This book solves several mathematical problems in the areas of Very Large Scale Integration (VLSI) and parallel computation. In particular, it describes optimal layouts for the shuffle-exchange graph, one of the best known networks for parallel computation. Attempts to design a shuffle-exchange computer have been hampered in part by the fact that, until now, no good layouts for the shuffle-exchange graph were known. The mesh of trees network (which may eventually prove as useful as the shuffle-exchange graph) is introduced and the book shows how it can be used to perform a variety of computations, including sorting and matrix multiplication, in a logarithmic number of steps. Next, the book introduces the tree of meshes, the first planar graph that was discovered not to have a linear-area layout. Most recently, the structure of this graph has been used to develop a general framework for solving VLSI graph layout problems. Finally, the book develops techniques for proving lower bounds on the bisection width, crossing number, and layout area of a graph. These techniques significantly extend the power and range of previous methods. Researchers in the fields of VLSI, parallel computation, and graph theory will find this study of particular value; it is also accessible to anyone with an elementary knowledge of mathematics and computer science. The book is self-contained and presents in a unified and original manner many results scattered in the technical literature, while also covering new and fundamental results for the first time.

This first part presents chapters on models of computation, complexity theory, data structures, and efficient computation in many recognized sub-disciplines of Theoretical Computer Science.

Offers a one-stop reference on the application of advanced modeling and simulation (M&S) in cyber physical systems (CPS) engineering This book provides the state-of-the-art in methods and technologies that aim to elaborate on the modeling and simulation support to cyber physical systems (CPS) engineering across many sectors such as healthcare, smart grid, or smart home. It presents a compilation of simulation-based methods, technologies, and approaches that encourage the reader to incorporate simulation technologies in their CPS engineering endeavors, supporting management of complexity challenges in such endeavors. Complexity Challenges in Cyber Physical Systems: Using Modeling and Simulation (M&S) to Support Intelligence, Adaptation and Autonomy is laid out in four sections. The first section provides an overview of complexities associated with the application of M&S to CPS Engineering. It discusses M&S in the context of autonomous systems involvement within the North Atlantic Treaty Organization (NATO). The second section provides a more detailed description of the challenges in applying modeling to the operation, risk and design of holistic CPS. The third section delves in details of simulation support to CPS engineering followed by the engineering practices to incorporate the cyber element to build resilient CPS sociotechnical systems. Finally, the fourth section presents a research agenda for handling complexity in application of M&S for CPS engineering. In addition, this text: Introduces a unifying framework for hierarchical co-simulations of cyber physical systems (CPS) Provides understanding of the cycle of macro-level behavior dynamically arising from spaciotemporal interactions between parts at the micro-level Describes a simulation platform for characterizing resilience of CPS Complexity Challenges in Cyber Physical Systems has been written for researchers, practitioners, lecturers, and graduate students in computer engineering who want to learn all about M&S support to addressing complexity in CPS and its applications in today’s and tomorrow’s world.

Aerodynamics and hydrodynamics are still the main domains that make greater use of flow visualization and classical optical techniques such as schlieren and interferometry than of more recent techniques such as holography speckle, laser light sheets, laser-induced tracers and laser-induced fluorescence. A number of studies are now under way on turbulent and vortex flows, within boundary layers or wakes, in the mixing layer of two flows. Other studies concern jets, two-phase flows and air-water interface. To review and discuss developments in flow visualization, four international symposia have been held. Following Tokyo, Bochum and Ann Arbor, the Fourth International Symposium on Flow Visualization (ISFV 4) was held in Paris in August 1986.

Parallel Sorting Algorithms explains how to use parallel algorithms to sort a sequence of items on a variety of parallel computers. The book reviews the sorting problem, the parallel models of computation, parallel algorithms, and the lower bounds on the parallel sorting problems. The text also presents twenty different algorithms, such as linear arrays, mesh-connected computers, cube-connected computers. Another example where algorithm can be applied is on the shared-memory SIMD (single instruction stream multiple data stream) computers in which the whole sequence to be sorted can fit in the respective primary memories of the computers (random access memory), or in a single shared memory. SIMD processors communicate through an interconnection network or the processors communicate through a common and shared memory. The text also investigates the case of external sorting in which the sequence to be sorted is bigger than the available primary memory. In this case, the algorithms used in external sorting is very similar to those used to describe internal sorting, that is, when the sequence can fit in the primary memory, The book explains that an algorithm can reach its optimum possible operating time for sorting when it is running on a particular set of architecture, depending on a constant multiplicative factor. The text is suitable for computer engineers and scientists interested in parallel algorithms.

New and classical results in computational complexity, including interactive proofs, PCP, derandomization, and quantum computation. Ideal for graduate students.

Introduction to Parallel Algorithms and Architectures: Arrays Trees Hypercubes provides an introduction to the expanding field of parallel algorithms and architectures. This book focuses on parallel computation involving the most popular network architectures, namely, arrays, trees, hypercubes, and some closely related networks. Organized into three chapters, this book begins with an overview of the simplest architectures of arrays and trees. This text then presents the structures and relationships between the dominant network architectures, as well as the most efficient parallel algorithms for a wide variety of problems. Other chapters focus on fundamental results and techniques and on rigorous analysis of algorithmic performance. This book discusses as well a hybrid of network architecture based on arrays and trees called the mesh of trees. The final chapter deals with the most important properties of hypercubes. This book is a valuable resource for readers with a general technical background.