Algebraic Methods for Trie Statistics
نویسندگان
چکیده
The trie structure is probably the most well-known amongst digital structures. It is a tree representation of sets of digital (e.g. binary) sequences that has been introduced by de la Briandais and Fredkin [9] t and bears analogies to binary search trees [ 11, 15, 17, 20, 1, 191 Operations like insert, delete, query, union, intersection ... can be performed efficiently on this representation of sets. Tries also appear as a structure underlying Radix Exchange Sort (a digital analogue of Quicksort, [ 1 1 1, p. 13 1).
منابع مشابه
An analytic approach to the asymptotic variance of trie statistics and related structures
We develop analytic tools for the asymptotics of general trie statistics, which are particularly advantageous for clarifying the asymptotic variance. Many concrete examples are discussed for which new Fourier expansions are given. The tools are also useful for other splitting processes with an underlying binomial distribution. We specially highlight Philippe Flajolet’s contribution in the analy...
متن کاملAn Algebraic Approach to the Pre x Model Analysis
The trie, or digital tree, is a standard data structure for representing sets of strings over a given nite alphabet. Since Knuth's original work Knu73], this data structures have been extensively studied and analyzed. In this paper, we present an algebraic approach to the analysis of average storage and average time required by the retrieval algorithms of trie structures under the preex model. ...
متن کاملMetal-insulator transition in two-dimensional Ando model
The transport properties of the Ando model on square lattice are studied numerically for box distribution of the diagonal disorder. The statistical properties of the Lyapunov exponents and of the conductance are discussed. It is shown that the statistics of the Lyapunov exponents agrees with the random matrix theory not only in the metallic regime, but even at the critical point. That confirms ...
متن کاملAS-Index: A Structure For String Search Using n-grams and Algebraic Signatures
AS-Index is a new index structure for exact string search in disk resident databases. It uses hashing, unlike known alternate structures, tree or trie based, and indexes every n-gram in the database. supported as well. The hash function relies on the algebraic signatures of the n-grams. Use of hashing provides for constant index access time for arbitrarily long patterns, unlike other structures...
متن کاملBernoulli collocation method with residual correction for solving integral-algebraic equations
The principal aim of this paper is to serve the numerical solution of an integral-algebraic equation (IAE) by using the Bernoulli polynomials and the residual correction method. After implementation of our scheme, the main problem would be transformed into a system of algebraic equations such that its solutions are the unknown Bernoulli coefficients. This method gives an analytic solution when ...
متن کامل