{"id":"https://openalex.org/W7153098510","doi":"https://doi.org/10.48550/arxiv.2604.08071","title":"Identifying bubble-like subgraphs in linear-time via a unified SPQR-tree framework","display_name":"Identifying bubble-like subgraphs in linear-time via a unified SPQR-tree framework","publication_year":2026,"publication_date":"2026-04-09","ids":{"openalex":"https://openalex.org/W7153098510","doi":"https://doi.org/10.48550/arxiv.2604.08071"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2604.08071","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.08071","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2604.08071","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5133375296","display_name":"Francisco Sena","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Sena, Francisco","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5026524868","display_name":"Aleksandr P. Politov","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Politov, Aleksandr","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5132621490","display_name":"Corentin Moumard","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Moumard, Corentin","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5007584366","display_name":"Massimo Cairo","orcid":"https://orcid.org/0000-0001-7247-756X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Cairo, Massimo","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5061874157","display_name":"Rom\u00e9o Rizzi","orcid":"https://orcid.org/0000-0002-2387-0952"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Rizzi, Romeo","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5064412838","display_name":"Manuel C\u00e1ceres","orcid":"https://orcid.org/0000-0003-0235-6951"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"C\u00e1ceres, Manuel","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5133316242","display_name":"Sebastian Schmidt","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Schmidt, Sebastian","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5002420527","display_name":"Juha Harviainen","orcid":"https://orcid.org/0000-0002-4581-840X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Harviainen, Juha","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5063897224","display_name":"Alexandru I. Tomescu","orcid":"https://orcid.org/0000-0002-5747-8350"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Tomescu, Alexandru I.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"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":0.6366000175476074,"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":0.6366000175476074,"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/T10015","display_name":"Genomics and Phylogenetic Studies","score":0.11540000140666962,"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"}},{"id":"https://openalex.org/T10222","display_name":"Genomics and Chromatin Dynamics","score":0.053199999034404755,"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/representation","display_name":"Representation (politics)","score":0.45350000262260437},{"id":"https://openalex.org/keywords/directed-acyclic-graph","display_name":"Directed acyclic graph","score":0.41760000586509705},{"id":"https://openalex.org/keywords/computational-complexity-theory","display_name":"Computational complexity theory","score":0.41429999470710754},{"id":"https://openalex.org/keywords/key","display_name":"Key (lock)","score":0.3959999978542328},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.3840999901294708},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.3756999969482422},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.3589000105857849},{"id":"https://openalex.org/keywords/communication-complexity","display_name":"Communication complexity","score":0.3560999929904938}],"concepts":[{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.5156000256538391},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5108000040054321},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.45350000262260437},{"id":"https://openalex.org/C74197172","wikidata":"https://www.wikidata.org/wiki/Q1195339","display_name":"Directed acyclic graph","level":2,"score":0.41760000586509705},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.41429999470710754},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3971000015735626},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.3959999978542328},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.3840999901294708},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.38089999556541443},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.3756999969482422},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.3589000105857849},{"id":"https://openalex.org/C179145077","wikidata":"https://www.wikidata.org/wiki/Q5154130","display_name":"Communication complexity","level":2,"score":0.3560999929904938},{"id":"https://openalex.org/C2778334786","wikidata":"https://www.wikidata.org/wiki/Q1586270","display_name":"Variation (astronomy)","level":2,"score":0.3465999960899353},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.33640000224113464},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.3334999978542328},{"id":"https://openalex.org/C146380142","wikidata":"https://www.wikidata.org/wiki/Q1137726","display_name":"Directed graph","level":2,"score":0.32499998807907104},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3239000141620636},{"id":"https://openalex.org/C103275481","wikidata":"https://www.wikidata.org/wiki/Q6787889","display_name":"Matrix representation","level":3,"score":0.31380000710487366},{"id":"https://openalex.org/C3018263672","wikidata":"https://www.wikidata.org/wiki/Q1296251","display_name":"Efficient algorithm","level":2,"score":0.30809998512268066},{"id":"https://openalex.org/C73301696","wikidata":"https://www.wikidata.org/wiki/Q5469984","display_name":"Formalism (music)","level":3,"score":0.2824999988079071},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.2777999937534332},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.26989999413490295},{"id":"https://openalex.org/C176032523","wikidata":"https://www.wikidata.org/wiki/Q753127","display_name":"Topological sorting","level":3,"score":0.26649999618530273},{"id":"https://openalex.org/C38754835","wikidata":"https://www.wikidata.org/wiki/Q2003238","display_name":"Strongly connected component","level":2,"score":0.26570001244544983},{"id":"https://openalex.org/C88230418","wikidata":"https://www.wikidata.org/wiki/Q131476","display_name":"Graph theory","level":2,"score":0.2646999955177307},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.2623000144958496}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2604.08071","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.08071","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2604.08071","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.08071","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"A":[0,126],"fundamental":[1,167],"algorithmic":[2],"problem":[3,145],"in":[4,20,37,80,150,184,192,281],"computational":[5,256],"biology":[6,257],"is":[7,132,195],"to":[8,29,75,114,123,242,251],"find":[9],"all":[10,50,53,71,91,148,178,223],"subgraphs":[11,138],"of":[12,31,40,70,78,93,101,135,146,175,227,255,263],"a":[13,21,66,94,117,121,151,166,210,216,260,270],"given":[14,118],"type":[15],"(superbubbles,":[16],"snarls,":[17],"and":[18,34,52,239,258],"ultrabubbles)":[19],"directed":[22,152],"or":[23],"bidirected":[24,170,189],"input":[25],"graph.":[26,82,96],"These":[27],"correspond":[28],"regions":[30],"genetic":[32],"variation":[33],"are":[35,230,236],"useful":[36],"analyzing":[38],"collections":[39],"genomes.":[41],"We":[42,83],"present":[43],"the":[44,76,81,85,144,204,228,233,252],"first":[45],"linear-time":[46,130,219],"algorithms":[47],"for":[48,62,129,169,187,221,273],"identifying":[49],"snarls":[51,63,72],"ultrabubbles,":[54],"resolving":[55],"problems":[56],"open":[57],"since":[58],"2018.":[59],"The":[60],"algorithm":[61,220],"relies":[64],"on":[65],"new":[67],"linear-size":[68],"representation":[69],"with":[73],"respect":[74],"number":[77],"vertices":[79],"employ":[84],"well-known":[86],"SPQR-tree":[87,267],"decomposition,":[88],"which":[89],"encodes":[90],"2-separators":[92],"biconnected":[95],"After":[97],"several":[98],"dynamic-programming-style":[99],"traversals":[100],"this":[102,194],"tree,":[103],"we":[104,164],"maintain":[105],"key":[106],"properties":[107],"(such":[108],"as":[109,198,200,269],"acyclicity)":[110],"that":[111,133,172,213,265],"allow":[112],"us":[113],"decide":[115],"whether":[116],"2-separator":[119],"defines":[120],"subgraph":[122],"be":[124,140,174,182],"reported.":[125],"crucial":[127],"ingredient":[128],"complexity":[131],"acyclicity":[134],"linearly":[136],"many":[137],"can":[139,181],"tested":[141],"simultaneously":[142],"via":[143],"computing":[147],"arcs":[149,180],"graph":[153,282],"whose":[154],"removal":[155],"renders":[156],"it":[157],"acyclic":[158],"(so-called":[159],"feedback":[160,179],"arcs).":[161],"As":[162],"such,":[163],"prove":[165],"result":[168],"graphs,":[171,190],"may":[173,240],"independent":[176],"interest:":[177],"computed":[183],"linear":[185],"time":[186],"tipless":[188],"while":[191],"general":[193,271],"at":[196],"least":[197],"hard":[199],"matrix":[201],"multiplication,":[202],"assuming":[203],"k-Clique":[205],"Conjecture.":[206],"Our":[207],"results":[208,229],"form":[209],"unified":[211],"framework":[212],"also":[214],"yields":[215],"completely":[217],"different":[218],"finding":[222],"superbubbles.":[224],"Although":[225],"some":[226],"technically":[231],"involved,":[232],"underlying":[234],"ideas":[235],"conceptually":[237],"simple,":[238],"extend":[241],"other":[243],"bubble-like":[244],"subgraphs.":[245],"More":[246],"broadly,":[247],"our":[248],"work":[249],"contributes":[250],"theoretical":[253],"foundations":[254],"advances":[259],"growing":[261],"line":[262],"research":[264],"uses":[266],"decompositions":[268],"tool":[272],"designing":[274],"efficient":[275],"algorithms,":[276],"beyond":[277],"their":[278],"traditional":[279],"role":[280],"drawing.":[283]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2026-04-11T00:00:00"}
