Parallel tree contraction is an important framework to develop efficient parallel algorithms on trees. Parallel tree contraction gives an appropriate scheduling for parallel computations on trees, and the scheduling brings efficient parallel algorithms to us. While there are many studies for efficient algorithms of parallel tree contraction and implementation of various parallel computations ba...

Weiru Liu, Xin Hong, and Kenny Adamson School of Computing and Mathematics, University of Ulster at Jordanstown, UK [email protected] Abstract. Binary join trees have been a popular structure to compute the impact of multiple belief functions initially assigned to nodes of trees or networks. Shenoy has proposed two alternative methods to transform a qualitative Markov tree into a binary tree. ...

Consider the complete rooted binary tree T. We construct a sequence Tn, n = 1, 2, . . . of subtrees of T recursively as follows. T1 consists only of the root. Given Tn, we choose a leaf u uniformly at random from the set of all leaves of Tn and add its two children to the tree to create Tn+1. Thus Tn+1 consists of Tn and the children u1, u2 of u, and contains in total 2n+ 1 nodes, including n+ ...

This paper empirically compares five linear-time algorithms for generating unbiased random binary trees. More specifically, we compare the relative asymptotic performance of the algorithms in terms of the numbers of various basic operations executed on average per tree node. Based on these numbers a ranking of the algorithms, which depends on the operation weights, can be deduced. A definitive ...

We study tree series and weighted tree automata over unranked trees. The message is that recognizable tree series for unranked trees can be defined and studied from recognizable tree series for binary representations of unranked trees. For this we prove results of [1] as follows. We extend hedge automata – a class of tree automata for unranked trees – to weighted hedge automata. We define weigh...

It has been shown that the cost W of a weight balanced binary tree satisfies the inequalities, H 5 W 5 H + 3, where H is the entropy of the set of the leaves. For a class of “smooth” distributions the inequalities, H 5 W 5 H + 2, are derived. These results imply that for sets with large entropy the search times provided by such trees cannot be substantially shortened when binary decisions are b...

Author(s): R. Kazemi and M. Q. Vahidi-Asl Abstract: What 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 in...

We study the number of records in a random binary search tree on n randomly labelled vertices. Equivalently the number of random cuttings required to eliminate a random binary search tree can be studied. After normalization the distribution is shown to be asymptotically 1-stable.

In this paper we derive a linear-time, constant-space algorithm to construct a binary heap whose inorder traversal equals a given sequence. We do so in two steps. First, we invert a program that computes the inorder traversal of a binary heap, using the proof rules for program inversion by W. Chen and J.T. Udding. This results in a linear-time solution in terms of binary trees. Subsequently, we...

We present a performance comparison of tree data structures for N -body simulation. The tree data structures examined are the balanced binary tree and the Barnes– Hut (BH) tree. Previous work has compared the performance of BH trees with that of nearest-neighbor trees and the fast multipole method, but the relative merits of BH and binary trees have not been compared systematically. In carrying...