Binary Space Partition (BSP) tree and Constructive Solid Geometry (CSG) tree representations are both set-theoretic binary tree representations of solid objects used in solid modeling and computer graphics. Recently, an extension of the traditional BSP tree definition has been presented, in which surfaces used in the binary partition include curved surfaces in addition to planar surfaces. We ex...

Preferences can be aggregated using voting rules. We consider here the family of rules which perform a sequence of pairwise majority comparisons between two candidates. The winner thus depends on the chosen sequence of comparisons, which can be represented by a binary tree. We address the difficulty of computing candidates that win for some trees, and then introduce and study the notion of fair...

Note that k must always equal i+ 1 in a binary tree. Prodinger [P] recently computed the probability that a random binary tree with n nodes has i nodes with 2 children (and hence i + 1 nodes without children and n − 2i − 1 nodes with 1 child). Since the total number of binary trees with n nodes is known—it is bn—, his formulas can be derived easily from the above theorem and vice versa. Proding...

We consider the class of channel graphs which can be viewed as compositions of two copies, right and left, of a complete binary tree with terminal nodes of the right tree connected to distinct terminal nodes of the left tree. We study the connection patterns of the two binary trees to minimize the blocking probability of the resulting channel graphs. We show that the connection patterns given b...

We propose to maintain a Binary Search Tree in the form of a forest in such a way that – (a) it provides faster node access and, (b) it becomes more compatible with the concurrent environment. Using a small array, the stated goals were achieved without applying any restructuring algorithm. Empirically, we have shown that the proposed method brings down the total internal pathlength of a Binary ...

Binary Space Partition (BSP) tree and Constructive Solid Geometry (CSG) tree representations are both set-theoretic binary tree representations of solid objects used in solid modeling and computer graphics. Recently, an extension of the traditional BSP tree definition has been presented, in which surfaces used in the binary partition include curved surfaces in addition to planar surfaces. We ex...

The double-rooted complete binary tree is a complete binary tree where the path (of length ) between the children of the root is replaced by a path of length . It is folklore that the double-rooted complete binary tree is a spanning tree of the hypercube of the same size. Unfortunately, the usual construction of an embedding of a double-rooted complete binary tree into the hypercube does not pr...

Gene tree reconciliation is a method to reconcile gene trees that are confounded by complex histories of gene duplications with a provided species tree. The trees involved are required to be rooted and full binary. Reconciling gene trees allows not only to identify and study such histories for gene families, but is also the base for several higher level applications including the estimation of ...

Applying a method to reconstruct a phylogenetic tree from random data provides a way to detect whether that method has an inherent bias towards certain tree 'shapes'. For maximum parsimony, applied to a sequence of random 2-state data, each possible binary phylogenetic tree has exactly the same distribution for its parsimony score. Despite this pleasing and slightly surprising symmetry, some bi...

The 2DR-tree is a novel approach for accessing spatial data, particularly when spatial relationships are defined among objects. The 2DR-tree uses nodes that are the same dimensionality as the data space. Therefore, all relationships between objects are preserved and different binary search strategies are supported. This paper presents the 2DR-tree binary search strategy. A preliminary performan...