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.

This textbook is a concise introduction to the basic toolbox of structures that allow efficient organization and retrieval of data, key algorithms for problems on graphs, and generic techniques for modeling, understanding, and solving algorithmic problems. The authors aim for a balance between simplicity and efficiency, between theory and practice, and between classical results and the forefront of research. Individual chapters cover arrays and linked lists, hash tables and associative arrays, sorting and selection, priority queues, sorted sequences, graph representation, graph traversal, shortest paths, minimum spanning trees, optimization, collective communication and computation, and load balancing. The authors also discuss important issues such as algorithm engineering, memory hierarchies, algorithm libraries, and certifying algorithms. Moving beyond the sequential algorithms and data structures of the earlier related title, this book takes into account the paradigm shift towards the parallel processing required to solve modern performance-critical applications and how this impacts on the teaching of algorithms. The book is suitable for undergraduate and graduate students and professionals familiar with programming and basic mathematical language. Most chapters have the same basic structure: the authors discuss a problem as it occurs in a real-life situation, they illustrate the most important applications, and then they introduce simple solutions as informally as possible and as formally as necessary so the reader really understands the issues at hand. As they move to more advanced and optional issues, their approach gradually leads to a more mathematical treatment, including theorems and proofs. The book includes many examples, pictures, informal explanations, and exercises, and the implementation notes introduce clean, efficient implementations in languages such as C++ and Java.

Focusing on algorithms for distributed-memory parallel architectures, Parallel Algorithms presents a rigorous yet accessible treatment of theoretical models of parallel computation, parallel algorithm design for homogeneous and heterogeneous platforms, complexity and performance analysis, and essential notions of scheduling. The book extract

Mathematics of Computing -- Parallelism.