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Finite metric spaces are an essential tool in discrete mathematics and have applications in several areas including computational biology, image analysis, speech recognition, and information retrieval. Given any such metric D on a ...

Split networks are a popular tool for the analysis and visualization of complex evolutionary histories. Every collection of splits (bipartitions) of a finite set can be represented by a split network. Here we characterize which collection of splits can ...

In evolutionary biology, biologists commonly use a phylogenetic tree to represent the evolutionary history of some set of species. A common approach taken to construct such a tree is to search through the space of all possible phylogenetic trees on the ...

We introduce and study a generalization of the well-known region of influence proximity drawings, called (@e"1,@e"2)-proximity drawings. Intuitively, given a definition of proximity and two real numbers @e"1>=0 and @e"2>=0, an (@e"1,@e"2)-proximity ...

To any metric D on a finite set X, one can associate a metric space T(D) known as its tight span. Properties of T(D) often reveal salient properties of D. For example, cut sets of T(D), i.e., subsets of T(D) whose removal disconnect T(D), can help to ...

Supertrees are a commonly used tool in phylogenetics to summarize collections of partial phylogenetic trees. As a generalization of supertrees, phylogenetic supernetworks allow, in addition, the visual representation of conflict between the trees that ...

We study the problem of computing leveled tree drawings, i.e., straight-line drawings of trees where the vertices have distinct preassigned y-coordinates. Our optimization goal is to maximize the crossing angle resolution (i.e., the minimum angle formed ...

Split networks are commonly used to visualize collections of bipartitions, also called splits, of a finite set. Such collections arise, for example, in evolutionary studies. Split networks can be viewed as a generalization of phylogenetic trees and may ...

In this paper we consider two challenging problems that arise in the context of computing a consensus of a collection of multilabeled trees, namely (1) selecting a compatible collection of clusters on a multiset from an ordered list of such clusters and (...

We introduce and study a generalization of the well-known region of influence proximity drawings, called (ε₁ ,ε₂ )-proximity drawings. Intuitively, given a definition of proximity and two real numbers ε₁ ≥0 and ε₂ ≥0, an (ε₁ ,ε₂ )-proximity drawing of a ...

Multilabeled trees or MUL-trees, for short, are trees whose leaves are labeled by elements of some nonempty finite set X such that more than one leaf may be labeled by the same element of X. This class of trees includes phylogenetic trees and tree ...

The ISTQB Certified Tester exam was developed toward an international standard which includes 47 international testing boards. Today more than 130,000 people have taken the International Software Testing Qualifications Board (ISTQB) Foundations Level ...

We consider the following two problems: Map Matching: Given a sequence of (imprecise) location measurements from a mobile user moving on a road network, determine the most likely path in the network this user has travelled along. Prediction of ...

The theory of the tight span, a cell complex that can be associated to every metric D, offers a unifying view on existing approaches for analyzing distance data, in particular for decomposing a metric D into a sum of simpler metrics as well as for ...

A straight-line drawing ź of a planar graph G need not be plane but can be made so by untangling it, that is, by moving some of the vertices of G. Let shift(G,ź) denote the minimum number of vertices that need to be moved to untangle ź. We show that ...

Summary: Recent advances in gene sequencing for polyploid species, coupled with standard phylogenetic tree reconstruction, leads to gene trees in which the same species can label several leaves. Such multi-labeled trees are then used to reconstruct the ...

Phylogenetic networks are a generalization of evolutionary or phylogenetic trees that allow the representation of conflicting signals or alternative evolutionary histories in a single diagram. Recently the Quartet-Net or ''QNet'' method was introduced, ...

In phylogenetics there are various methods available for understanding the evolutionary history of a set of species based on the analysis of its 4-element subsets. Guided by biological data, such techniques usually require the initial computation of a ...

We present a fixed-parameter algorithm for the Minimum Convex Partition and the Minimum Weight Convex Partition problem. The algorithm is based on techniques developed for the Minimum Weight Triangulation problem. On a set P of n points the algorithm ...

In phylogenetics it is common practice to summarize collections of partial phylogenetic trees in the form of supertrees. Recently it has been proposed to construct phylogenetic supernetworks as an alternative to supertrees as these allow the ...