This is the first book that focuses on practical algorithms for polynomial inequality proving and discovering. It is a summary of the work by the authors and their collaborators on automated inequality proving and discovering in recent years. Besides brief introduction to some classical results and related work in corresponding chapters, the book mainly focuses on the algorithms initiated by the authors and their collaborators, such as real root counting, real root classification, improved...

Classical computer science textbooks tell us that some problems are 'hard'. Yet many areas, from machine learning and computer vision to theorem proving and software verification, have defined their own set of tools for effectively solving complex problems. Tractability provides an overview of these different techniques, and of the fundamental concepts and properties used to tame intractability. This book will help you understand what to do when facing a hard computational problem. Can the...

From the reviews of the previous editions".... The book is a first class textbook and seems to be indispensable for everybody who has to teach combinatorial optimization. It is very helpful for students, teachers, and researchers in this area. The author finds a striking synthesis of nice and interesting mathematical results and practical applications. ... the author pays much attention to the inclusion of well-chosen exercises. The reader does not remain helpless; solutions or at ...

Martin Grötschel is one of the most influential mathematicians of our time. He has received numerous honors and holds a number of key positions in the international mathematical community. He celebrated his 65th birthday on September 10, 2013. Martin Grötschel’s doctoral descendant tree 1983–2012, i.e., the first 30 years, features 39 children, 74 grandchildren, 24 great-grandchildren and 2 great-great-grandchildren, a total of 139 doctoral descendants.This book starts with a perso...

This textbook, the first of its kind, presents the fundamentals of distance geometry: theory, useful methodologies for obtaining solutions, and real world applications. Concise proofs are given and step-by-step algorithms for solving fundamental problems efficiently and precisely are presented in Mathematica®, enabling the reader to experiment with concepts and methods as they are introduced. Descriptive graphics, examples, and problems, accompany the real gems of the text, namely...

Matroid theory is a vibrant area of research that provides a unified way to understand graph theory, linear algebra and combinatorics via finite geometry. This book provides the first comprehensive introduction to the field which will appeal to undergraduate students and to any mathematician interested in the geometric approach to matroids. Written in a friendly, fun-to-read style and developed from the authors' own undergraduate courses, the book is ideal for students. Beginning with a ba...

Although they are believed to be unsolvable in general, tractability results suggest that some practical NP-hard problems can be efficiently solved. Combinatorial search algorithms are designed to efficiently explore the usually large solution space of these instances by reducing the search space to feasible regions and using heuristics to efficiently explore these regions. Various mathematical formalisms may be used to express and tackle combinatorial problems, among them the constraint s...

These lecture notes provide a systematic introduction to matrix models of quantum field theories with non-commutative and fuzzy geometries.The book initially focuses on the matrix formulation of non-commutative and fuzzy spaces, followed by a description of the non-perturbative treatment of the corresponding field theories. As an example, the phase structure of non-commutative phi-four theory is treated in great detail, with a separate chapter on the multitrace approach. The last c...

This book constitutes the proceedings of the 9th International Conference on Discrete Optimization and Operations Research, DOOR 2016, held in Vladivostok, Russia, in September 2016.The 39 full papers presented in this volume were carefully reviewed and selected from 181 submissions. They were organized in topical sections named: discrete optimization; scheduling problems; facility location; mathematical programming; mathematical economics and games; applications of operational rese...

This book explores fundamental aspects of geometric network optimisation with applications to a variety of real world problems. It presents, for the first time in the literature, a cohesive mathematical framework within which the properties of such optimal interconnection networks can be understood across a wide range of metrics and cost functions. The book makes use of this mathematical theory to develop efficient algorithms for constructing such networks, with an emphasis on exact soluti...

This highly readable book aims to ease the many challenges of starting undergraduate research. It accomplishes this by presenting a diverse series of self-contained, accessible articles which include specific open problems and prepare the reader to tackle them with ample background material and references. Each article also contains a carefully selected bibliography for further reading.The content spans the breadth of mathematics, including many topics that are not normally address...

The proceedings represent the state of knowledge in the area of algorithmic differentiation (AD). The 31 contributed papers presented at the AD2012 conference cover the application of AD to many areas in science and engineering as well as aspects of AD theory and its implementation in tools. For all papers the referees, selected from the program committee and the greater community, as well as the editors have emphasized accessibility of the presented ideas also to non-AD experts. In the AD...