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A hierarchical structure describing the inter-relationships of species has long been a fundamental concept in systematic biology, from Linnean classification through to the more recent quest for a 'Tree of Life'. In this paper we use an approach based on discrete mathematics to address a basic question: could one delineate this hierarchical structure in(More)
We investigate the computational complexity of finding an element of a permutation group H ⊆ S n with a minimal distance to a given π ∈ S n , for different metrics on S n. We assume that H is given by a set of generators, such that the problem cannot be solved in polynomial time by exhaustive enumeration. For the case of the Cayley Distance, this problem(More)
INTRODUCTION A gene tree for a gene family is often discordant with the containing species tree because of its complex evolutionary course during which gene duplication, gene loss and incomplete lineage sorting events might occur. Hence, it is of great challenge to infer the containing species tree from a set of gene trees. One common approach to this(More)
Various topological indices have been put forward in different studies from bio-chemistry to pure mathematics. Among them the Wiener index, the number of subtrees and the Randić index have received great attention from mathematicians. While studying the extremal problems regarding these indices among trees, one interesting phenomenon is that they share the(More)
Given a metric d on a permutation group G, the corresponding weight problem is to decide whether there exists an element π ∈ G such that d(π, e) = k, for some given value k. Here we show that this problem is NP-complete for many well-known metrics. An analogous problem in matrix groups, eigenvalue-free problem, and two related problems in permutation(More)
Evolutionary history of protein-protein interaction (PPI) networks provides valuable insight into molecular mechanisms of network growth. In this paper, we study how to infer the evolutionary history of a PPI network from its protein duplication relationship. We show that for a plausible evolutionary history of a PPI network, its relative quality, measured(More)
Phylogenetic networks are a generalization of evolutionary trees and are an important tool for analyzing reticulate evolutionary histories. Recently, there has been great interest in developing new methods to construct rooted phylogenetic networks, that is, networks whose internal vertices correspond to hypothetical ancestors, whose leaves correspond to(More)
Tree rearrangement operations typically induce a metric on the space of phylogenetic trees. One important property of these metrics is the size of the neighborhood, that is, the number of trees exactly one operation from a given tree. We present an exact expression for the size of the TBR (tree bisection and reconnection) neighborhood, thus answering a(More)
Phylogenetic networks are a generalization of evolutionary or phylogenetic trees that are used to represent the evolution of species which have undergone reticulate evolution. In this paper we consider spaces of such networks defined by some novel local operations that we introduce for converting one phylogenetic network into another. These operations are(More)