Shortest Connectivity An Introduction with Applications in Phylogeny [Hardcover]

The aim in this graduate level text is to outline the key mathematical concepts that underpin these important questions in applied mathematics. These concepts involve discrete mathematics (particularly graph theory), optimization, computer science, and several ideas in biology.The aim in this graduate level text is to outline the key mathematical concepts that underpin these important questions in applied mathematics. These concepts involve discrete mathematics (particularly graph theory), optimization, computer science, and several ideas in biology.Two Classical Optimization Problems.- Gauss Question.- What Does Solution Mean?.- Network Design Problems.- A New Challenge: The Phylogeny.- An Analysis of Steiners Problem in Phylogenetic Spaces.- Tree Building Algorithms.

From the reviews of the first edition:

The aim of this graduate-level text is to summarize mathematical concepts concerned with problems of shortest connectivity, and to demonstrate important applications of the theory, in particular in biology. & The book contains extensive references and gives rise to many problems for further research. & Examples are discussed in the history of evolution, taxonomy, historical linguistics and others. (G?nther Karigl, Zentralblatt MATH, Vol. 1086, 2006)

The problem of Shortest Connectivity has a long and convoluted history: given a finite set of points in a metric space, search for a network that connects these points with the shortest possible length. This shortest network must be a tree and may contain vertices different from the points which are to be connected. Over the years more and more real-life problems are given, which use this problem or one of its relatives as an application, as a subproblem or a model.

This volume is an introduction to the theory of Shortest Connectivity , as the core of the so-called Geometric Network Design Problems , where the general problem canlC$