{"id":"https://openalex.org/W2089920149","doi":"https://doi.org/10.1137/0218060","title":"Ranking the Best Binary Trees","display_name":"Ranking the Best Binary Trees","publication_year":1989,"publication_date":"1989-10-01","ids":{"openalex":"https://openalex.org/W2089920149","doi":"https://doi.org/10.1137/0218060","mag":"2089920149"},"language":"en","primary_location":{"id":"doi:10.1137/0218060","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0218060","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"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 Computing","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/A5037889951","display_name":"Shoshana Anily","orcid":"https://orcid.org/0000-0001-8527-1659"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"S. Anily","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5022008503","display_name":"Refael Hassin","orcid":"https://orcid.org/0000-0001-9631-6162"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"R. Hassin","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5037889951"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.4681,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.64901551,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"18","issue":"5","first_page":"882","last_page":"892"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9972000122070312,"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":0.9972000122070312,"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/T11269","display_name":"Algorithms and Data Compression","score":0.9955000281333923,"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"}},{"id":"https://openalex.org/T11106","display_name":"Data Management and Algorithms","score":0.9919000267982483,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/weight-balanced-tree","display_name":"Weight-balanced tree","score":0.7844496965408325},{"id":"https://openalex.org/keywords/ranking","display_name":"Ranking (information retrieval)","score":0.7378847599029541},{"id":"https://openalex.org/keywords/binary-tree","display_name":"Binary tree","score":0.7165468335151672},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6985965967178345},{"id":"https://openalex.org/keywords/random-binary-tree","display_name":"Random binary tree","score":0.6454606652259827},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6372146606445312},{"id":"https://openalex.org/keywords/tree","display_name":"Tree (set theory)","score":0.5385532975196838},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.5368068814277649},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.5368016362190247},{"id":"https://openalex.org/keywords/binary-search-tree","display_name":"Binary search tree","score":0.5149189233779907},{"id":"https://openalex.org/keywords/ternary-search-tree","display_name":"Ternary search tree","score":0.5128112435340881},{"id":"https://openalex.org/keywords/optimal-binary-search-tree","display_name":"Optimal binary search tree","score":0.49944114685058594},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.47768455743789673},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.4701423943042755},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3695628046989441},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.36919891834259033},{"id":"https://openalex.org/keywords/k-ary-tree","display_name":"K-ary tree","score":0.2957860231399536},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.24332767724990845},{"id":"https://openalex.org/keywords/interval-tree","display_name":"Interval tree","score":0.22919419407844543},{"id":"https://openalex.org/keywords/tree-structure","display_name":"Tree structure","score":0.20551317930221558},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.1448349952697754},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.12064212560653687},{"id":"https://openalex.org/keywords/biology","display_name":"Biology","score":0.07369136810302734}],"concepts":[{"id":"https://openalex.org/C57900377","wikidata":"https://www.wikidata.org/wiki/Q7979855","display_name":"Weight-balanced tree","level":4,"score":0.7844496965408325},{"id":"https://openalex.org/C189430467","wikidata":"https://www.wikidata.org/wiki/Q7293293","display_name":"Ranking (information retrieval)","level":2,"score":0.7378847599029541},{"id":"https://openalex.org/C197855036","wikidata":"https://www.wikidata.org/wiki/Q380172","display_name":"Binary tree","level":2,"score":0.7165468335151672},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6985965967178345},{"id":"https://openalex.org/C11829167","wikidata":"https://www.wikidata.org/wiki/Q751292","display_name":"Random binary tree","level":3,"score":0.6454606652259827},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6372146606445312},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.5385532975196838},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.5368068814277649},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.5368016362190247},{"id":"https://openalex.org/C91154448","wikidata":"https://www.wikidata.org/wiki/Q623818","display_name":"Binary search tree","level":3,"score":0.5149189233779907},{"id":"https://openalex.org/C136519935","wikidata":"https://www.wikidata.org/wiki/Q2859802","display_name":"Ternary search tree","level":5,"score":0.5128112435340881},{"id":"https://openalex.org/C27628562","wikidata":"https://www.wikidata.org/wiki/Q17154715","display_name":"Optimal binary search tree","level":5,"score":0.49944114685058594},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.47768455743789673},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4701423943042755},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3695628046989441},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.36919891834259033},{"id":"https://openalex.org/C100560664","wikidata":"https://www.wikidata.org/wiki/Q3608019","display_name":"K-ary tree","level":4,"score":0.2957860231399536},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.24332767724990845},{"id":"https://openalex.org/C84927040","wikidata":"https://www.wikidata.org/wiki/Q6057306","display_name":"Interval tree","level":4,"score":0.22919419407844543},{"id":"https://openalex.org/C163797641","wikidata":"https://www.wikidata.org/wiki/Q2067937","display_name":"Tree structure","level":3,"score":0.20551317930221558},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.1448349952697754},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.12064212560653687},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.07369136810302734},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/0218060","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0218060","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"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 Computing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W1969791744","https://openalex.org/W1984407615","https://openalex.org/W2009938762","https://openalex.org/W2011087880","https://openalex.org/W2039339864","https://openalex.org/W2041809674","https://openalex.org/W2060108852","https://openalex.org/W2065954102","https://openalex.org/W2070330498","https://openalex.org/W2078948975","https://openalex.org/W2091507391","https://openalex.org/W2116064088","https://openalex.org/W2125690626","https://openalex.org/W2126711987","https://openalex.org/W2144050074"],"related_works":["https://openalex.org/W270522628","https://openalex.org/W2072924299","https://openalex.org/W2038309235","https://openalex.org/W1973074590","https://openalex.org/W2077383771","https://openalex.org/W2149064492","https://openalex.org/W2146997899","https://openalex.org/W2364382882","https://openalex.org/W2091985989","https://openalex.org/W2501849745"],"abstract_inverted_index":{"The":[0],"problem":[1],"of":[2,25,42,76,92,110],"ranking":[3,67,85],"the":[4,19,23,26,29,40,43,46,58,68,98],"K-best":[5,69],"binary":[6],"trees":[7,70,82],"with":[8],"respect":[9],"to":[10],"their":[11],"weighted":[12],"average":[13],"leaves\u2019":[14],"levels":[15],"is":[16,53,64,95],"considered.":[17],"Both":[18],"alphabetic":[20,59],"case,":[21,48],"where":[22,49],"order":[24],"weights":[27],"in":[28,39],"sequence":[30],"$w_1":[31],",":[32],"\\cdots":[33],",w_n":[34],"$":[35],"must":[36],"be":[37,103],"preserved":[38],"leaves":[41],"tree,":[44],"and":[45,89],"nonalphabetic":[47,81],"no":[50],"such":[51],"restriction":[52],"imposed,":[54],"are":[55,87],"studied.":[56],"For":[57,80],"case":[60],"a":[61,73,106],"simple":[62],"algorithm":[63],"provided":[65],"for":[66,90],"based":[71],"on":[72],"recursive":[74],"formula":[75,109],"complexity":[77,112],"$O(Kn^3":[78],")$.":[79],"two":[83],"different":[84],"problems":[86],"considered,":[88],"each":[91],"them":[93],"it":[94],"shown":[96],"that":[97],"next":[99],"best":[100],"tree":[101],"can":[102],"solved":[104],"by":[105],"dynamic":[107],"programming":[108],"low":[111],"order.":[113]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2014,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}