{"id":"https://openalex.org/W7155031881","doi":"https://doi.org/10.48550/arxiv.2604.17461","title":"Optimal Phylogenetic Reconstruction from Sampled Quartets","display_name":"Optimal Phylogenetic Reconstruction from Sampled Quartets","publication_year":2026,"publication_date":"2026-04-19","ids":{"openalex":"https://openalex.org/W7155031881","doi":"https://doi.org/10.48550/arxiv.2604.17461"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2604.17461","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.17461","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2604.17461","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5134101654","display_name":"Dionysis Arvanitakis","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Arvanitakis, Dionysis","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5054031027","display_name":"Vaggos Chatziafratis","orcid":"https://orcid.org/0000-0002-4475-4504"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Chatziafratis, Vaggos","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5134121120","display_name":"Yiyuan Luo","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Luo, Yiyuan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5033681881","display_name":"Konstantin Makarychev","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Makarychev, Konstantin","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":4,"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/T10015","display_name":"Genomics and Phylogenetic Studies","score":0.6223000288009644,"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"}},"topics":[{"id":"https://openalex.org/T10015","display_name":"Genomics and Phylogenetic Studies","score":0.6223000288009644,"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/T13664","display_name":"Genome Rearrangement Algorithms","score":0.31029999256134033,"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/T12072","display_name":"Machine Learning and Algorithms","score":0.006899999920278788,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/tree","display_name":"Tree (set theory)","score":0.6927000284194946},{"id":"https://openalex.org/keywords/phylogenetic-tree","display_name":"Phylogenetic tree","score":0.6782000064849854},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.552299976348877},{"id":"https://openalex.org/keywords/tree-rearrangement","display_name":"Tree rearrangement","score":0.5421000123023987},{"id":"https://openalex.org/keywords/random-tree","display_name":"Random tree","score":0.4975000023841858},{"id":"https://openalex.org/keywords/k-ary-tree","display_name":"K-ary tree","score":0.44369998574256897},{"id":"https://openalex.org/keywords/embedding","display_name":"Embedding","score":0.4203000068664551},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.41780000925064087},{"id":"https://openalex.org/keywords/random-graph","display_name":"Random graph","score":0.3294999897480011}],"concepts":[{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.6927000284194946},{"id":"https://openalex.org/C193252679","wikidata":"https://www.wikidata.org/wiki/Q242125","display_name":"Phylogenetic tree","level":3,"score":0.6782000064849854},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6510999798774719},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5698999762535095},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.552299976348877},{"id":"https://openalex.org/C53208351","wikidata":"https://www.wikidata.org/wiki/Q7837630","display_name":"Tree rearrangement","level":4,"score":0.5421000123023987},{"id":"https://openalex.org/C2776839635","wikidata":"https://www.wikidata.org/wiki/Q14942679","display_name":"Random tree","level":4,"score":0.4975000023841858},{"id":"https://openalex.org/C100560664","wikidata":"https://www.wikidata.org/wiki/Q3608019","display_name":"K-ary tree","level":4,"score":0.44369998574256897},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.435699999332428},{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.4203000068664551},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.41780000925064087},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3443000018596649},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.33250001072883606},{"id":"https://openalex.org/C47458327","wikidata":"https://www.wikidata.org/wiki/Q910404","display_name":"Random graph","level":3,"score":0.3294999897480011},{"id":"https://openalex.org/C84927040","wikidata":"https://www.wikidata.org/wiki/Q6057306","display_name":"Interval tree","level":4,"score":0.32580000162124634},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.3249000012874603},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.31779998540878296},{"id":"https://openalex.org/C198531522","wikidata":"https://www.wikidata.org/wiki/Q485146","display_name":"Sample (material)","level":2,"score":0.31209999322891235},{"id":"https://openalex.org/C55919133","wikidata":"https://www.wikidata.org/wiki/Q7644297","display_name":"Supertree","level":4,"score":0.3061999976634979},{"id":"https://openalex.org/C41168302","wikidata":"https://www.wikidata.org/wiki/Q3772859","display_name":"Computational phylogenetics","level":5,"score":0.30300000309944153},{"id":"https://openalex.org/C207024777","wikidata":"https://www.wikidata.org/wiki/Q621673","display_name":"Search tree","level":3,"score":0.3003999888896942},{"id":"https://openalex.org/C2778445095","wikidata":"https://www.wikidata.org/wiki/Q18354077","display_name":"Sample complexity","level":2,"score":0.2913999855518341},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.28929999470710754},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.28110000491142273},{"id":"https://openalex.org/C2780451532","wikidata":"https://www.wikidata.org/wiki/Q759676","display_name":"Task (project management)","level":2,"score":0.2678000032901764},{"id":"https://openalex.org/C11829167","wikidata":"https://www.wikidata.org/wiki/Q751292","display_name":"Random binary tree","level":3,"score":0.25940001010894775},{"id":"https://openalex.org/C163797641","wikidata":"https://www.wikidata.org/wiki/Q2067937","display_name":"Tree structure","level":3,"score":0.2590999901294708},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.2533999979496002},{"id":"https://openalex.org/C88230418","wikidata":"https://www.wikidata.org/wiki/Q131476","display_name":"Graph theory","level":2,"score":0.25200000405311584}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2604.17461","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.17461","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2604.17461","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.17461","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Quartet":[0],"Reconstruction,":[1],"the":[2,76,82,93,136,166,174,221,252],"task":[3],"of":[4,67,85,161,224,228],"recovering":[5],"a":[6,18,35,56,87,158,191,199,205,216,238],"phylogenetic":[7,154],"tree":[8,47,57,88,155,182,192,206],"from":[9,119,157,251],"smaller":[10],"trees":[11],"on":[12,49,220,237],"four":[13],"species":[14],"called":[15],"\\textit{quartets},":[16],"is":[17,61,141,186],"well-studied":[19],"problem":[20,84],"in":[21,65,99,210,231],"theoretical":[22],"computer":[23],"science":[24],"with":[25,92,109],"far-reaching":[26],"connections":[27],"to":[28,54,63,81,122,134,208],"statistics,":[29],"graph":[30],"theory":[31],"and":[32,70,96,138,242,247],"biology.":[33],"Given":[34],"random":[36,159],"sample":[37,160],"containing":[38],"$m$":[39],"noisy":[40],"quartets,":[41,95,111,163],"labeled":[42],"by":[43],"an":[44,142,152],"unknown":[45,127,153],"ground-truth":[46,254],"$T$":[48,64,156,209,255],"$n$":[50],"taxa,":[51],"we":[52,189,214],"want":[53],"output":[55],"$\\widehat":[58],"T$":[59],"that":[60,89,245],"\\textit{close}":[62],"terms":[66],"quartet":[68,211],"distance":[69],"can":[71],"predict":[72],"unseen":[73],"quartets.":[74],"Unfortunately,":[75],"empirical":[77],"risk":[78],"minimizer":[79],"corresponds":[80],"$\\mathsf{NP}$-hard":[83],"finding":[86],"maximizes":[90],"agreements":[91],"sampled":[94,118],"earlier":[97],"works":[98],"approximation":[100],"algorithms":[101],"gave":[102],"$(1-\\eps)$-approximation":[103],"schemes":[104],"(PTAS)":[105],"for":[106,113,150,179],"dense":[107],"instances":[108],"$m=\u0398(n^4)$":[110],"or":[112],"$m=\u0398(n^2\\log":[114],"n)$":[115],"quartets":[116],"\\textit{randomly}":[117],"$T$.":[120],"Prior":[121],"our":[123],"work,":[124],"it":[125],"was":[126],"how":[128],"many":[129],"samples":[130],"are":[131],"information-theoretically":[132],"required":[133,178],"learn":[135],"tree,":[137],"whether":[139],"there":[140],"efficient":[143],"reconstruction":[144,193],"algorithm.":[145],"We":[146],"present":[147],"optimal":[148],"results":[149],"reconstructing":[151],"$m=\u0398(n)$":[162],"corrupted":[164],"under":[165],"Random":[167],"Classification":[168],"Noise":[169],"(RCN)":[170],"model.":[171],"This":[172],"matches":[173],"$\u03a9(n)$":[175],"lower":[176],"bound":[177,219],"any":[180],"meaningful":[181],"reconstruction.":[183],"Our":[184,234],"contribution":[185],"twofold:":[187],"first,":[188],"give":[190],"algorithm":[194],"that,":[195],"not":[196],"only":[197],"achieves":[198],"$(1-\\eps)$-approximation,":[200],"but":[201],"most":[202],"importantly":[203],"\\textit{recovers}":[204],"close":[207],"distance;":[212],"second,":[213],"show":[215],"new":[217,239],"$\u0398(n)$":[218],"Natarajan":[222],"dimension":[223,230],"phylogenies":[225],"(an":[226],"analog":[227],"VC":[229],"multiclass":[232],"classification).":[233],"analysis":[235],"relies":[236],"\\textit{Quartet-based":[240],"Embedding":[241],"Detection}":[243],"procedure":[244],"identifies":[246],"removes":[248],"well-clustered":[249],"subtrees":[250],"(unknown)":[253],"via":[256],"semidefinite":[257],"programming.":[258]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2026-04-22T00:00:00"}