{"id":"https://openalex.org/W2046167819","doi":"https://doi.org/10.1137/130941043","title":"On the Compatibility of Quartet Trees","display_name":"On the Compatibility of Quartet Trees","publication_year":2014,"publication_date":"2014-01-01","ids":{"openalex":"https://openalex.org/W2046167819","doi":"https://doi.org/10.1137/130941043","mag":"2046167819"},"language":"en","primary_location":{"id":"doi:10.1137/130941043","is_oa":false,"landing_page_url":"https://doi.org/10.1137/130941043","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","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/A5083469386","display_name":"Noga Alon","orcid":"https://orcid.org/0000-0003-1332-4883"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Noga Alon","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5063493591","display_name":"Sagi Snir","orcid":"https://orcid.org/0000-0001-5833-7659"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Sagi Snir","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5026016357","display_name":"Raphael Yuster","orcid":"https://orcid.org/0000-0001-7550-6506"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Raphael Yuster","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5083469386"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.4671,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.71296675,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"28","issue":"3","first_page":"1493","last_page":"1507"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T13664","display_name":"Genome Rearrangement Algorithms","score":0.9815000295639038,"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":0.9815000295639038,"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":0.9740999937057495,"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/T11269","display_name":"Algorithms and Data Compression","score":0.9258000254631042,"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/mathematics","display_name":"Mathematics","score":0.779045820236206},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.736279308795929},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.6383166909217834},{"id":"https://openalex.org/keywords/phylogenetic-tree","display_name":"Phylogenetic tree","score":0.6182011961936951},{"id":"https://openalex.org/keywords/cardinality","display_name":"Cardinality (data modeling)","score":0.5678879022598267},{"id":"https://openalex.org/keywords/compatibility","display_name":"Compatibility (geochemistry)","score":0.4839930534362793},{"id":"https://openalex.org/keywords/probabilistic-logic","display_name":"Probabilistic logic","score":0.4826089143753052},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4308148920536041},{"id":"https://openalex.org/keywords/tree","display_name":"Tree (set theory)","score":0.4190105199813843},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.15439042448997498},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.1070837676525116},{"id":"https://openalex.org/keywords/biology","display_name":"Biology","score":0.06686744093894958},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.061961591243743896}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.779045820236206},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.736279308795929},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.6383166909217834},{"id":"https://openalex.org/C193252679","wikidata":"https://www.wikidata.org/wiki/Q242125","display_name":"Phylogenetic tree","level":3,"score":0.6182011961936951},{"id":"https://openalex.org/C87117476","wikidata":"https://www.wikidata.org/wiki/Q362383","display_name":"Cardinality (data modeling)","level":2,"score":0.5678879022598267},{"id":"https://openalex.org/C2778648169","wikidata":"https://www.wikidata.org/wiki/Q967768","display_name":"Compatibility (geochemistry)","level":2,"score":0.4839930534362793},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.4826089143753052},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4308148920536041},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.4190105199813843},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.15439042448997498},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.1070837676525116},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.06686744093894958},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.061961591243743896},{"id":"https://openalex.org/C17409809","wikidata":"https://www.wikidata.org/wiki/Q161764","display_name":"Geochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C127313418","wikidata":"https://www.wikidata.org/wiki/Q1069","display_name":"Geology","level":0,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/130941043","is_oa":false,"landing_page_url":"https://doi.org/10.1137/130941043","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.643.8638","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.643.8638","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.tau.ac.il/~nogaa/PDFS/subsetcomp2.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.724.6037","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.724.6037","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://research.haifa.ac.il/%7Essagi/published%20papers/subsetcomp-SODA-final.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.5799999833106995,"id":"https://metadata.un.org/sdg/15","display_name":"Life in Land"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W160062981","https://openalex.org/W1970170219","https://openalex.org/W1971820137","https://openalex.org/W1972805029","https://openalex.org/W1977694535","https://openalex.org/W1995615099","https://openalex.org/W2009661773","https://openalex.org/W2026340248","https://openalex.org/W2031620310","https://openalex.org/W2037055526","https://openalex.org/W2037749900","https://openalex.org/W2042959539","https://openalex.org/W2045875391","https://openalex.org/W2053552499","https://openalex.org/W2060425093","https://openalex.org/W2063021676","https://openalex.org/W2066327035","https://openalex.org/W2075503802","https://openalex.org/W2081804360","https://openalex.org/W2083229322","https://openalex.org/W2083497080","https://openalex.org/W2109596230","https://openalex.org/W2150911766","https://openalex.org/W2164997158"],"related_works":["https://openalex.org/W2002177687","https://openalex.org/W2390255551","https://openalex.org/W2367511445","https://openalex.org/W2381930792","https://openalex.org/W2058438338","https://openalex.org/W2358901819","https://openalex.org/W745733672","https://openalex.org/W2019471580","https://openalex.org/W2983545107","https://openalex.org/W2615250133"],"abstract_inverted_index":{"Phylogenetic":[0],"tree":[1,25],"reconstruction":[2],"is":[3,39,113,125,140,180],"a":[4,70],"fundamental":[5],"biological":[6],"problem.":[7],"Quartet":[8],"trees,":[9],"trees":[10],"over":[11,26],"four":[12],"species,":[13],"are":[14,93,168],"the":[15,49,59,67,84,128,134,141,148,187,194],"minimal":[16],"informational":[17],"unit":[18],"for":[19,163,172,207],"phylogenetic":[20,24,43],"classification.":[21],"While":[22],"every":[23,35,105,174],"$n$":[27],"species":[28],"defines":[29],"${n":[30],"\\choose":[31,145,165],"4}$":[32,146],"quartets,":[33],"not":[34],"set":[36,71,152],"of":[37,51,61,69,76,97,107,119,123,150,153,176,189],"quartets":[38,155],"compatible":[40],"with":[41],"some":[42],"tree.":[44],"Here":[45],"we":[46,89,159],"focus":[47],"on":[48],"compatibility":[50,68,149],"quartet":[52,94,196],"sets.":[53],"We":[54,200],"provide":[55,201],"several":[56],"results":[57,78],"addressing":[58],"question":[60],"what":[62],"can":[63],"be":[64],"inferred":[65],"about":[66],"from":[72],"its":[73],"subsets.":[74],"Most":[75],"our":[77],"use":[79],"probabilistic":[80],"arguments":[81],"to":[82,133,186],"prove":[83],"sought":[85],"characteristics.":[86],"In":[87],"particular":[88],"show":[90,160],"that":[91,161],"there":[92,167],"sets":[95,171],"$Q$":[96,124,139],"size":[98],"$m=c":[99],"n":[100],"\\log":[101,111],"n$":[102,112],"in":[103,131],"which":[104,173],"subset":[106,175],"cardinality":[108,179],"$c'":[109],"n/":[110],"compatible,":[114],"and":[115,147,191,204],"yet":[116],"no":[117],"fraction":[118],"more":[120],"than":[121],"$1/3+\\epsilon$":[122],"compatible.":[126,181],"On":[127],"other":[129],"hand,":[130],"contrast":[132],"classical":[135],"result":[136,184],"stating":[137],"when":[138],"densest,":[142],"i.e.,":[143],"$m={n":[144],"any":[151],"three":[154],"implies":[156],"full":[157],"compatibility,":[158],"even":[162],"$m=\\Theta\\big({n":[164],"4}\\big)$":[166],"(very)":[169],"incompatible":[170],"large":[177],"constant":[178],"Our":[182],"final":[183],"relates":[185],"conjecture":[188],"Bandelt":[190],"Dress":[192],"regarding":[193],"maximum":[195],"distance":[197],"between":[198],"trees.":[199],"asymptotic":[202],"upper":[203],"lower":[205],"bounds":[206],"this":[208],"value.":[209]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}