Motivation: Millions of genes in the modern species belong to only thousands of gene families. Genes duplicate and are lost during evolution. A gene family includes instances of the same gene in different species and duplicate genes in the same species. Two genes in different species are ortholog if their common ancestor lies in the most recent common ancestor of the species. Because of complex...

In a binary tree T of N leaves, the left (right) level l i (r i) of leaf i is the number of left (right) edges in path from the root to that leaf. The level n i of leaf i is n i = l i +r i. Kraft-McMillan's characteristic inequality gives a necessary and suucient condition for a multiset of integers fn 1 ; n 2 ; :::; n N g to be the length ensemble of a binary tree T. Similarly, Yeung's charact...

One of the criteria for inferring a species tree from a collection of gene trees, when gene tree incongruence is assumed to be due to incomplete lineage sorting (ILS), is Minimize Deep Coalescence (MDC). Exact algorithms for inferring the species tree from rooted, binary trees under MDC were recently introduced. Nevertheless, in phylogenetic analyses of biological data sets, estimated gene tree...

This paper proposes a binary classification tree aiming at solving multi-class classification problems using binary classifiers. The tree design is achieved in a way that a class group is partitioned into two distinct subgroups at a node. The node adopts the class-modular scheme to improve the binary classification capability. The partitioning is formulated as an optimization problem and a gene...

A fundamental part of many computer algorithms involves traversing a binary tree. One notable example is traversing a space-partitioning acceleration structure when computing ray-traced images. Traditionally, the traversal requires a stack to be temporarily stored for each ray, which results in both additional storage and memorybandwidth usage. We present a novel algorithm for traversing a bina...