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Multilayer networks has become a central topic in Network Science. The book presents a comprehensive account of this emerging field. Multilayer networks are formed by several networks and include social networks, financial markets, multi-modal transportation systems, infrastructu...res, molecular networks and the brain.
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This book describes the mathematical theory of regularizing element transformations as foundation for mesh smoothing. It gives a thorough introduction to GETMe based mesh smoothing and its algorithms providing a framework to focus on efficiently improving minimal element quality,... overal mesh quality, and mesh validity. It addresses the improvement of various types of meshes like planar, surface, volumetric, mixed, isotropic or anisotropic meshes and addresses aspects of combining mesh smoothign with topological mesh modifications.
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The crossing number is a popular object of study with surprising connections. A rich body of material illustrates a wide variety of ideas and techniques in topological graph theory, discrete geometry, and computer science. The first part deals with the traditional crossing number..., crossing number values, crossing lemma, related parameters, computational complexity, and algorithms. The second part includes the rich history of alternative crossing numbers, the rectilinear crossing number, the pair crossing number, the independent odd crossing number, with interesting and non-trivial results. Finally, applications of the crossing number outside topological graph theory are included.
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This enumerative combinatorics text focuses on set partitions. It presents a complete survey of the field, open problems, and results in set partitions and pattern matching. The advantages and drawbacks of various solution techniques and approaches are also examined.
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While much information can be found on discrete and computational geometry, it is scattered among many sources. The Handbook of Discrete and Computational Geometry, Third Edition brings together all of the major results in both these fields into one volume. Thousands of results, ...theorems, algorithms, and tables definitively cover the field, while numerous applications from many different fields demonstrate practical usage. The material is readily accessible to the novice, but offers enough depth to appeal to the specialist. Every technical term is defined in an easy-to-use glossary. Over 200 figures illustrate the concepts presented and provide supporting examples.
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Concerns the use of graphs for the simulation and representation of transport networks. This book covers networks in both spatial analysis and urban management, together with the simulation by graph theory, a tool that makes it possible to solve various classic problems, such as ...high-speed roads between one or more origins and destinations.
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This text, presented in three parts (Combinatorics, Probability, Graphs) addresses all those who wish to acquire basic or advanced knowledge in combinatorial theories. Basic and advanced theoretical elements are presented through simple applications like the Sudoku game, search e...ngine algorithm and other easy to grasp applications.
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Graph partitioning is a theoretical subject with applications in many areas, principally: numerical analysis, programs mapping onto parallel architectures, image segmentation, VLSI design. During the last 40 years, the literature has strongly increased and big improvements have b...een made.
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Covers spatial analysis and urban management using graph theory simulation.
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A 2006 CHOICE Outstanding Academic Title, this text provides comprehensive coverage of permutations. The second edition features a new chapter on modeling genomes by using permutations. Along with new applications such as genome sorting, this edition includes a set of warm-up exe...rcises to ease readers into a problem solving mode as well as new sections addressing the growth rate of permutation classes, permutation tableaux, superpatterns, and alternating subsequences. The text also discusses pattern avoidance, inversions, and linear orders.
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