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":true,"oa_status":"green","oa_url":"https://tohoku.repo.nii.ac.jp/records/66883","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5067169957","display_name":"Akiyoshi Shioura","orcid":"https://orcid.org/0000-0002-5216-7190"},"institutions":[{"id":"https://openalex.org/I114531698","display_name":"Tokyo Institute of Technology","ror":"https://ror.org/0112mx960","country_code":"JP","type":"education","lineage":["https://openalex.org/I114531698"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Akiyoshi Shioura","raw_affiliation_strings":["Tokyo Inst. of Tech"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Tokyo Inst. of Tech","institution_ids":["https://openalex.org/I114531698"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5049807890","display_name":"Akihisa Tamura","orcid":"https://orcid.org/0000-0001-9528-7582"},"institutions":[{"id":"https://openalex.org/I20529979","display_name":"University of Electro-Communications","ror":"https://ror.org/02x73b849","country_code":"JP","type":"education","lineage":["https://openalex.org/I20529979"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Akihisa Tamura","raw_affiliation_strings":["the University of Electro-Communications"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"the University of Electro-Communications","institution_ids":["https://openalex.org/I20529979"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5076101253","display_name":"Takeaki Uno","orcid":"https://orcid.org/0000-0001-7274-279X"},"institutions":[{"id":"https://openalex.org/I114531698","display_name":"Tokyo Institute of Technology","ror":"https://ror.org/0112mx960","country_code":"JP","type":"education","lineage":["https://openalex.org/I114531698"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Takeaki Uno","raw_affiliation_strings":["Tokyo Inst. of Tech"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Tokyo Inst. of Tech","institution_ids":["https://openalex.org/I114531698"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.5568,"has_fulltext":false,"cited_by_count":102,"citation_normalized_percentile":{"value":0.88299168,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"26","issue":"3","first_page":"678","last_page":"692"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9998999834060669,"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"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/T11106","display_name":"Data Management and Algorithms","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/spanning-tree","display_name":"Spanning tree","score":0.8118672370910645},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6442584991455078},{"id":"https://openalex.org/keywords/minimum-spanning-tree","display_name":"Minimum spanning tree","score":0.6351395845413208},{"id":"https://openalex.org/keywords/backtracking","display_name":"Backtracking","score":0.6088168621063232},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.561008095741272},{"id":"https://openalex.org/keywords/kruskals-algorithm","display_name":"Kruskal's algorithm","score":0.5579847693443298},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.522068202495575},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.5145506262779236},{"id":"https://openalex.org/keywords/computational-complexity-theory","display_name":"Computational complexity theory","score":0.42366504669189453},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4178541302680969}],"concepts":[{"id":"https://openalex.org/C64331007","wikidata":"https://www.wikidata.org/wiki/Q831672","display_name":"Spanning tree","level":2,"score":0.8118672370910645},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6442584991455078},{"id":"https://openalex.org/C13743678","wikidata":"https://www.wikidata.org/wiki/Q240464","display_name":"Minimum spanning tree","level":2,"score":0.6351395845413208},{"id":"https://openalex.org/C156884757","wikidata":"https://www.wikidata.org/wiki/Q798554","display_name":"Backtracking","level":2,"score":0.6088168621063232},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.561008095741272},{"id":"https://openalex.org/C63645285","wikidata":"https://www.wikidata.org/wiki/Q797860","display_name":"Kruskal's algorithm","level":3,"score":0.5579847693443298},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.522068202495575},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.5145506262779236},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.42366504669189453},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4178541302680969}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/s0097539794270881","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0097539794270881","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"},{"id":"pmh:oai:irdb.nii.ac.jp:00918:0000486940","is_oa":true,"landing_page_url":"https://tohoku.repo.nii.ac.jp/records/66883","pdf_url":null,"source":{"id":"https://openalex.org/S7407056385","display_name":"Institutional Repositories DataBase (IRDB)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I184597095","host_organization_name":"National Institute of Informatics","host_organization_lineage":["https://openalex.org/I184597095"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM journal on computing","raw_type":"journal article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.38.9434","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.38.9434","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ftp://ftp.is.titech.ac.jp/pub/OpRes/articles/b285.ps.Z","raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:irdb.nii.ac.jp:00918:0000486940","is_oa":true,"landing_page_url":"https://tohoku.repo.nii.ac.jp/records/66883","pdf_url":null,"source":{"id":"https://openalex.org/S7407056385","display_name":"Institutional Repositories DataBase (IRDB)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I184597095","host_organization_name":"National Institute of Informatics","host_organization_lineage":["https://openalex.org/I184597095"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM journal on computing","raw_type":"journal article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":8,"referenced_works":["https://openalex.org/W2022871748","https://openalex.org/W2030996579","https://openalex.org/W2073647226","https://openalex.org/W2091045890","https://openalex.org/W2118382442","https://openalex.org/W2136620308","https://openalex.org/W2767970464","https://openalex.org/W4234356172"],"related_works":["https://openalex.org/W4380840098","https://openalex.org/W2418231958","https://openalex.org/W4206043061","https://openalex.org/W2942013815","https://openalex.org/W2387385213","https://openalex.org/W4242086819","https://openalex.org/W2074214908","https://openalex.org/W2138987445","https://openalex.org/W1842018596","https://openalex.org/W4302939663"],"abstract_inverted_index":{"Let":[0],"G":[1],"be":[2],"an":[3,99],"undirected":[4],"graph":[5],"with":[6,122],"V":[7,102],"vertices":[8],"and":[9,46,51,53,95,131,157,160,187],"E":[10],"edges.":[11,93],"Many":[12],"algorithms":[13,28,36],"have":[14,41],"been":[15,42],"developed":[16],"for":[17],"enumerating":[18],"all":[19,84],"spanning":[20,60,85,118],"trees":[21,86],"in":[22,136,144,181],"G.":[23],"Most":[24],"of":[25,66,75,83,92,117,139,146,184],"the":[26,73,80,115,123,137,162,173,182],"early":[27],"use":[29],"a":[30,38,58,67,109],"technique":[31,40,71],"called":[32],"\"backtracking.\"":[33],"Recently,":[34],"several":[35],"using":[37],"different":[39],"proposed":[43,98],"by":[44,62,87,106,129],"Kapoor":[45,94],"Ramesh":[47,96],"(1992),":[48],"Matsui":[49],"(1993),":[50],"Shioura":[52,130,156],"Tamura":[54],"(1993).":[55],"They":[56],"find":[57],"new":[59],"tree":[61],"exchanging":[63],"one":[64],"edge":[65],"current":[68],"one.":[69],"This":[70],"has":[72],"merit":[74],"enabling":[76],"us":[77],"to":[78,167],"compress":[79],"whole":[81],"output":[82],"outputting":[88],"only":[89],"relative":[90],"changes":[91],"first":[97],"O(N":[100],"+":[101,103,169],"E)-time":[104],"algorithm":[105,121,159,178],"adopting":[107],"such":[108],"\"compact\"":[110],"output,":[111],"where":[112],"N":[113],"is":[114,179],"number":[116],"trees.":[119],"Another":[120],"same":[124],"time":[125,140,174,186],"complexity":[126,141,148,164],"was":[127],"constructed":[128],"Tamura.":[132],"These":[133],"are":[134],"optimal":[135,180],"sense":[138,183],"but":[142],"not":[143],"terms":[145],"space":[147,163,188],"because":[149],"they":[150],"take":[151],"O(VE)":[152,166],"space.":[153],"We":[154],"refine":[155],"Tamura's":[158],"decrease":[161],"from":[165],"O(V":[168],"E)":[170],"while":[171],"preserving":[172],"complexity.":[175],"Therefore,":[176],"our":[177],"both":[185],"complexities.":[189]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":6},{"year":2017,"cited_by_count":5},{"year":2016,"cited_by_count":5},{"year":2015,"cited_by_count":5},{"year":2014,"cited_by_count":9},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":6}],"updated_date":"2026-08-03T07:22:36.454288","created_date":"2025-10-10T00:00:00"}
