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Building Bridges
Discrete mathematics and theoretical computer science are closely linked research areas with strong impacts on applications and various other scientific disciplines. Both fields deeply cross fertilize each other. One of the persons who particularly contributed to building bridges between these and many other areas is László Lovász, a scholar whose outstanding scientific work has defined and shaped many research directions in the last 40 years. A number of friends and colleagues, all top authorities in their fields of expertise and all invited plenary speakers at one of two conferences in August 2008 in Hungary, both celebrating Lovász’s 60th birthday, have contributed their latest research papers to this volume. This collection of articles offers an excellent view on the state of combinatorics and related topics and will be of interest for experienced specialists as well as young researchers.
A Beginner's Guide to Graph Theory
Concisely written, gentle introduction to graph theory suitable as a textbook or for self-study Graph-theoretic applications from diverse fields (computer science, engineering, chemistry, management science) 2nd ed. includes new chapters on labeling and communications networks and small worlds, as well as expanded beginner's material Many additional changes, improvements, and corrections resulting from classroom use
Interconnection Networks
Most of the articles in this book deal with static or point-to-pointInterconnection Networks. In particular, new constructions are proposed basedon different tools from discrete mathematics. Many new records have beenestablished in the table of the maximum number of vertices of graphs withmaximum degree &Dgr; and diameter D. Properties of thesenetworks (and of more classical ones) are analyzed in many of the otherpapers. About 40% of the articles deal with fault tolerance orvulnerability properties using either combinatorial tools or probabilisticones.
Analysis and Design of Algorithms for Combinatorial Problems
Combinatorial problems have been from the very beginning part of the history of mathematics. By the Sixties, the main classes of combinatorial problems had been defined. During that decade, a great number of research contributions in graph theory had been produced, which laid the foundations for most of the research in graph optimization in the following years. During the Seventies, a large number of special purpose models were developed.The impressive growth of this field since has been strongly determined by the demand of applications and influenced by the technological increases in computing power and the availability of data and software. The availability of such basic tools has led to the feasibility of the exact or well approximate solution of large scale realistic combinatorial optimization problems and has created a number of new combinatorial problems.
Introduction to Global Variational Geometry
This book provides a comprehensive introduction to modern global variational theory on fibred spaces. It is based on differentiation and integration theory of differential forms on smooth manifolds, and on the concepts of global analysis and geometry such as jet prolongations of manifolds, mappings, and Lie groups. The book will be invaluable for researchers and PhD students in differential geometry, global analysis, differential equations on manifolds, and mathematical physics, and for the readers who wish to undertake further rigorous study in this broad interdisciplinary field. Featured topics - Analysis on manifolds - Differential forms on jet spaces - Global variational functionals - Eu...
Recent Advances in Algorithms and Combinatorics
Excellent authors, such as Lovasz, one of the five best combinatorialists in the world; Thematic linking that makes it a coherent collection; Will appeal to a variety of communities, such as mathematics, computer science and operations research
Combinatorial Mathematics
The object of this book is to provide an account of the results and methods used in combinatorial theories: Graph Theory, Matching Theory, Hamiltonian Problems, Hypergraph Theory, Designs, Steiner Systems, Latin Squares, Coding Matroids, Complexity Theory.In publishing this volume, the editors do not intend to discuss all the classical open problems in combinatorics for which an algebraic approach turns out to be useful. The work is a selection which is intended for specialists, as well as for graduate students who may also be interested in survey papers. The work features a special section which contains a list of unsolved problems proposed by the participants.
The Sharpest Cut
This collection presents recent results in the areas of theoretical and computational sides of integer programming and combinatorial optimization.
Graphs and Matrices
Graphs and Matrices provides a welcome addition to the rapidly expanding selection of literature in this field. As the title suggests, the book’s primary focus is graph theory, with an emphasis on topics relating to linear algebra and matrix theory. Information is presented at a relatively elementary level with the view of leading the student into further research. In the first part of the book matrix preliminaries are discussed and the basic properties of graph-associated matrices highlighted. Further topics include those of graph theory such as regular graphs and algebraic connectivity, Laplacian eigenvalues of threshold graphs, positive definite completion problem and graph-based matrix games. Whilst this book will be invaluable to researchers in graph theory, it may also be of benefit to a wider, cross-disciplinary readership.
Semantics of the Probabilistic Typed Lambda Calculus
This book takes a foundational approach to the semantics of probabilistic programming. It elaborates a rigorous Markov chain semantics for the probabilistic typed lambda calculus, which is the typed lambda calculus with recursion plus probabilistic choice. The book starts with a recapitulation of the basic mathematical tools needed throughout the book, in particular Markov chains, graph theory and domain theory, and also explores the topic of inductive definitions. It then defines the syntax and establishes the Markov chain semantics of the probabilistic lambda calculus and, furthermore, both a graph and a tree semantics. Based on that, it investigates the termination behavior of probabilistic programs. It introduces the notions of termination degree, bounded termination and path stoppability and investigates their mutual relationships. Lastly, it defines a denotational semantics of the probabilistic lambda calculus, based on continuous functions over probability distributions as domains. The work mostly appeals to researchers in theoretical computer science focusing on probabilistic programming, randomized algorithms, or programming language theory.
