{"id":"https://openalex.org/W1966878439","doi":"https://doi.org/10.1137/0216026","title":"A Polynomial-Time Algorithm to Find the Shortest Cycle Basis of a Graph","display_name":"A Polynomial-Time Algorithm to Find the Shortest Cycle Basis of a Graph","publication_year":1987,"publication_date":"1987-04-01","ids":{"openalex":"https://openalex.org/W1966878439","doi":"https://doi.org/10.1137/0216026","mag":"1966878439"},"language":"en","primary_location":{"id":"doi:10.1137/0216026","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0216026","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/A5084176957","display_name":"Joseph D. Horton","orcid":null},"institutions":[{"id":"https://openalex.org/I106938459","display_name":"University of New Brunswick","ror":"https://ror.org/05nkf0n29","country_code":"CA","type":"education","lineage":["https://openalex.org/I106938459"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"J. D. Horton","raw_affiliation_strings":["University of New Brunswick Fredericton New Brunswick Canada"],"affiliations":[{"raw_affiliation_string":"University of New Brunswick Fredericton New Brunswick Canada","institution_ids":["https://openalex.org/I106938459"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5084176957"],"corresponding_institution_ids":["https://openalex.org/I106938459"],"apc_list":null,"apc_paid":null,"fwci":2.6615,"has_fulltext":false,"cited_by_count":282,"citation_normalized_percentile":{"value":0.87852575,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":98,"max":100},"biblio":{"volume":"16","issue":"2","first_page":"358","last_page":"366"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11522","display_name":"VLSI and FPGA Design Techniques","score":0.9997000098228455,"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"}},"topics":[{"id":"https://openalex.org/T11522","display_name":"VLSI and FPGA Design Techniques","score":0.9997000098228455,"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/T10829","display_name":"Interconnection Networks and Systems","score":0.9991999864578247,"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":0.9976999759674072,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/cycle-basis","display_name":"Cycle basis","score":0.9134769439697266},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7337465286254883},{"id":"https://openalex.org/keywords/basis","display_name":"Basis (linear algebra)","score":0.7197942733764648},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7084184885025024},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.550163209438324},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.43486976623535156},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.42553621530532837},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.40344130992889404},{"id":"https://openalex.org/keywords/graph-power","display_name":"Graph power","score":0.14630922675132751},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.10224413871765137}],"concepts":[{"id":"https://openalex.org/C26752605","wikidata":"https://www.wikidata.org/wiki/Q16766188","display_name":"Cycle basis","level":5,"score":0.9134769439697266},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7337465286254883},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.7197942733764648},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7084184885025024},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.550163209438324},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.43486976623535156},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.42553621530532837},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.40344130992889404},{"id":"https://openalex.org/C149530733","wikidata":"https://www.wikidata.org/wiki/Q5597091","display_name":"Graph power","level":4,"score":0.14630922675132751},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.10224413871765137},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/0216026","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0216026","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":10,"referenced_works":["https://openalex.org/W1965919443","https://openalex.org/W1984040953","https://openalex.org/W2007572995","https://openalex.org/W2053957335","https://openalex.org/W2066967348","https://openalex.org/W2095458137","https://openalex.org/W2111413685","https://openalex.org/W2129090681","https://openalex.org/W2162278146","https://openalex.org/W2169528473"],"related_works":["https://openalex.org/W91800244","https://openalex.org/W2072943779","https://openalex.org/W2074467278","https://openalex.org/W2249499697","https://openalex.org/W4386448439","https://openalex.org/W1629505938","https://openalex.org/W2767824041","https://openalex.org/W1519201794","https://openalex.org/W1987322712","https://openalex.org/W4313561101"],"abstract_inverted_index":{"Define":[0],"the":[1,7,15,18,24,36,47,54,60,75,94],"length":[2,39,107],"of":[3,6,10,17,20,49,56,106],"a":[4,11,32,102],"basis":[5,34,78,105],"cycle":[8,33,77,104],"space":[9],"graph":[12],"to":[13,81,100],"be":[14,70],"sum":[16],"lengths":[19],"all":[21],"cycles":[22],"in":[23,40],"basis.":[25],"An":[26],"algorithm":[27,64,99],"is":[28,46,53,59,79,113],"given":[29],"that":[30],"finds":[31],"with":[35],"shortest":[37,76],"possible":[38],"$O(m^3":[41],"n)$":[42],"operations,":[43],"where":[44],"m":[45],"number":[48,55],"edges":[50,92],"and":[51],"n":[52],"vertices.":[57],"This":[58],"first":[61],"known":[62],"polynomial-time":[63],"for":[65,93,110],"this":[66],"problem.":[67],"Edges":[68],"may":[69],"weighted":[71],"or":[72],"unweighted.":[73],"Also,":[74],"shown":[80],"have":[82],"at":[83],"most":[84],"${{3(n":[85],"-":[86,88],"1)(n":[87],"2)}":[89],"/":[90],"2}$":[91],"unweighted":[95,111],"case.":[96],"$O(mn^2":[97],")$":[98,109],"obtain":[101],"suboptimal":[103],"$O(n^2":[108],"graphs":[112],"also":[114],"given.":[115]},"counts_by_year":[{"year":2026,"cited_by_count":7},{"year":2025,"cited_by_count":8},{"year":2024,"cited_by_count":13},{"year":2023,"cited_by_count":9},{"year":2022,"cited_by_count":9},{"year":2021,"cited_by_count":7},{"year":2020,"cited_by_count":6},{"year":2019,"cited_by_count":7},{"year":2018,"cited_by_count":7},{"year":2017,"cited_by_count":8},{"year":2016,"cited_by_count":12},{"year":2015,"cited_by_count":10},{"year":2014,"cited_by_count":8},{"year":2013,"cited_by_count":10},{"year":2012,"cited_by_count":9}],"updated_date":"2026-04-23T09:07:50.710637","created_date":"2025-10-10T00:00:00"}