{"id":"https://openalex.org/W7138832765","doi":"https://doi.org/10.7155/jgaa.v30i1.2967","title":"Largest Common Subgraph of Two Forests","display_name":"Largest Common Subgraph of Two Forests","publication_year":2026,"publication_date":"2026-03-17","ids":{"openalex":"https://openalex.org/W7138832765","doi":"https://doi.org/10.7155/jgaa.v30i1.2967"},"language":null,"primary_location":{"id":"doi:10.7155/jgaa.v30i1.2967","is_oa":true,"landing_page_url":"https://doi.org/10.7155/jgaa.v30i1.2967","pdf_url":"https://jgaa.info/index.php/jgaa/article/download/2967/3020","source":{"id":"https://openalex.org/S33451491","display_name":"Journal of Graph Algorithms and Applications","issn_l":"1526-1719","issn":["1526-1719"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"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 Graph Algorithms and Applications","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://jgaa.info/index.php/jgaa/article/download/2967/3020","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5032828042","display_name":"Dieter Rautenbach","orcid":"https://orcid.org/0000-0002-7214-042X"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Dieter Rautenbach","raw_affiliation_strings":["Ulm University"],"affiliations":[{"raw_affiliation_string":"Ulm University","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5130192509","display_name":"Florian Werner","orcid":null},"institutions":[{"id":"https://openalex.org/I196349391","display_name":"Universit\u00e4t Ulm","ror":"https://ror.org/032000t02","country_code":"DE","type":"education","lineage":["https://openalex.org/I196349391"]},{"id":"https://openalex.org/I4210163522","display_name":"Technische Hochschule Ulm","ror":"https://ror.org/05e5kd476","country_code":"DE","type":"education","lineage":["https://openalex.org/I4210163522"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Florian Werner","raw_affiliation_strings":["Institute of Optimization and Operations Research , Ulm University , Ulm , Germany"],"affiliations":[{"raw_affiliation_string":"Institute of Optimization and Operations Research , Ulm University , Ulm , Germany","institution_ids":["https://openalex.org/I4210163522","https://openalex.org/I196349391"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5032828042"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.8366886,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"30","issue":"1","first_page":"47","last_page":"63"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.37310001254081726,"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":0.37310001254081726,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.29829999804496765,"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":0.17000000178813934,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/induced-subgraph-isomorphism-problem","display_name":"Induced subgraph isomorphism problem","score":0.8604999780654907},{"id":"https://openalex.org/keywords/subgraph-isomorphism-problem","display_name":"Subgraph isomorphism problem","score":0.7882999777793884},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.5248000025749207},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.483599990606308},{"id":"https://openalex.org/keywords/isomorphism","display_name":"Isomorphism (crystallography)","score":0.4731999933719635},{"id":"https://openalex.org/keywords/induced-subgraph","display_name":"Induced subgraph","score":0.4262999892234802},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.4138000011444092},{"id":"https://openalex.org/keywords/tree","display_name":"Tree (set theory)","score":0.3734000027179718}],"concepts":[{"id":"https://openalex.org/C191241153","wikidata":"https://www.wikidata.org/wiki/Q6027240","display_name":"Induced subgraph isomorphism problem","level":5,"score":0.8604999780654907},{"id":"https://openalex.org/C131992880","wikidata":"https://www.wikidata.org/wiki/Q2528185","display_name":"Subgraph isomorphism problem","level":3,"score":0.7882999777793884},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7275999784469604},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6926000118255615},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.5248000025749207},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.483599990606308},{"id":"https://openalex.org/C203436722","wikidata":"https://www.wikidata.org/wiki/Q902950","display_name":"Isomorphism (crystallography)","level":3,"score":0.4731999933719635},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4478999972343445},{"id":"https://openalex.org/C2778012994","wikidata":"https://www.wikidata.org/wiki/Q24743362","display_name":"Induced subgraph","level":4,"score":0.4262999892234802},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.4138000011444092},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.3734000027179718},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.3546000123023987},{"id":"https://openalex.org/C128115575","wikidata":"https://www.wikidata.org/wiki/Q5597083","display_name":"Graph factorization","level":5,"score":0.3522000014781952},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.33399999141693115},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.33219999074935913},{"id":"https://openalex.org/C3018263672","wikidata":"https://www.wikidata.org/wiki/Q1296251","display_name":"Efficient algorithm","level":2,"score":0.31450000405311584},{"id":"https://openalex.org/C147792647","wikidata":"https://www.wikidata.org/wiki/Q5282847","display_name":"Distance-hereditary graph","level":5,"score":0.3009999990463257},{"id":"https://openalex.org/C59824394","wikidata":"https://www.wikidata.org/wiki/Q5141281","display_name":"Cograph","level":5,"score":0.2985999882221222},{"id":"https://openalex.org/C61665672","wikidata":"https://www.wikidata.org/wiki/Q303100","display_name":"Graph isomorphism","level":4,"score":0.2985999882221222},{"id":"https://openalex.org/C36038622","wikidata":"https://www.wikidata.org/wiki/Q5428703","display_name":"Factor-critical graph","level":5,"score":0.27320000529289246},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.27070000767707825},{"id":"https://openalex.org/C63553672","wikidata":"https://www.wikidata.org/wiki/Q581168","display_name":"Binary logarithm","level":2,"score":0.2581999897956848},{"id":"https://openalex.org/C2780451532","wikidata":"https://www.wikidata.org/wiki/Q759676","display_name":"Task (project management)","level":2,"score":0.25049999356269836}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.7155/jgaa.v30i1.2967","is_oa":true,"landing_page_url":"https://doi.org/10.7155/jgaa.v30i1.2967","pdf_url":"https://jgaa.info/index.php/jgaa/article/download/2967/3020","source":{"id":"https://openalex.org/S33451491","display_name":"Journal of Graph Algorithms and Applications","issn_l":"1526-1719","issn":["1526-1719"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"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 Graph Algorithms and Applications","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.7155/jgaa.v30i1.2967","is_oa":true,"landing_page_url":"https://doi.org/10.7155/jgaa.v30i1.2967","pdf_url":"https://jgaa.info/index.php/jgaa/article/download/2967/3020","source":{"id":"https://openalex.org/S33451491","display_name":"Journal of Graph Algorithms and Applications","issn_l":"1526-1719","issn":["1526-1719"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"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 Graph Algorithms and Applications","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.6639110445976257,"id":"https://metadata.un.org/sdg/15","display_name":"Life in Land"}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7138832765.pdf","grobid_xml":"https://content.openalex.org/works/W7138832765.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"A":[0],"common":[1,24,33,107],"subgraph":[2,25,34,108],"of":[3,17,44,69,95,110,146,157,159,170],"two":[4,36,89],"graphs":[5,38],"$G_1$":[6,18,39],"and":[7,19,40,62,93,112,167],"$G_2$":[8,41],"is":[9,13,29,43],"a":[10,32,73,106,135],"graph":[11,56],"that":[12,42,154],"isomorphic":[14],"to":[15,30,67,122],"subgraphs":[16],"$G_2$.":[20],"In":[21],"the":[22,27,54,144,147,171,174],"largest":[23],"problem":[26,52],"task":[28],"determine":[31,102],"for":[35,77,80,88,128,173],"given":[37,90,148],"maximum":[45],"possible":[46],"size":[47],"${\\rm":[48,117,125],"lcs}(G_1,G_2)$.":[49],"This":[50],"natural":[51],"generalizes":[53],"well-studied":[55],"isomorphism":[57],"problem,":[58],"has":[59],"many":[60],"applications,":[61],"remains":[63],"NP-hard":[64],"even":[65],"restricted":[66],"unions":[68],"paths.":[70],"We":[71],"present":[72],"simple":[74],"$4$-approximation":[75],"algorithm":[76],"forests,":[78],"and,":[79],"every":[81],"fixed":[82,130],"$\\epsilon\\in":[83],"(0,1)$,":[84],"we":[85],"show":[86],"that,":[87],"forests":[91,149,153],"$F_1$":[92,111],"$F_2$":[94,113],"order":[96],"at":[97,115],"most":[98],"$n$,":[99],"one":[100],"can":[101],"in":[103],"polynomial":[104,136],"time":[105,137],"$F$":[109],"with":[114,124],"least":[116],"lcs}(F_1,F_2)-\\epsilon":[118],"n$":[119],"edges.":[120],"Restricted":[121],"instances":[123],"lcs}(F_1,F_2)\\geq":[126],"cn$":[127],"some":[129],"positive":[131],"$c$,":[132],"this":[133],"yields":[134],"approximation":[138,145],"scheme.":[139],"Our":[140],"approach":[141],"relies":[142],"on":[143],"by":[150],"structurally":[151],"simpler":[152],"are":[155],"composed":[156],"copies":[158],"only":[160],"$O(\\log":[161],"(n))$":[162],"different":[163],"starlike":[164],"rooted":[165],"trees":[166],"iterative":[168],"quantizations":[169],"options":[172],"solutions.":[175]},"counts_by_year":[],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2026-03-20T00:00:00"}