{"id":"https://openalex.org/W7134137597","doi":"https://doi.org/10.1007/s10878-026-01405-8","title":"Maximum alternating clean balanced cycle decomposition and applications in rearrangement distance problems","display_name":"Maximum alternating clean balanced cycle decomposition and applications in rearrangement distance problems","publication_year":2026,"publication_date":"2026-03-01","ids":{"openalex":"https://openalex.org/W7134137597","doi":"https://doi.org/10.1007/s10878-026-01405-8"},"language":"en","primary_location":{"id":"doi:10.1007/s10878-026-01405-8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10878-026-01405-8","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10878-026-01405-8.pdf","source":{"id":"https://openalex.org/S107925523","display_name":"Journal of Combinatorial Optimization","issn_l":"1382-6905","issn":["1382-6905","1573-2886"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Combinatorial Optimization","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s10878-026-01405-8.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5013933267","display_name":"Gabriel Siqueira","orcid":"https://orcid.org/0000-0001-5745-399X"},"institutions":[{"id":"https://openalex.org/I181391015","display_name":"Universidade Estadual de Campinas (UNICAMP)","ror":"https://ror.org/04wffgt70","country_code":"BR","type":"education","lineage":["https://openalex.org/I181391015"]}],"countries":["BR"],"is_corresponding":true,"raw_author_name":"Gabriel Siqueira","raw_affiliation_strings":["Instituto de Computa\u00e7\u00e3o, Universidade Estadual de Campinas (Unicamp), Av. Albert Einstein, 1251, 13083-852, Campinas, S\u00e3o Paulo, Brazil"],"affiliations":[{"raw_affiliation_string":"Instituto de Computa\u00e7\u00e3o, Universidade Estadual de Campinas (Unicamp), Av. Albert Einstein, 1251, 13083-852, Campinas, S\u00e3o Paulo, Brazil","institution_ids":["https://openalex.org/I181391015"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5030811687","display_name":"Klairton Lima Brito","orcid":"https://orcid.org/0000-0001-5287-2925"},"institutions":[{"id":"https://openalex.org/I181391015","display_name":"Universidade Estadual de Campinas (UNICAMP)","ror":"https://ror.org/04wffgt70","country_code":"BR","type":"education","lineage":["https://openalex.org/I181391015"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Klairton Lima Brito","raw_affiliation_strings":["Instituto de Computa\u00e7\u00e3o, Universidade Estadual de Campinas (Unicamp), Av. Albert Einstein, 1251, 13083-852, Campinas, S\u00e3o Paulo, Brazil"],"affiliations":[{"raw_affiliation_string":"Instituto de Computa\u00e7\u00e3o, Universidade Estadual de Campinas (Unicamp), Av. Albert Einstein, 1251, 13083-852, Campinas, S\u00e3o Paulo, Brazil","institution_ids":["https://openalex.org/I181391015"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5128299276","display_name":"Alexsandro Oliveira Alexandrino","orcid":null},"institutions":[{"id":"https://openalex.org/I181391015","display_name":"Universidade Estadual de Campinas (UNICAMP)","ror":"https://ror.org/04wffgt70","country_code":"BR","type":"education","lineage":["https://openalex.org/I181391015"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Alexsandro Oliveira Alexandrino","raw_affiliation_strings":["Instituto de Computa\u00e7\u00e3o, Universidade Estadual de Campinas (Unicamp), Av. Albert Einstein, 1251, 13083-852, Campinas, S\u00e3o Paulo, Brazil"],"affiliations":[{"raw_affiliation_string":"Instituto de Computa\u00e7\u00e3o, Universidade Estadual de Campinas (Unicamp), Av. Albert Einstein, 1251, 13083-852, Campinas, S\u00e3o Paulo, Brazil","institution_ids":["https://openalex.org/I181391015"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5069714194","display_name":"Andre Rodrigues Oliveira","orcid":"https://orcid.org/0000-0002-0568-1859"},"institutions":[{"id":"https://openalex.org/I18167132","display_name":"Universidade Presbiteriana Mackenzie","ror":"https://ror.org/006nc8n95","country_code":"BR","type":"education","lineage":["https://openalex.org/I18167132"]},{"id":"https://openalex.org/I4210111188","display_name":"Universidade Paulista","ror":"https://ror.org/020v13m88","country_code":"BR","type":"education","lineage":["https://openalex.org/I4210111188"]},{"id":"https://openalex.org/I879563668","display_name":"Universidade Estadual Paulista (Unesp)","ror":"https://ror.org/00987cb86","country_code":"BR","type":"education","lineage":["https://openalex.org/I879563668"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Andre Rodrigues Oliveira","raw_affiliation_strings":["Faculdade de Computa\u00e7\u00e3o e Inform\u00e1tica, Universidade Presbiteriana Mackenzie, Rua da Consola\u00e7\u00e3o, 930, 01302-907, S\u00e3o Paulo, S\u00e3o Paulo, Brazil","Universidade Virtual do Estado de S\u00e3o Paulo (Univesp), Av. Paulista, 352, 01310-905, S\u00e3ao Paulo, Brazil"],"affiliations":[{"raw_affiliation_string":"Faculdade de Computa\u00e7\u00e3o e Inform\u00e1tica, Universidade Presbiteriana Mackenzie, Rua da Consola\u00e7\u00e3o, 930, 01302-907, S\u00e3o Paulo, S\u00e3o Paulo, Brazil","institution_ids":["https://openalex.org/I18167132"]},{"raw_affiliation_string":"Universidade Virtual do Estado de S\u00e3o Paulo (Univesp), Av. Paulista, 352, 01310-905, S\u00e3ao Paulo, Brazil","institution_ids":["https://openalex.org/I879563668","https://openalex.org/I4210111188"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5052555109","display_name":"Ulisses Dias","orcid":"https://orcid.org/0000-0002-4763-3046"},"institutions":[{"id":"https://openalex.org/I181391015","display_name":"Universidade Estadual de Campinas (UNICAMP)","ror":"https://ror.org/04wffgt70","country_code":"BR","type":"education","lineage":["https://openalex.org/I181391015"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Ulisses Dias","raw_affiliation_strings":["Faculdade de Tecnologia, Universidade Estadual de Campinas (Unicamp), Rua Paschoal Marmo, 1888, 13484-332, Limeira, S\u00e3o Paulo, Brazil"],"affiliations":[{"raw_affiliation_string":"Faculdade de Tecnologia, Universidade Estadual de Campinas (Unicamp), Rua Paschoal Marmo, 1888, 13484-332, Limeira, S\u00e3o Paulo, Brazil","institution_ids":["https://openalex.org/I181391015"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5099353992","display_name":"Zanoni Dias","orcid":null},"institutions":[{"id":"https://openalex.org/I181391015","display_name":"Universidade Estadual de Campinas (UNICAMP)","ror":"https://ror.org/04wffgt70","country_code":"BR","type":"education","lineage":["https://openalex.org/I181391015"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Zanoni Dias","raw_affiliation_strings":["Instituto de Computa\u00e7\u00e3o, Universidade Estadual de Campinas (Unicamp), Av. Albert Einstein, 1251, 13083-852, Campinas, S\u00e3o Paulo, Brazil"],"affiliations":[{"raw_affiliation_string":"Instituto de Computa\u00e7\u00e3o, Universidade Estadual de Campinas (Unicamp), Av. Albert Einstein, 1251, 13083-852, Campinas, S\u00e3o Paulo, Brazil","institution_ids":["https://openalex.org/I181391015"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5013933267"],"corresponding_institution_ids":["https://openalex.org/I181391015"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":{"value":2390,"currency":"EUR","value_usd":2990},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.70501796,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"51","issue":"2","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T13664","display_name":"Genome Rearrangement Algorithms","score":0.989799976348877,"subfield":{"id":"https://openalex.org/subfields/1311","display_name":"Genetics"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},"topics":[{"id":"https://openalex.org/T13664","display_name":"Genome Rearrangement Algorithms","score":0.989799976348877,"subfield":{"id":"https://openalex.org/subfields/1311","display_name":"Genetics"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T10567","display_name":"Vehicle Routing Optimization Methods","score":0.0012000000569969416,"subfield":{"id":"https://openalex.org/subfields/2209","display_name":"Industrial and Manufacturing 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/T10015","display_name":"Genomics and Phylogenetic Studies","score":0.0007999999797903001,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/sorting","display_name":"Sorting","score":0.5551999807357788},{"id":"https://openalex.org/keywords/heuristic","display_name":"Heuristic","score":0.482699990272522},{"id":"https://openalex.org/keywords/approximation-algorithm","display_name":"Approximation algorithm","score":0.453000009059906},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4447000026702881},{"id":"https://openalex.org/keywords/theory-of-computation","display_name":"Theory of computation","score":0.4047999978065491},{"id":"https://openalex.org/keywords/intergenic-region","display_name":"Intergenic region","score":0.3944000005722046},{"id":"https://openalex.org/keywords/greedy-algorithm","display_name":"Greedy algorithm","score":0.35010001063346863},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.3361000120639801}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5554999709129333},{"id":"https://openalex.org/C111696304","wikidata":"https://www.wikidata.org/wiki/Q2303697","display_name":"Sorting","level":2,"score":0.5551999807357788},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5063999891281128},{"id":"https://openalex.org/C173801870","wikidata":"https://www.wikidata.org/wiki/Q201413","display_name":"Heuristic","level":2,"score":0.482699990272522},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.453000009059906},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4447000026702881},{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.4047999978065491},{"id":"https://openalex.org/C195139083","wikidata":"https://www.wikidata.org/wiki/Q3463539","display_name":"Intergenic region","level":4,"score":0.3944000005722046},{"id":"https://openalex.org/C51823790","wikidata":"https://www.wikidata.org/wiki/Q504353","display_name":"Greedy algorithm","level":2,"score":0.35010001063346863},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.3361000120639801},{"id":"https://openalex.org/C16345878","wikidata":"https://www.wikidata.org/wiki/Q107472979","display_name":"Orientation (vector space)","level":2,"score":0.3264000117778778},{"id":"https://openalex.org/C124681953","wikidata":"https://www.wikidata.org/wiki/Q339062","display_name":"Decomposition","level":2,"score":0.3212999999523163},{"id":"https://openalex.org/C119054055","wikidata":"https://www.wikidata.org/wiki/Q1576681","display_name":"Indel","level":5,"score":0.31859999895095825},{"id":"https://openalex.org/C141231307","wikidata":"https://www.wikidata.org/wiki/Q7020","display_name":"Genome","level":3,"score":0.3077999949455261},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.3073999881744385},{"id":"https://openalex.org/C2778258933","wikidata":"https://www.wikidata.org/wiki/Q16918986","display_name":"Decomposition method (queueing theory)","level":2,"score":0.3009999990463257},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.30070000886917114},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.29750001430511475},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.28940001130104065},{"id":"https://openalex.org/C74197172","wikidata":"https://www.wikidata.org/wiki/Q1195339","display_name":"Directed acyclic graph","level":2,"score":0.2750000059604645},{"id":"https://openalex.org/C88230418","wikidata":"https://www.wikidata.org/wiki/Q131476","display_name":"Graph theory","level":2,"score":0.26660001277923584},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.2648000121116638},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.2578999996185303},{"id":"https://openalex.org/C31266012","wikidata":"https://www.wikidata.org/wiki/Q6554340","display_name":"Linkage (software)","level":3,"score":0.25780001282691956},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.25060001015663147}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s10878-026-01405-8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10878-026-01405-8","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10878-026-01405-8.pdf","source":{"id":"https://openalex.org/S107925523","display_name":"Journal of Combinatorial Optimization","issn_l":"1382-6905","issn":["1382-6905","1573-2886"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Combinatorial Optimization","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1007/s10878-026-01405-8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10878-026-01405-8","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10878-026-01405-8.pdf","source":{"id":"https://openalex.org/S107925523","display_name":"Journal of Combinatorial Optimization","issn_l":"1382-6905","issn":["1382-6905","1573-2886"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Combinatorial Optimization","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/9","display_name":"Industry, innovation and infrastructure","score":0.4587554633617401}],"awards":[{"id":"https://openalex.org/G1950316668","display_name":null,"funder_award_id":"CAPES","funder_id":"https://openalex.org/F4320320997","funder_display_name":"Funda\u00e7\u00e3o de Amparo \u00e0 Pesquisa do Estado de S\u00e3o Paulo"},{"id":"https://openalex.org/G347084277","display_name":null,"funder_award_id":"2021/13824-8","funder_id":"https://openalex.org/F4320320997","funder_display_name":"Funda\u00e7\u00e3o de Amparo \u00e0 Pesquisa do Estado de S\u00e3o Paulo"},{"id":"https://openalex.org/G3690646728","display_name":null,"funder_award_id":"00x0ma614","funder_id":"https://openalex.org/F4320321091","funder_display_name":"Coordena\u00e7\u00e3o de Aperfei\u00e7oamento de Pessoal de N\u00edvel Superior"},{"id":"https://openalex.org/G3938906640","display_name":null,"funder_award_id":"(CAPES)","funder_id":"https://openalex.org/F4320321091","funder_display_name":"Coordena\u00e7\u00e3o de Aperfei\u00e7oamento de Pessoal de N\u00edvel Superior"},{"id":"https://openalex.org/G4600047395","display_name":null,"funder_award_id":"FAPESP","funder_id":"https://openalex.org/F4320321091","funder_display_name":"Coordena\u00e7\u00e3o de Aperfei\u00e7oamento de Pessoal de N\u00edvel Superior"},{"id":"https://openalex.org/G5139334624","display_name":null,"funder_award_id":"Coordena\u00e7\u00e3o","funder_id":"https://openalex.org/F4320321091","funder_display_name":"Coordena\u00e7\u00e3o de Aperfei\u00e7oamento de Pessoal de N\u00edvel Superior"},{"id":"https://openalex.org/G6438247056","display_name":null,"funder_award_id":"2021/","funder_id":"https://openalex.org/F4320320997","funder_display_name":"Funda\u00e7\u00e3o de Amparo \u00e0 Pesquisa do Estado de S\u00e3o Paulo"},{"id":"https://openalex.org/G963174003","display_name":null,"funder_award_id":"de Aperfei\u00e7","funder_id":"https://openalex.org/F4320321091","funder_display_name":"Coordena\u00e7\u00e3o de Aperfei\u00e7oamento de Pessoal de N\u00edvel Superior"}],"funders":[{"id":"https://openalex.org/F4320320997","display_name":"Funda\u00e7\u00e3o de Amparo \u00e0 Pesquisa do Estado de S\u00e3o Paulo","ror":"https://ror.org/02ddkpn78"},{"id":"https://openalex.org/F4320321091","display_name":"Coordena\u00e7\u00e3o de Aperfei\u00e7oamento de Pessoal de N\u00edvel Superior","ror":"https://ror.org/00x0ma614"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7134137597.pdf","grobid_xml":"https://content.openalex.org/works/W7134137597.grobid-xml"},"referenced_works_count":28,"referenced_works":["https://openalex.org/W1527607312","https://openalex.org/W1536222765","https://openalex.org/W1554477894","https://openalex.org/W1557322746","https://openalex.org/W1574897100","https://openalex.org/W1989978323","https://openalex.org/W2003985385","https://openalex.org/W2014859375","https://openalex.org/W2038225707","https://openalex.org/W2070642495","https://openalex.org/W2103333868","https://openalex.org/W2140118062","https://openalex.org/W2157622572","https://openalex.org/W2163195596","https://openalex.org/W2363554425","https://openalex.org/W2401610261","https://openalex.org/W2501571505","https://openalex.org/W2552354420","https://openalex.org/W2622515803","https://openalex.org/W2763373928","https://openalex.org/W2946012035","https://openalex.org/W2997079781","https://openalex.org/W3022620622","https://openalex.org/W3115388211","https://openalex.org/W3166911619","https://openalex.org/W3203485543","https://openalex.org/W4377939787","https://openalex.org/W4392995987"],"related_works":[],"abstract_inverted_index":{"Abstract":[0],"In":[1,15],"genome":[2,44],"rearrangement,":[3],"graph-based":[4],"representations":[5],"are":[6,95],"widely":[7],"used":[8],"to":[9,80,97,105,147],"analyze":[10],"and":[11,92,119,124,132,139,154,175,205,223,229,236,241,270],"solve":[12],"rearrangement":[13,45,82,107],"problems.":[14],"particular,":[16],"when":[17],"each":[18],"gene":[19,122],"occurs":[20],"at":[21],"most":[22],"once,":[23],"the":[24,53,63,85,88,117,136,144,158,161,171,195,198,201,207,215,219,226,232,237],"breakpoint":[25],"graph":[26,37],"is":[27,77,90,163,203],"a":[28,50,129,133,155],"useful":[29],"tool.":[30],"A":[31],"maximum":[32],"cycle":[33],"decomposition":[34],"of":[35,52,87,116,160,184,200,248],"this":[36],"yields":[38],"immediate":[39],"lower":[40],"bounds":[41],"for":[42,135,170,214],"several":[43],"distances.":[46],"This":[47],"paper":[48],"introduces":[49],"generalization":[51],"Maximum":[54,64],"Alternating":[55,65],"Cycle":[56,68],"Decomposition":[57,69],"problem":[58,70,76,102,178],"(":[59,71],"MAX-ACD":[60,75],"),":[61],"called":[62],"Clean":[66],"Balanced":[67],"MAX-ACBCD":[72,101,137,208],").":[73],"The":[74,100],"closely":[78],"related":[79,106],"some":[81],"problems,":[83,108],"where":[84,157,197,274],"orientation":[86,159,199],"genes":[89,94,111,162,202],"unknown,":[91,204],"all":[93],"common":[96],"both":[98,121],"genomes.":[99,150],"has":[103],"applications":[104],"which":[109],"allow":[110],"present":[112,128],"in":[113],"only":[114],"one":[115],"genomes":[118],"consider":[120],"order":[123],"intergenic-region":[125],"information.":[126],"We":[127],"constant-factor":[130],"approximation":[131,182,212,246],"heuristic":[134,145],"problem,":[138,209],"we":[140,165,210],"performed":[141],"tests":[142],"with":[143,245],"applied":[146],"artificially":[148],"generated":[149],"Considering":[151],"intergenic":[152],"regions":[153],"scenario":[156,196],"known,":[164],"design":[166],"an":[167,181],"improved":[168],"algorithm":[169],"Sorting":[172,216,220,233,238],"by":[173,217,221,234,239],"Reversals":[174,222],"Intergenic":[176,224,242],"Indels":[177,243],"that":[179],"guarantees":[180],"factor":[183],"$$\\frac{3}{2}$$":[185],"<mml:math":[186,253,277],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">":[187,254,278],"<mml:mfrac>":[188,255,282],"<mml:mn>3</mml:mn>":[189,257],"<mml:mn>2</mml:mn>":[190,260],"</mml:mfrac>":[191,261,285],"</mml:math>":[192,262,289],".":[193,290],"For":[194],"using":[206],"develop":[211],"algorithms":[213],"Reversals,":[218],"Indels,":[225],"Reversal,":[227],"Transposition":[228],"Indel":[230],"Distance,":[231],"DCJ,":[235],"DCJ":[240],"problems":[244],"factors":[247],"2":[249,267],"k":[250,265,268,271],",":[251,263,266,269,272],"$$\\frac{3k}{2}$$":[252],"<mml:mrow>":[256,279],"<mml:mi>k</mml:mi>":[258,280],"</mml:mrow>":[259,288],"4":[264],"respectively,":[273],"$$k=\\frac{31}{21}+\\epsilon":[275],"$$":[276],"<mml:mo>=</mml:mo>":[281],"<mml:mn>31</mml:mn>":[283],"<mml:mn>21</mml:mn>":[284],"<mml:mo>+</mml:mo>":[286],"<mml:mi>\u03f5</mml:mi>":[287]},"counts_by_year":[],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2026-03-08T00:00:00"}
