THE VARIANCE OF A PARTIAL MATCH RETRIEVAL IN A MULTIDIMENSIONAL SYMMETRICAL TRIE

Let 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 C-N(omega) of a partial match retrieval is Var C-N(omega) = N-u/M.tau(omega)(log(2M) N) + O(N-2u/M-1) with continuous periodic function tau(omega), where u is the number of unspecified components in a query omega 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 C-N(omega) 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. (C) 1995 John Wiley and Sons, Inc.