{"id":"https://openalex.org/W2112241657","doi":"https://doi.org/10.1142/s0129054194000062","title":"ON THE AVERAGE ALTITUDE OF HEAP-ORDERED TREES","display_name":"ON THE AVERAGE ALTITUDE OF HEAP-ORDERED TREES","publication_year":1994,"publication_date":"1994-03-01","ids":{"openalex":"https://openalex.org/W2112241657","doi":"https://doi.org/10.1142/s0129054194000062","mag":"2112241657"},"language":"en","primary_location":{"id":"doi:10.1142/s0129054194000062","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0129054194000062","pdf_url":null,"source":{"id":"https://openalex.org/S68047077","display_name":"International Journal of Foundations of Computer Science","issn_l":"0129-0541","issn":["0129-0541","1793-6373"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Foundations of Computer Science","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/A5063157211","display_name":"Wen\u2010Chin Chen","orcid":"https://orcid.org/0000-0002-0076-1171"},"institutions":[{"id":"https://openalex.org/I16733864","display_name":"National Taiwan University","ror":"https://ror.org/05bqach95","country_code":"TW","type":"education","lineage":["https://openalex.org/I16733864"]}],"countries":["TW"],"is_corresponding":false,"raw_author_name":"WEN-CHIN CHEN","raw_affiliation_strings":["Department of Computer Science and Information Engineering, National Taiwan University, Taipei, Taiwan, R.O.C","[Department of Computer Science & Information Engineering, National Taiwan University, Taipei, Taiwan, R.O.C.]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science and Information Engineering, National Taiwan University, Taipei, Taiwan, R.O.C","institution_ids":["https://openalex.org/I16733864"]},{"raw_affiliation_string":"[Department of Computer Science & Information Engineering, National Taiwan University, Taipei, Taiwan, R.O.C.]","institution_ids":["https://openalex.org/I16733864"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5047329456","display_name":"Wen-Chun Ni","orcid":null},"institutions":[{"id":"https://openalex.org/I16733864","display_name":"National Taiwan University","ror":"https://ror.org/05bqach95","country_code":"TW","type":"education","lineage":["https://openalex.org/I16733864"]}],"countries":["TW"],"is_corresponding":false,"raw_author_name":"WEN-CHUN NI","raw_affiliation_strings":["Department of Computer Science and Information Engineering, National Taiwan University, Taipei, Taiwan, R.O.C","[Department of Computer Science & Information Engineering, National Taiwan University, Taipei, Taiwan, R.O.C.]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science and Information Engineering, National Taiwan University, Taipei, Taiwan, R.O.C","institution_ids":["https://openalex.org/I16733864"]},{"raw_affiliation_string":"[Department of Computer Science & Information Engineering, National Taiwan University, Taipei, Taiwan, R.O.C.]","institution_ids":["https://openalex.org/I16733864"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.9795,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.77484472,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"05","issue":"01","first_page":"99","last_page":"109"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11106","display_name":"Data Management and Algorithms","score":0.9886999726295471,"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"}},"topics":[{"id":"https://openalex.org/T11106","display_name":"Data Management and Algorithms","score":0.9886999726295471,"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"}},{"id":"https://openalex.org/T12536","display_name":"Topological and Geometric Data Analysis","score":0.948199987411499,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/heap","display_name":"Heap (data structure)","score":0.9319426417350769},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6211147904396057},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4972241222858429},{"id":"https://openalex.org/keywords/altitude","display_name":"Altitude (triangle)","score":0.4126884937286377},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.38147133588790894},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.16239133477210999},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.11021226644515991}],"concepts":[{"id":"https://openalex.org/C134757568","wikidata":"https://www.wikidata.org/wiki/Q274089","display_name":"Heap (data structure)","level":2,"score":0.9319426417350769},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6211147904396057},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4972241222858429},{"id":"https://openalex.org/C6350597","wikidata":"https://www.wikidata.org/wiki/Q339495","display_name":"Altitude (triangle)","level":2,"score":0.4126884937286377},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.38147133588790894},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.16239133477210999},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.11021226644515991}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0129054194000062","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0129054194000062","pdf_url":null,"source":{"id":"https://openalex.org/S68047077","display_name":"International Journal of Foundations of Computer Science","issn_l":"0129-0541","issn":["0129-0541","1793-6373"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Foundations of Computer Science","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":0,"referenced_works":[],"related_works":["https://openalex.org/W3158777280","https://openalex.org/W2093687902","https://openalex.org/W2949158926","https://openalex.org/W4301885003","https://openalex.org/W1979597421","https://openalex.org/W1996981508","https://openalex.org/W1989205740","https://openalex.org/W4387561287","https://openalex.org/W2005058894","https://openalex.org/W2007980826"],"abstract_inverted_index":{"We":[0],"consider":[1],"heap-ordered":[2,32],"trees":[3],"in":[4,10,28],"this":[5,11],"paper.":[6],"The":[7],"main":[8],"theorems":[9],"paper":[12],"show":[13],"that":[14],"the":[15,18,21,26,46],"average":[16],"and":[17,38],"variance":[19],"of":[20,25],"altitude":[22],"(or":[23],"level)":[24],"nodes":[27],"a":[29],"random":[30],"n-node":[31],"tree":[33],"are":[34],"[Formula:":[35,39],"see":[36,40],"text]":[37],"text],":[41],"respectively":[42],"where":[43],"\u03b3=0.5772156649\u2026":[44],"is":[45],"Euler\u2019s":[47],"constant.":[48]},"counts_by_year":[{"year":2022,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}