Andreas Dress - Böcker

Phylogenetic combinatorics is a branch of discrete applied mathematics concerned with the combinatorial description and analysis of phylogenetic trees and related mathematical structures such as phylogenetic networks and tight spans. Based on a natural conceptual framework, the book focuses on the interrelationship between the principal options for encoding phylogenetic trees: split systems, quartet systems and metrics. Such encodings provide useful options for analyzing and manipulating phylogenetic trees and networks, and are at the basis of much of phylogenetic data processing. This book highlights how each one provides a unique perspective for viewing and perceiving the combinatorial structure of a phylogenetic tree and is, simultaneously, a rich source for combinatorial analysis and theory building. Graduate students and researchers in mathematics and computer science will enjoy exploring this fascinating new area and learn how mathematics may be used to help solve topical problems arising in evolutionary biology.

The non-transitivity of similarity relations is the main problem encountered when - as in taxonomic studies in biology - one wants to base classification schemes on observed similarities and dissimilarities. While recent advances in molecular biology give rise to new and rather abstract data structures which can easily be used as input for automatic classification procedures we are still very much in need of a better and deeper understanding of the many delicate points which need consideration once (semi-)automatic classification procedures are applied to biological or other data. The papers collected in this volume are devoted to precisely this problem. They study various theoretical aspects of three reconstruction methods in biology, and psychology, discuss their value in specific biological contexts, apply tree-like recursion networks in chess programming and indicate a conceptual framework for studying cluster analysis from a purely mathematical point of view.

Running to almost 400 pages, and featuring more than 40 papers, this work on combinatorial optimization and applications will be seen as an important addition to the literature. It constitutes the refereed proceedings of the first International Conference on Combinatorial Optimization and Applications, COCOA 2007, held in Xi'an, China in August of that year. The 29 revised full papers presented together with 8 invited papers and 2 invited presentations were carefully reviewed and selected from 114 submissions and cover both theoretical issues and practical applications.