The variance of a partial match retrieval in a multidimensional symmetric trie

Abstract

AbstractLet N records be stored in an M‐dimensional trie (M‐d trie). It is shown that under the symmetric Bernoulli model the variance of the cost CNω of a partial match retrieval is magnified image with continuous periodic function τω, where u is the number of unspecified components in a query ω of size M. This confirms in quantitative manner a conjecture by Kirschenhofer, Prodinger, and Szpankowski [Int. J. Found. Comput. Sci., 4, 69–84 (1993)], who presented a detailed analysis of Var CNω in the M = 2, u = 1‐case, but used in their proof a transformation formula of Ramanujan, which does not seem to have an analogue for M > 2. Our analysis is based on exponential approximations and Mellin inversion.