A new method for building a gene tree from Single Nucleotide Polymorphism (SNP) data was developed by Chen and Lindsay (Biometrika 93(4):843–860, 2006). Called the mixture tree, it was based on an ancestral mixture model. The sieve parameter in the model plays the role of time in the evolutionary tree of the sequences. By varying the sieve parameter, one can create a hierarchical tree that esti...

An evolutionary tree analyzes the nucleotide and amino acid sequencesis to infer phylogenetic relationships and evolutionary hypotheses. It is an unrooted binary tree. The sequence of the leaves are not given on the internal nodes. An evolutionary tree with n leaves has n − 2 internal nodes and m = 2n − 3 edges. The number of possible trees with n leaves is ∏n i−3 (2i− 5). Most version of evolu...

Probabilistic (or randomized) decision trees can be used to compute Boolean functions. We consider two types of probabilistic decision trees one has a certain probability to give correct answer (but can also give nothing at all) and is not allowed to give wrong answers, but other always manages to give correct answer, but may require more computation. We provide a method, which can be used to c...

The construction of an efficient tree structure should take into account parameters which can be optimised. Coverage of a node, "dead area" of a node and overlap between nodes are examples of such parameters. Taking these parameters under account is important since minimization of a node coverage leads to more precise searching within the tree, minimization of a node "dead area" reduces the num...

We propose an univesal scheme to design loop-free and superstabilizing protocols for constructing spanning trees optimizing any tree metrics (not only those that are isomorphic to a shortest path tree). Our scheme combines a novel super-stabilizing loop-free BFS with an existing self-stabilizing spanning tree that optimizes a given metric. The composition result preserves the best properties of...

We consider the problem of constructing a sparse suffix tree (or suffix array) for b suffixes of a given text T of size n, using only O(b) words of space during construction time. Breaking the naive bound of Ω(nb) time for this problem has occupied many algorithmic researchers since a different structure, the (evenly spaced) sparse suffix tree, was introduced by Kärkkäinen and Ukkonen in 1996. ...

A widely used method for constructing phylogenetic trees is the neighbour-joining method of Saitou and Nei. We develope heuristics for speeding up the neighbour-joining method which generate the same phylogenetic trees as the original method. All heuristics are based on using a quad-tree to guide the search for the next pair of nodes to join, but differ in the information stored in quad-tree no...

Generally, data mining is the process of analyzing data from different perspectives and summarizing it into useful information information that can be used to increase revenue, cuts costs, or both. Data mining software is one of a number of analytical tools for analyzing data. It allows users to analyze data from many different dimensions or angles, categorize it, and summarize the relationship...

Notice: this is the author's version of a work that was accepted for publication in Theoretical Computer Science. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. An unedited ve...

Phylogenetic invariants are certain polynomials in the joint probability distribution of a Markov model on a phylogenetic tree. Such polynomials are of theoretical interest in the field of algebraic statistics and they are also of practical interest — they can be used to construct phylogenetic trees. This paper is a self-contained introduction to the algebraic, statistical, and computational ch...