SIAM Monographs on Discrete Mathematics and Applications – serie

This monograph offers a systematic quantitative approach to the analysis, evaluation, and design of electoral systems. Today, electoral reform is of concern to newborn democracies as well as many old ones. The authors use mathematical models and automatic procedures, when possible, to solve some of the problems that arise in the comparison of existing systems as well as in the construction of new ones. One distinctive feature of the book is the emphasis on single- and multiple-criteria optimization methods. This powerful tool kit will help political researchers evaluate and choose an appropriate electoral system.A general formal model is included as well as a coding system to describe, identify, and classify electoral systems. Evaluation criteria and the corresponding performance indicators are discussed. A treatment of electoral formulas as algorithms to minimize actual cost functions or disproportionality indexes is also included. Neutral automatic procedures for political districting are presented, and the process of electoral reform is analyzed from historical and political points of view.

Finally there is a book that presents real applications of graph theory in a unified format. This book is the only source for an extended, concentrated focus on the theory and techniques common to various types of intersection graphs. It is a concise treatment of the aspects of intersection graphs that interconnect many standard concepts and form the foundation of a surprising array of applications to biology, computing, psychology, matrices, and statistics. The authors emphasize the underlying tools and techniques and demonstrate how this approach constitutes a definite theory within graph theory. Some of the applications are not widely known or available in the graph theoretic literature and are presented here for the first time. The book also includes a detailed literature guide for many specialized and related areas, a current bibliography, and more than 100 exercises.

This volume presents the locality-sensitive approach to distributed network algorithms - the utilization of locality to simplify control structures and algorithms and reduce their costs. The author begins with an introductory exposition of distributed network algorithms focusing on topics that illustrate the role of locality in distributed algorithmic techniques. He then introduces locality-preserving network representations and describes sequential and distributed techniques for their construction. Finally, the applicability of the locality-sensitive approach is demonstrated through several applications.Distributed Computing: A Locality-Sensitive Approach is the only book that gives a thorough exposition of network spanners and other locality-preserving network representations such as sparse covers and partitions. The book is useful for computer scientists interested in distributed computing, electrical engineers interested in network architectures and protocols, and for discrete mathematicians and graph theorists.

Combinatorial data analysis (CDA) refers to a wide class of methods for the study of relevant data sets in which the arrangement of a collection of objects is absolutely central. The focus of this monograph is on the identification of arrangements, which are then further restricted to where the combinatorial search is carried out by a recursive optimization process based on the general principles of dynamic programming (DP).The authors provide a comprehensive and self-contained review delineating a very general DP paradigm or schema that can serve two functions. First, the paradigm can be applied in various special forms to encompass all previously proposed applications suggested in the classification literature. Second, the paradigm can lead directly to many more novel uses. An appendix is included as a user's manual for a collection of programs available as freeware.The incorporation of a wide variety of CDA tasks under one common optimization framework based on DP is one of the book's strongest points. The authors include verifiably optimal solutions to nontrivially sized problems over the array of data analysis tasks discussed.

This concise, readable book provides a sampling of the very large, active, and expanding field of artificial neural network theory. It considers select areas of discrete mathematics linking combinatorics and the theory of the simplest types of artificial neural networks.