{"id":"https://openalex.org/W2064212735","doi":"https://doi.org/10.1017/s0963548307008796","title":"An Analysis of the Height of Tries with Random Weights on the Edges","display_name":"An Analysis of the Height of Tries with Random Weights on the Edges","publication_year":2007,"publication_date":"2007-11-26","ids":{"openalex":"https://openalex.org/W2064212735","doi":"https://doi.org/10.1017/s0963548307008796","mag":"2064212735"},"language":"en","primary_location":{"id":"doi:10.1017/s0963548307008796","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0963548307008796","pdf_url":null,"source":{"id":"https://openalex.org/S7291079","display_name":"Combinatorics Probability Computing","issn_l":"0963-5483","issn":["0963-5483","1469-2163"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorics, Probability and 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/A5068016630","display_name":"Nicolas Broutin","orcid":null},"institutions":[{"id":"https://openalex.org/I5023651","display_name":"McGill University","ror":"https://ror.org/01pxwe438","country_code":"CA","type":"education","lineage":["https://openalex.org/I5023651"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"N. BROUTIN","raw_affiliation_strings":["School of Computer Science, McGill University, Montreal H3A2K6Canada (e-mail:","School of computer science, mcgill university, montreal h3a2k6canada (e-mail: nicolas.broutin@m4x.org, luc@cs.mcgill.ca)"],"affiliations":[{"raw_affiliation_string":"School of Computer Science, McGill University, Montreal H3A2K6Canada (e-mail:","institution_ids":["https://openalex.org/I5023651"]},{"raw_affiliation_string":"School of computer science, mcgill university, montreal h3a2k6canada (e-mail: nicolas.broutin@m4x.org, luc@cs.mcgill.ca)","institution_ids":["https://openalex.org/I5023651"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5070394029","display_name":"Luc Devroye","orcid":"https://orcid.org/0009-0001-4330-8991"},"institutions":[{"id":"https://openalex.org/I5023651","display_name":"McGill University","ror":"https://ror.org/01pxwe438","country_code":"CA","type":"education","lineage":["https://openalex.org/I5023651"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"L. DEVROYE","raw_affiliation_strings":["School of Computer Science, McGill University, Montreal H3A2K6Canada (e-mail:","School of computer science, mcgill university, montreal h3a2k6canada (e-mail: nicolas.broutin@m4x.org, luc@cs.mcgill.ca)"],"affiliations":[{"raw_affiliation_string":"School of Computer Science, McGill University, Montreal H3A2K6Canada (e-mail:","institution_ids":["https://openalex.org/I5023651"]},{"raw_affiliation_string":"School of computer science, mcgill university, montreal h3a2k6canada (e-mail: nicolas.broutin@m4x.org, luc@cs.mcgill.ca)","institution_ids":["https://openalex.org/I5023651"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5068016630"],"corresponding_institution_ids":["https://openalex.org/I5023651"],"apc_list":null,"apc_paid":null,"fwci":0.4836,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.75749427,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":96},"biblio":{"volume":"17","issue":"2","first_page":"161","last_page":"202"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11269","display_name":"Algorithms and Data Compression","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T11269","display_name":"Algorithms and Data Compression","score":0.9998999834060669,"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/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11567","display_name":"semigroups and automata theory","score":0.9958000183105469,"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/trie","display_name":"Trie","score":0.8916319012641907},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6882697343826294},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6848398447036743},{"id":"https://openalex.org/keywords/exponent","display_name":"Exponent","score":0.5895578265190125},{"id":"https://openalex.org/keywords/string","display_name":"String (physics)","score":0.5648086071014404},{"id":"https://openalex.org/keywords/enhanced-data-rates-for-gsm-evolution","display_name":"Enhanced Data Rates for GSM Evolution","score":0.5072076320648193},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.45324695110321045},{"id":"https://openalex.org/keywords/alphabet","display_name":"Alphabet","score":0.4238799810409546},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.41826409101486206},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.40805861353874207},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.17243486642837524},{"id":"https://openalex.org/keywords/data-structure","display_name":"Data structure","score":0.09224006533622742}],"concepts":[{"id":"https://openalex.org/C190290938","wikidata":"https://www.wikidata.org/wiki/Q387015","display_name":"Trie","level":3,"score":0.8916319012641907},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6882697343826294},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6848398447036743},{"id":"https://openalex.org/C2780388253","wikidata":"https://www.wikidata.org/wiki/Q5421508","display_name":"Exponent","level":2,"score":0.5895578265190125},{"id":"https://openalex.org/C157486923","wikidata":"https://www.wikidata.org/wiki/Q1376436","display_name":"String (physics)","level":2,"score":0.5648086071014404},{"id":"https://openalex.org/C162307627","wikidata":"https://www.wikidata.org/wiki/Q204833","display_name":"Enhanced Data Rates for GSM Evolution","level":2,"score":0.5072076320648193},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.45324695110321045},{"id":"https://openalex.org/C112876837","wikidata":"https://www.wikidata.org/wiki/Q837518","display_name":"Alphabet","level":2,"score":0.4238799810409546},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.41826409101486206},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.40805861353874207},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.17243486642837524},{"id":"https://openalex.org/C162319229","wikidata":"https://www.wikidata.org/wiki/Q175263","display_name":"Data structure","level":2,"score":0.09224006533622742},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","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/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1017/s0963548307008796","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0963548307008796","pdf_url":null,"source":{"id":"https://openalex.org/S7291079","display_name":"Combinatorics Probability Computing","issn_l":"0963-5483","issn":["0963-5483","1469-2163"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorics, Probability and Computing","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.126.7702","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.126.7702","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://cg.scs.carleton.ca/~luc/tries_weighted.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Quality Education","id":"https://metadata.un.org/sdg/4","score":0.41999998688697815}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":51,"referenced_works":["https://openalex.org/W201436835","https://openalex.org/W1491961545","https://openalex.org/W1500202606","https://openalex.org/W1517147669","https://openalex.org/W1597637931","https://openalex.org/W1597723816","https://openalex.org/W1773656139","https://openalex.org/W1854930219","https://openalex.org/W1965516463","https://openalex.org/W1966552686","https://openalex.org/W1982250524","https://openalex.org/W2000484009","https://openalex.org/W2008188815","https://openalex.org/W2010816129","https://openalex.org/W2016995838","https://openalex.org/W2023807842","https://openalex.org/W2039379906","https://openalex.org/W2042587503","https://openalex.org/W2045083286","https://openalex.org/W2048858877","https://openalex.org/W2053183761","https://openalex.org/W2058822978","https://openalex.org/W2081715952","https://openalex.org/W2081805893","https://openalex.org/W2089678569","https://openalex.org/W2091484423","https://openalex.org/W2091851562","https://openalex.org/W2112729204","https://openalex.org/W2123024824","https://openalex.org/W2134926765","https://openalex.org/W2139886628","https://openalex.org/W2145929705","https://openalex.org/W2172208172","https://openalex.org/W2182108204","https://openalex.org/W2337480916","https://openalex.org/W2343461779","https://openalex.org/W2478722229","https://openalex.org/W2492998062","https://openalex.org/W2494129288","https://openalex.org/W2496163386","https://openalex.org/W2500470525","https://openalex.org/W2796425996","https://openalex.org/W3038470872","https://openalex.org/W3109965631","https://openalex.org/W3144881883","https://openalex.org/W4244638572","https://openalex.org/W4249667877","https://openalex.org/W4301258660","https://openalex.org/W6653082000","https://openalex.org/W6660250807","https://openalex.org/W6703323115"],"related_works":["https://openalex.org/W1978042415","https://openalex.org/W2030128136","https://openalex.org/W2315492480","https://openalex.org/W4225349735","https://openalex.org/W4312833556","https://openalex.org/W4294533808","https://openalex.org/W2062836726","https://openalex.org/W2017624463","https://openalex.org/W2287565596","https://openalex.org/W2092824970"],"abstract_inverted_index":{"We":[0],"analyse":[1],"the":[2,16,34,46,54,61,80,97,116,119,122,136,139,144,169,173,176],"weighted":[3,83,98],"height":[4,99],"of":[5,12,36,49,56,73,118,121,133,138,143,172,175],"random":[6,28],"tries":[7,48],"built":[8],"from":[9],"independent":[10],"strings":[11,37],"i.i.d.":[13],"symbols":[14],"on":[15],"finite":[17],"alphabet":[18],"{1,":[19],".":[20,21,22],"d":[23],"}.":[24],"The":[25],"edges":[26],"receive":[27],"weights":[29],"whose":[30],"distribution":[31,174],"depends":[32],"upon":[33],"number":[35],"that":[38,40,165],"visit":[39],"edge.":[41],"Such":[42],"a":[43,65,71,130,163],"model":[44,85],"covers":[45],"hybrid":[47],"de":[50],"la":[51],"Briandais":[52],"and":[53,58,135,152],"TST":[55],"Bentley":[57],"Sedgewick,":[59],"where":[60,111,126,146],"search":[62],"time":[63],"for":[64,76],"string":[66],"can":[67,158],"be":[68,103,159],"decomposed":[69],"as":[70],"sum":[72],"processing":[74],"times":[75],"each":[77],"symbol":[78],"in":[79,109],"string.":[81],"Our":[82],"trie":[84,123,140,145],"also":[86],"permits":[87],"one":[88,150],"to":[89,102,105,168],"study":[90],"maximal":[91],"path":[92],"imbalance.":[93],"In":[94],"all":[95,127],"cases,":[96],"is":[100,113,166],"shown":[101],"asymptotic":[104],"c":[106,112],"log":[107],"n":[108],"probability,":[110],"determined":[114],"by":[115,161],"behaviour":[117],"core":[120],"(the":[124,141],"part":[125,142],"nodes":[128,147],"have":[129,148],"full":[131],"set":[132],"children)":[134],"fringe":[137],"only":[149],"child":[151],"form":[153],"spaghetti":[154],"-like":[155],"trees).":[156],"It":[157],"found":[160],"maximizing":[162],"function":[164],"related":[167],"Cram\u00e9r":[170],"exponent":[171],"edge":[177],"weights.":[178]},"counts_by_year":[{"year":2013,"cited_by_count":2}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
