Binary Search Trees are a frequently used data structure for rapid access to the stored data. Data structures like arrays, vectors and linked lists are limited by the trade-off between the ability to perform a fast search and resize easily. They are an alternative that is both dynamic in size and easily searchable. Due to efficiency reason, complete and nearly complete binary search trees are o...

We present algorithms for a new self-adjusting binary search tree, which we call a shuffle tree. The tree is easy to implement and does not require parent pointers or balancing information to be stored in tree nodes. A maximum of one rotation is probabilistically applied during each traversal, which keeps the cost of balancing activity low. We present tests to compare the performance of shuffle...

Memory reference locality is widely known to have an increasingly important eeect on the performance of algorithms. We demonstrate and explain why the performance of the binary tree search algorithm varies considerably depending on how the tree is laid out in the main memory. We present an algorithm which relocates a binary tree so that maximal performance can be achieved and discuss how update...

The rotation graph, G n , has vertex set consisting of all binary trees with n nodes. Two vertices are connected by an edge if a single rotation will transform one tree into the other. We provide a simpler proof of a result of Lucas 7] that G n contains a Hamilton path. Our proof deals directly with the pointer representation of the binary tree. This proof provides the basis of an algorithm for...

To investigate the fundamental causes of bloat, six artificial random binary tree search spaces are presented. Fitness is given by program syntax (the genetic programming genotype). GP populations are evolved on both random problems and problems with “building blocks”. These are compared to problems with explicit ineffective code (introns, junk code, inviable code). Our results suggest the entr...

Considering a random binary tree with n labelled leaves, we use a pruning procedure on this tree in order to construct a Beta(3/2, 1/2)coalescent process. We also use the continuous analogue of this construction, i.e. a pruning procedure on Aldous’s continuumrandom tree, to construct a continuous state space process that has the same structure as the beta-coalescent process up to some time chan...

We consider random binary search trees when the input consists of a multiset, i.e. a set with multiple occurrences of equal elements, and prove that the randomized insertion and deletion algorithms produce random search trees regardless of multiplicities; even if all the elements are equal during the tree updates, a search tree will maintain its randomness. Thus, equal elements do not degenerat...

A bstract-A new balanced multidimensional tree structure called a k-dimensional balanced binary tree, k a positive integer, is presented and investigated. It is shown that the data structure can be used to manage a set of n k-dimensional data items such that access, insertion, and deletion operations can be supported in Ooog n + k) time. The data structure is a multidimensional generalization o...

Dempster's rule of evidence combination is computational expensive. This paper presents a parallel approach to evidence combination on a qualitative Markov tree. Binarization algorithm transforms a qualitative Markov tree into a binary tree based on the computational workload in nodes for an exact implementation of evidence combination. A binary tree is then partitioned into clusters with each ...