{"id":"https://openalex.org/W3088209886","doi":"https://doi.org/10.1137/19m1297403","title":"A Structure Theorem for Rooted Binary Phylogenetic Networks and Its Implications for Tree-Based Networks","display_name":"A Structure Theorem for Rooted Binary Phylogenetic Networks and Its Implications for Tree-Based Networks","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W3088209886","doi":"https://doi.org/10.1137/19m1297403","mag":"3088209886"},"language":"en","primary_location":{"id":"doi:10.1137/19m1297403","is_oa":true,"landing_page_url":"https://doi.org/10.1137/19m1297403","pdf_url":"https://epubs.siam.org/doi/pdf/10.1137/19M1297403","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://epubs.siam.org/doi/pdf/10.1137/19M1297403","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5074697331","display_name":"Momoko Hayamizu","orcid":"https://orcid.org/0000-0001-8825-6331"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Momoko Hayamizu","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5074697331"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.4787,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.77372401,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"35","issue":"4","first_page":"2490","last_page":"2516"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11354","display_name":"Evolution and Paleontology Studies","score":0.996999979019165,"subfield":{"id":"https://openalex.org/subfields/1911","display_name":"Paleontology"},"field":{"id":"https://openalex.org/fields/19","display_name":"Earth and Planetary Sciences"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11354","display_name":"Evolution and Paleontology Studies","score":0.996999979019165,"subfield":{"id":"https://openalex.org/subfields/1911","display_name":"Paleontology"},"field":{"id":"https://openalex.org/fields/19","display_name":"Earth and Planetary Sciences"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10015","display_name":"Genomics and Phylogenetic Studies","score":0.9939000010490417,"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/T10012","display_name":"Genetic diversity and population structure","score":0.9818999767303467,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/subdivision","display_name":"Subdivision","score":0.8539076447486877},{"id":"https://openalex.org/keywords/phylogenetic-tree","display_name":"Phylogenetic tree","score":0.6709492206573486},{"id":"https://openalex.org/keywords/tree","display_name":"Tree (set theory)","score":0.6102284789085388},{"id":"https://openalex.org/keywords/binary-tree","display_name":"Binary tree","score":0.6013663411140442},{"id":"https://openalex.org/keywords/phylogenetic-network","display_name":"Phylogenetic network","score":0.5928889513015747},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5574039816856384},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5246745944023132},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.4687122702598572},{"id":"https://openalex.org/keywords/k-ary-tree","display_name":"K-ary tree","score":0.4371616840362549},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.4361857771873474},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3916751742362976},{"id":"https://openalex.org/keywords/tree-structure","display_name":"Tree structure","score":0.3742978572845459},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.36625567078590393},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3501433730125427},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3430001735687256},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.33557558059692383},{"id":"https://openalex.org/keywords/geography","display_name":"Geography","score":0.09315738081932068}],"concepts":[{"id":"https://openalex.org/C143392562","wikidata":"https://www.wikidata.org/wiki/Q449111","display_name":"Subdivision","level":2,"score":0.8539076447486877},{"id":"https://openalex.org/C193252679","wikidata":"https://www.wikidata.org/wiki/Q242125","display_name":"Phylogenetic tree","level":3,"score":0.6709492206573486},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.6102284789085388},{"id":"https://openalex.org/C197855036","wikidata":"https://www.wikidata.org/wiki/Q380172","display_name":"Binary tree","level":2,"score":0.6013663411140442},{"id":"https://openalex.org/C26619641","wikidata":"https://www.wikidata.org/wiki/Q3142246","display_name":"Phylogenetic network","level":4,"score":0.5928889513015747},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5574039816856384},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5246745944023132},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.4687122702598572},{"id":"https://openalex.org/C100560664","wikidata":"https://www.wikidata.org/wiki/Q3608019","display_name":"K-ary tree","level":4,"score":0.4371616840362549},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.4361857771873474},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3916751742362976},{"id":"https://openalex.org/C163797641","wikidata":"https://www.wikidata.org/wiki/Q2067937","display_name":"Tree structure","level":3,"score":0.3742978572845459},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.36625567078590393},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3501433730125427},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3430001735687256},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.33557558059692383},{"id":"https://openalex.org/C205649164","wikidata":"https://www.wikidata.org/wiki/Q1071","display_name":"Geography","level":0,"score":0.09315738081932068},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"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/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C166957645","wikidata":"https://www.wikidata.org/wiki/Q23498","display_name":"Archaeology","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/19m1297403","is_oa":true,"landing_page_url":"https://doi.org/10.1137/19m1297403","pdf_url":"https://epubs.siam.org/doi/pdf/10.1137/19M1297403","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1811.05849","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1811.05849","pdf_url":"https://arxiv.org/pdf/1811.05849","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"mag:3088209886","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1811.05849v4","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.1811.05849","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1811.05849","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:10.1137/19m1297403","is_oa":true,"landing_page_url":"https://doi.org/10.1137/19m1297403","pdf_url":"https://epubs.siam.org/doi/pdf/10.1137/19M1297403","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G5480257718","display_name":null,"funder_award_id":"JPMJPR16EB","funder_id":"https://openalex.org/F4320338111","funder_display_name":"Precursory Research for Embryonic Science and Technology"},{"id":"https://openalex.org/G6441459165","display_name":null,"funder_award_id":"JPMJPR1929","funder_id":"https://openalex.org/F4320338111","funder_display_name":"Precursory Research for Embryonic Science and Technology"}],"funders":[{"id":"https://openalex.org/F4320338111","display_name":"Precursory Research for Embryonic Science and Technology","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3088209886.pdf","grobid_xml":"https://content.openalex.org/works/W3088209886.grobid-xml"},"referenced_works_count":25,"referenced_works":["https://openalex.org/W1536830218","https://openalex.org/W2005892692","https://openalex.org/W2007940874","https://openalex.org/W2055298722","https://openalex.org/W2062269505","https://openalex.org/W2100152398","https://openalex.org/W2112400707","https://openalex.org/W2115826669","https://openalex.org/W2127964182","https://openalex.org/W2157529519","https://openalex.org/W2259163152","https://openalex.org/W2259553647","https://openalex.org/W2266356354","https://openalex.org/W2294772499","https://openalex.org/W2530251111","https://openalex.org/W2607237371","https://openalex.org/W2775777653","https://openalex.org/W2890390314","https://openalex.org/W2897014278","https://openalex.org/W2963197845","https://openalex.org/W2963852331","https://openalex.org/W2964058114","https://openalex.org/W2964163957","https://openalex.org/W3000744837","https://openalex.org/W3130461072"],"related_works":["https://openalex.org/W2911964621","https://openalex.org/W2890390314","https://openalex.org/W2765484734","https://openalex.org/W2942410761","https://openalex.org/W1720643834","https://openalex.org/W2785801105","https://openalex.org/W3106915313","https://openalex.org/W2980045187","https://openalex.org/W2914009758","https://openalex.org/W2258607074","https://openalex.org/W2564532582","https://openalex.org/W3184756267","https://openalex.org/W2951063089","https://openalex.org/W2951025023","https://openalex.org/W3199950031","https://openalex.org/W2405727068","https://openalex.org/W2127964182","https://openalex.org/W2208195214","https://openalex.org/W2323107696","https://openalex.org/W2206773845"],"abstract_inverted_index":{"Attempting":[0],"to":[1,53,110,130,234],"recognize":[2],"a":[3,6,10,29,33,68,80,103,108,143,147,165,180,193,231,238,280,285,299],"tree":[4,31,195,233,283],"inside":[5],"phylogenetic":[7,23,116,183,305],"network":[8,117,184],"is":[9,48],"fundamental":[11],"undertaking":[12],"in":[13,139,146,248,292],"evolutionary":[14],"analysis.":[15],"In":[16,63],"the":[17,43,86,132,140,151,160,176,205,214,277],"last":[18],"few":[19],"years,":[20],"therefore,":[21],"tree-based":[22,286],"networks,":[24],"which":[25],"are":[26,59,124,246],"defined":[27],"by":[28,97],"spanning":[30],"called":[32],"subdivision":[34,135,194,217,224,232],"tree,":[35],"have":[36],"attracted":[37],"attention":[38],"of":[39,45,88,134,137,142,150,167,207,216,219,226,250,279,302],"theoretical":[40],"biologists.":[41],"However,":[42],"application":[44],"such":[46,275],"networks":[47],"still":[49,295],"not":[50,60,190,256],"easy,":[51],"due":[52],"many":[54,267],"problems":[55,78],"whose":[56],"time":[57,169,172,251],"complexities":[58],"clearly":[61],"understood.":[62],"this":[64,293],"paper,":[65],"we":[66,101,163],"provide":[67],"general":[69],"framework":[70],"for":[71,154,175,298],"solving":[72],"those":[73],"various":[74,261],"old":[75],"or":[76,92,189,236],"new":[77],"from":[79,209],"coherent":[81],"perspective,":[82],"rather":[83],"than":[84],"analyzing":[85],"complexity":[87],"each":[89],"individual":[90],"problem":[91],"developing":[93],"an":[94],"algorithm":[95],"one":[96,198],"one.":[98],"More":[99],"precisely,":[100],"establish":[102],"structure":[104,152],"theorem":[105,153],"that":[106,123],"gives":[107],"way":[109,148],"canonically":[111],"decompose":[112],"any":[113],"rooted":[114,181,303],"binary":[115,182],"N":[118,138,191,208],"into":[119],"maximal":[120],"zig-zag":[121],"trails":[122],"uniquely":[125],"determined,":[126],"and":[127,170,196,228,259,270,290],"use":[128],"it":[129],"characterize":[131],"set":[133],"trees":[136,218,225],"form":[141],"direct":[144],"product,":[145],"reminiscent":[149],"finitely":[155],"generated":[156],"Abelian":[157],"groups.":[158],"From":[159],"main":[161],"results,":[162,263],"derive":[164],"series":[166],"linear":[168,171],"delay":[173],"algorithms":[174,243,291],"following":[177],"problems:":[178],"given":[179],"N,":[185],"1)":[186],"determine":[187],"whether":[188],"has":[192],"find":[197,230],"if":[199],"there":[200],"exists":[201],"any;":[202],"2)":[203],"measure":[204],"deviation":[206],"being":[210],"tree-based;":[211],"3)":[212],"compute":[213],"number":[215],"N;":[220,227],"4)":[221],"list":[222],"all":[223],"5)":[229],"maximize":[235],"minimize":[237],"prescribed":[239],"objective":[240],"function.":[241],"All":[242],"proposed":[244],"here":[245],"optimal":[247],"terms":[249],"complexity.":[252],"Our":[253],"results":[254,289],"do":[255],"only":[257],"imply":[258],"unify":[260],"known":[262],"but":[264],"also":[265],"answer":[266],"open":[268],"questions":[269],"moreover":[271],"enable":[272],"novel":[273],"applications,":[274],"as":[276],"estimation":[278],"maximum":[281],"likelihood":[282],"underlying":[284],"network.":[287],"The":[288],"paper":[294],"hold":[296],"true":[297],"special":[300],"class":[301],"non-binary":[304],"networks.":[306]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1}],"updated_date":"2026-04-09T08:11:56.329763","created_date":"2025-10-10T00:00:00"}