{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,21]],"date-time":"2026-02-21T08:18:49Z","timestamp":1771661929987,"version":"3.50.1"},"reference-count":11,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2006,10,11]],"date-time":"2006-10-11T00:00:00Z","timestamp":1160524800000},"content-version":"vor","delay-in-days":4089,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Random Struct Algorithms"],"published-print":{"date-parts":[[1995,8]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Let <jats:italic>N<\/jats:italic> records be stored in an M\u2010dimensional trie (<jats:italic>M<\/jats:italic>\u2010d trie). It is shown that under the symmetric Bernoulli model the variance of the cost <jats:italic>C<jats:sub>N<\/jats:sub><\/jats:italic><jats:sup>\u03c9<\/jats:sup> of a partial match retrieval is <jats:chem-struct-wrap><jats:chem-struct><jats:graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mimetype=\"image\/gif\" position=\"anchor\" specific-use=\"enlarged-web-image\" xlink:href=\"graphic\/must001.gif\"><jats:alt-text>magnified image<\/jats:alt-text><\/jats:graphic><\/jats:chem-struct><\/jats:chem-struct-wrap> with continuous periodic function \u03c4<jats:sub>\u03c9<\/jats:sub>, where <jats:italic>u<\/jats:italic> is the number of unspecified components in a query \u03c9 of size <jats:italic>M<\/jats:italic>. This confirms in quantitative manner a conjecture by Kirschenhofer, Prodinger, and Szpankowski [<jats:italic>Int. J. Found. Comput. Sci.<\/jats:italic>, <jats:bold>4<\/jats:bold>, 69\u201384 (1993)], who presented a detailed analysis of Var <jats:italic>C<jats:sub>N<\/jats:sub><\/jats:italic><jats:sup>\u03c9<\/jats:sup> in the <jats:italic>M<\/jats:italic> = 2, <jats:italic>u<\/jats:italic> = 1\u2010case, but used in their proof a transformation formula of Ramanujan, which does not seem to have an analogue for <jats:italic>M<\/jats:italic> &gt; 2. Our analysis is based on exponential approximations and Mellin inversion.<\/jats:p>","DOI":"10.1002\/rsa.3240070106","type":"journal-article","created":{"date-parts":[[2007,5,26]],"date-time":"2007-05-26T18:48:16Z","timestamp":1180205296000},"page":"81-95","source":"Crossref","is-referenced-by-count":5,"title":["The variance of a partial match retrieval in a multidimensional symmetric trie"],"prefix":"10.1002","volume":"7","author":[{"given":"Werner","family":"Schachinger","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2006,10,11]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.1145\/361002.361007"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-0348-4147-4"},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.1145\/5383.5453"},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.1145\/367390.367400"},{"key":"e_1_2_1_6_2","doi-asserted-by":"publisher","DOI":"10.1142\/S0129054193000055"},{"key":"e_1_2_1_7_2","doi-asserted-by":"publisher","DOI":"10.1002\/rsa.3240050112"},{"key":"e_1_2_1_8_2","first-page":"493","volume-title":"The Art of Computer Programming","author":"Knuth D. E.","year":"1973"},{"key":"e_1_2_1_9_2","volume-title":"Evolution of Random Search Trees","author":"Mahmoud H. M.","year":"1992"},{"key":"e_1_2_1_10_2","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0060951"},{"key":"e_1_2_1_11_2","doi-asserted-by":"publisher","DOI":"10.1137\/0205003"},{"key":"e_1_2_1_12_2","unstructured":"W.Schachinger Beitr\u00e4ge zur Analyse von Datenstrukturen zur Digitalen Suche Doctoral thesis Vienna University of Technology Faculty of Sciences 1992."}],"container-title":["Random Structures &amp; Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Frsa.3240070106","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/rsa.3240070106","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,26]],"date-time":"2023-10-26T05:38:06Z","timestamp":1698298686000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/rsa.3240070106"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1995,8]]},"references-count":11,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1995,8]]}},"alternative-id":["10.1002\/rsa.3240070106"],"URL":"https:\/\/doi.org\/10.1002\/rsa.3240070106","archive":["Portico"],"relation":{},"ISSN":["1042-9832","1098-2418"],"issn-type":[{"value":"1042-9832","type":"print"},{"value":"1098-2418","type":"electronic"}],"subject":[],"published":{"date-parts":[[1995,8]]}}}