The hardness of perfect phylogeny, feasible register assignment and other problems on thin colored graphs

AbstractIn this paper, we consider the complexity of a number of combinatorial problems; namely, Intervalizing Colored Graphs (DNA physical mapping), Triangulating Colored Graphs (perfect phylogeny), (Directed) (Modified) Colored Cutwidth, Feasible Register Assignment and Module Allocation for graphs of bounded pathwidth. Each of these problems has as a characteristic a uniform upper bound on the tree or path width of the graphs in “yes”-instances. For all of these problems with the exceptions of Feasible Register Assignment and Module Allocation, a vertex or edge coloring is given as part of the input. Our main results are that the parameterized variant of each of the considered problems is hard for the complexity classes W[t] for all t∈N. We also show that Intervalizing Colored Graphs, Triangulating Colored Graphs, and Colored Cutwidth are NP-Complete

Algorithms for weighted multidimensional search and perfect phylogeny

This dissertation is a collection of papers from two independent areas: convex optimization problems in R[superscript]d and the construction of evolutionary trees;The paper on convex optimization problems in R[superscript]d gives improved algorithms for solving the Lagrangian duals of problems that have both of the following properties. First, in absence of the bad constraints, the problems can be solved in strongly polynomial time by combinatorial algorithms. Second, the number of bad constraints is fixed. As part of our solution to these problems, we extend Cole\u27s circuit simulation approach and develop a weighted version of Megiddo\u27s multidimensional search technique;The papers on evolutionary tree construction deal with the perfect phylogeny problem, where species are specified by a set of characters and each character can occur in a species in one of a fixed number of states. This problem is known to be NP-complete. The dissertation contains the following results on the perfect phylogeny problem: (1) A linear time algorithm when all the characters have two states. (2) A polynomial time algorithm when the number of character states is fixed. (3) A polynomial time algorithm when the number of characters is fixed

A list of parameterized problems in bioinformatics

In this report we present a list of problems that originated in bionformatics. Our aim is to collect information on such problems that have been analyzed from the point of view of Parameterized Complexity. For every problem we give its definition and biological motivation together with known complexity results.Postprint (published version

Unique perfect phylogeny is NP-hard

We answer, in the affirmative, the following question proposed by Mike Steel as a $100 challenge: "Is the following problem NP-hard? Given a ternary phylogenetic X-tree T and a collection Q of quartet subtrees on X, is T the only tree that displays Q ?

Algorithms For Phylogeny Reconstruction In a New Mathematical Model

The evolutionary history of a set of species is represented by a tree called phylogenetic tree or phylogeny. Its structure depends on precise biological assumptions about the evolution of species. Problems related to phylogeny reconstruction (i.e., finding a tree representation of information regarding a set of items) are widely studied in computer science. Most of these problems have found to be NP-hard. Sometimes they can solved polynomially if appropriate restrictions on the structure of the tree are fixed. This paper summarizes the most recent problems and results in phylogeny reconstruction, and introduces an innovative tree model, called Phylogenetic Parsimonious Tree, which is justified by significant biological hypothesis. Using PPT two problems are studied: the existence and the reconstruction of a tree both when sequences of characters and partial order on interspecies distances are given. We rove complexity results that confirm the hardness of this class of problems

A tourist guide through treewidth

A short overview is given of many recent results in algorithmic graph theory that deal with the notions treewidth, and pathwidth. We discuss algorithms that find tree-decompositions, algorithms that use tree-decompositions to solve hard problems efficiently, graph minor theory, and some applications. The paper contains an extensive bibliography

Computational Molecular Biology

Computational Biology is a fairly new subject that arose in response to the computational problems posed by the analysis and the processing of biomolecular sequence and structure data. The field was initiated in the late 60's and early 70's largely by pioneers working in the life sciences. Physicists and mathematicians entered the field in the 70's and 80's, while Computer Science became involved with the new biological problems in the late 1980's. Computational problems have gained further importance in molecular biology through the various genome projects which produce enormous amounts of data. For this bibliography we focus on those areas of computational molecular biology that involve discrete algorithms or discrete optimization. We thus neglect several other areas of computational molecular biology, like most of the literature on the protein folding problem, as well as databases for molecular and genetic data, and genetic mapping algorithms. Due to the availability of review papers and a bibliography this bibliography

Computational Evolutionary Linguistics

Languages and species both evolve by a process of repeated divergences, which can be described with the branching of a phylogenetic tree or phylogeny. Taking advantage of this fact, it is possible to study language change using computational tree building techniques developed for evolutionary biology. Mathematical approaches to the construction of phylogenies fall into two major categories: character based and distance based methods. Character based methods were used in prior work in the application of phylogenetic methods to the Indo-European family of languages by researchers at the University of Pennsylvania. Discussion of the limitations of character-based models leads to a similar presentation of distance based models. We present an adaptation of these methods to linguistic data, and the phylogenies generated by applying these methods to several modern Germanic languages and Spanish. We conclude that distance based for phylogenies are useful for historical linguistic reconstruction, and that it would be useful to extend existing tree drawing methods to better model the evolutionary effects of language contact