{"id":"https://openalex.org/W1986453029","doi":"https://doi.org/10.1142/s0218196715500162","title":"Time complexity of the conjugacy problem in relatively hyperbolic groups","display_name":"Time complexity of the conjugacy problem in relatively hyperbolic groups","publication_year":2015,"publication_date":"2015-04-06","ids":{"openalex":"https://openalex.org/W1986453029","doi":"https://doi.org/10.1142/s0218196715500162","mag":"1986453029"},"language":"en","primary_location":{"id":"doi:10.1142/s0218196715500162","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196715500162","pdf_url":null,"source":{"id":"https://openalex.org/S23260266","display_name":"International Journal of Algebra and Computation","issn_l":"0218-1967","issn":["0218-1967","1793-6500"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Algebra and Computation","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/A5019148832","display_name":"Inna Bumagin","orcid":null},"institutions":[{"id":"https://openalex.org/I67031392","display_name":"Carleton University","ror":"https://ror.org/02qtvee93","country_code":"CA","type":"education","lineage":["https://openalex.org/I67031392"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Inna Bumagin","raw_affiliation_strings":["School of Mathematics and Statistics, Carleton University, Ottawa, ON, Canada K1S 5B6, Canada"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Carleton University, Ottawa, ON, Canada K1S 5B6, Canada","institution_ids":["https://openalex.org/I67031392"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5019148832"],"corresponding_institution_ids":["https://openalex.org/I67031392"],"apc_list":null,"apc_paid":null,"fwci":2.1374,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.85402531,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"25","issue":"05","first_page":"689","last_page":"723"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10304","display_name":"Geometric and Algebraic Topology","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10304","display_name":"Geometric and Algebraic Topology","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11567","display_name":"semigroups and automata theory","score":0.9973999857902527,"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9939000010490417,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/conjugacy-class","display_name":"Conjugacy class","score":0.9115563631057739},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.9008011817932129},{"id":"https://openalex.org/keywords/conjugacy-problem","display_name":"Conjugacy problem","score":0.7949694395065308},{"id":"https://openalex.org/keywords/hyperbolic-group","display_name":"Hyperbolic group","score":0.6890326738357544},{"id":"https://openalex.org/keywords/relatively-hyperbolic-group","display_name":"Relatively hyperbolic group","score":0.654774010181427},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5238116979598999},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.4996373653411865},{"id":"https://openalex.org/keywords/element","display_name":"Element (criminal law)","score":0.4935656785964966},{"id":"https://openalex.org/keywords/hyperbolic-manifold","display_name":"Hyperbolic manifold","score":0.45861271023750305},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.4116385579109192},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.410754919052124},{"id":"https://openalex.org/keywords/hyperbolic-function","display_name":"Hyperbolic function","score":0.36889737844467163},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3343357443809509},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3181501626968384},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.24203607439994812}],"concepts":[{"id":"https://openalex.org/C87945829","wikidata":"https://www.wikidata.org/wiki/Q1353233","display_name":"Conjugacy class","level":2,"score":0.9115563631057739},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9008011817932129},{"id":"https://openalex.org/C2780526409","wikidata":"https://www.wikidata.org/wiki/Q5161137","display_name":"Conjugacy problem","level":3,"score":0.7949694395065308},{"id":"https://openalex.org/C167150821","wikidata":"https://www.wikidata.org/wiki/Q81194","display_name":"Hyperbolic group","level":4,"score":0.6890326738357544},{"id":"https://openalex.org/C40020168","wikidata":"https://www.wikidata.org/wiki/Q7310818","display_name":"Relatively hyperbolic group","level":4,"score":0.654774010181427},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5238116979598999},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.4996373653411865},{"id":"https://openalex.org/C200288055","wikidata":"https://www.wikidata.org/wiki/Q2621792","display_name":"Element (criminal law)","level":2,"score":0.4935656785964966},{"id":"https://openalex.org/C70984080","wikidata":"https://www.wikidata.org/wiki/Q2619102","display_name":"Hyperbolic manifold","level":3,"score":0.45861271023750305},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.4116385579109192},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.410754919052124},{"id":"https://openalex.org/C92047909","wikidata":"https://www.wikidata.org/wiki/Q204034","display_name":"Hyperbolic function","level":2,"score":0.36889737844467163},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3343357443809509},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3181501626968384},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.24203607439994812},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C178790620","wikidata":"https://www.wikidata.org/wiki/Q11351","display_name":"Organic chemistry","level":1,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218196715500162","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196715500162","pdf_url":null,"source":{"id":"https://openalex.org/S23260266","display_name":"International Journal of Algebra and Computation","issn_l":"0218-1967","issn":["0218-1967","1793-6500"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Algebra and Computation","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":46,"referenced_works":["https://openalex.org/W28957298","https://openalex.org/W70112514","https://openalex.org/W1548977175","https://openalex.org/W1573620260","https://openalex.org/W1627083394","https://openalex.org/W1632002092","https://openalex.org/W1645174048","https://openalex.org/W1967512719","https://openalex.org/W1968065171","https://openalex.org/W1978029823","https://openalex.org/W1981151457","https://openalex.org/W1981155305","https://openalex.org/W2007770633","https://openalex.org/W2013748069","https://openalex.org/W2016474213","https://openalex.org/W2019453185","https://openalex.org/W2025977311","https://openalex.org/W2038781886","https://openalex.org/W2046619616","https://openalex.org/W2055527098","https://openalex.org/W2060685167","https://openalex.org/W2068638265","https://openalex.org/W2086494818","https://openalex.org/W2087184562","https://openalex.org/W2093981152","https://openalex.org/W2107913628","https://openalex.org/W2115539268","https://openalex.org/W2126872770","https://openalex.org/W2134086356","https://openalex.org/W2135126413","https://openalex.org/W2140489090","https://openalex.org/W2152615135","https://openalex.org/W2153280354","https://openalex.org/W2158684550","https://openalex.org/W2283605069","https://openalex.org/W2962751036","https://openalex.org/W2963196760","https://openalex.org/W3098881614","https://openalex.org/W3102255413","https://openalex.org/W3103938366","https://openalex.org/W3105616315","https://openalex.org/W4206038095","https://openalex.org/W4210393840","https://openalex.org/W4235484205","https://openalex.org/W4297571775","https://openalex.org/W6603772978"],"related_works":["https://openalex.org/W2622280211","https://openalex.org/W2963847473","https://openalex.org/W4302192524","https://openalex.org/W2189283419","https://openalex.org/W2149889673","https://openalex.org/W2081281167","https://openalex.org/W4240041676","https://openalex.org/W2067549982","https://openalex.org/W3134333986","https://openalex.org/W2093981152"],"abstract_inverted_index":{"If":[0],"u":[1,21,138,160],"and":[2,22,60,103,139,161],"v":[3,23,140,162],"are":[4,141],"two":[5,142],"conjugate":[6,143],"elements":[7,145],"of":[8,15,31,34,46,66,146,154,167],"a":[9,16,28,74,115,147,155],"hyperbolic":[10,47,75,92,117,144,149],"group":[11,76,150],"then":[12,151],"the":[13,32,77,100,104,120,152],"length":[14,153],"shortest":[17,156],"conjugating":[18,157],"element":[19,158],"for":[20,159],"can":[24,80,108,123],"be":[25,81,109,124],"bounded":[26],"by":[27,40],"linear":[29,164],"function":[30],"sum":[33],"their":[35,168],"lengths,":[36],"as":[37],"was":[38],"proved":[39],"Lysenok":[41],"in":[42,63,73,83,111,114,126,129,165],"[Some":[43],"algorithmic":[44],"properties":[45],"groups,":[48],"Izv.":[49],"Akad.":[50],"Nauk":[51],"SSSR":[52],"Ser.":[53],"Mat.":[54],"53(4)":[55],"(1989)":[56],"814\u2013832,":[57],"912].":[58],"Bridson":[59],"Haefliger":[61],"showed":[62],"[Metrics":[64],"Spaces":[65],"Non-Positive":[67],"Curvature":[68],"(Springer-Verlag,":[69],"Berlin,":[70],"1999)]":[71],"that":[72,98,136],"conjugacy":[78,101,105],"problem":[79,102,107,122],"solved":[82,110,125],"polynomial":[84,112,127],"time.":[85],"We":[86,133],"extend":[87],"these":[88],"results":[89],"to":[90],"relatively":[91,116,148],"groups.":[93],"In":[94],"particular,":[95],"we":[96],"show":[97],"both":[99],"search":[106],"time":[113,128],"group,":[118],"whenever":[119],"corresponding":[121],"each":[130],"parabolic":[131],"subgroup.":[132],"also":[134],"prove":[135],"if":[137],"is":[163],"terms":[166],"lengths.":[169]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}