Analysis of digital search trees incorporated with paging

Ordinary digital search trees (DSTs) stores one word in each of its internal nodes and leaves, but a DST with paging size b allows storing b words in the leaves, which corresponds to pages in auxiliary storage. In this paper, we analyse the average number of nodes, the average node-wise path length and 2-protected nodes in DSTs with paging size b. We utilize recurrence relations, analytical Poissonization and de-Poissonization, the Mellin transform, and complex analysis. We also compare the storage usage in paged DSTs to that in DSTs. For example, for b = 2,3,4,5,6, the approximate average number of nodes in paged DSTs is, respectively, 82%, 67%, 55%, 47%, 41% of the size of DSTs (when b = 1). Thus the results are nontrivial and interesting for computer scientists

The Variance of the Profile in Digital Search Trees

Analysis of AlgorithmsWhat today we call digital search tree (DST) is Coffman and Eve's sequence tree introduced in 1970. A digital search tree is a binary tree whose ordering of nodes is based on the values of bits in the binary representation of a node's key. In fact, a digital search tree is a digital tree in which strings (keys, words) are stored directly in internal nodes. The profile of a digital search tree is a parameter that counts the number of nodes at the same distance from the root. In this paper we concentrate on external profile, i.e., the number of external nodes at level k when n strings are sorted. By assuming that the n input strings are independent and follow a (binary) memoryless source the asymptotic behaviour of the average profile was determined by Drmota and Szpankowski (2011). The purpose of the present paper is to extend their analysis and to provide a precise analysis of variance of the profile. The main (technical) difference is that we have to deal with an inhomogeneous part in a proper functional-differential equations satisfied by the second moment and Poisson variance. However, we show that the variance is asymptotically of the same order as the expected value which implies concentration. These results are derived by methods of analytic combinatorics such as generating functions, Mellin transform, Poissonization, the saddle point method and singularity analysis

The Variance of the Profile in Digital Search Trees

Analysis of Algorithm

Point pattern analysis of regional city distributions

Point processes, Complete spatial randomness, Maximum pseudo-likelihood estimation, MCMC maximum likelihood estimation,