The prefix problem consists of computing all the products $x_{0}x_{1}\ldots x_{j} (j=0,\ldots,N-1)$, given a sequence $X = (x_{0},x_{1},\ldots,x_{N-1})$ of elements in a semigroup. In this paper we completely characterize the size-time complexity of computing prefixes with boolean networks, which are synchronized interconnections of boolean gates and one-bit storage devices. This complexity crucially depends upon a property of the underlying semigroup, which we call cycle-freedom (no cycle of length greater than one in the Cayley graph of the semigroup). Denoting by $S$ and $T$ size and computation time, respectively, we have $S = \Theta((N/T) \log(N/T))$, for non-cycle-free semigroups, and $S = \Theta((N/T)$, for cycle-free semigroups. In both cases, $T \in [\Omega(\logN),O(N)]$.

The prefix operation on a set of data is one of the simplest and most useful building blocks in parallel algorithms. This introduction to those aspects of parallel programming and parallel algorithms that relate to the prefix problem emphasizes its use in a broad range of familiar and important problems. The book illustrates how the prefix operation approach to parallel computing leads to fast and efficient solutions to many different kinds of problems. Students, teachers, programmers, and computer scientists will want to read this clear exposition of an important approach.

Containing over 300 entries in an A-Z format, the Encyclopedia of Parallel Computing provides easy, intuitive access to relevant information for professionals and researchers seeking access to any aspect within the broad field of parallel computing. Topics for this comprehensive reference were selected, written, and peer-reviewed by an international pool of distinguished researchers in the field. The Encyclopedia is broad in scope, covering machine organization, programming languages, algorithms, and applications. Within each area, concepts, designs, and specific implementations are presented. The highly-structured essays in this work comprise synonyms, a definition and discussion of the topic, bibliographies, and links to related literature. Extensive cross-references to other entries within the Encyclopedia support efficient, user-friendly searchers for immediate access to useful information. Key concepts presented in the Encyclopedia of Parallel Computing include; laws and metrics; specific numerical and non-numerical algorithms; asynchronous algorithms; libraries of subroutines; benchmark suites; applications; sequential consistency and cache coherency; machine classes such as clusters, shared-memory multiprocessors, special-purpose machines and dataflow machines; specific machines such as Cray supercomputers, IBM’s cell processor and Intel’s multicore machines; race detection and auto parallelization; parallel programming languages, synchronization primitives, collective operations, message passing libraries, checkpointing, and operating systems. Topics covered: Speedup, Efficiency, Isoefficiency, Redundancy, Amdahls law, Computer Architecture Concepts, Parallel Machine Designs, Benmarks, Parallel Programming concepts & design, Algorithms, Parallel applications. This authoritative reference will be published in two formats: print and online. The online edition features hyperlinks to cross-references and to additional significant research. Related Subjects: supercomputing, high-performance computing, distributed computing

Fault-Tolerant Parallel Computation presents recent advances in algorithmic ways of introducing fault-tolerance in multiprocessors under the constraint of preserving efficiency. The difficulty associated with combining fault-tolerance and efficiency is that the two have conflicting means: fault-tolerance is achieved by introducing redundancy, while efficiency is achieved by removing redundancy. This monograph demonstrates how in certain models of parallel computation it is possible to combine efficiency and fault-tolerance and shows how it is possible to develop efficient algorithms without concern for fault-tolerance, and then correctly and efficiently execute these algorithms on parallel machines whose processors are subject to arbitrary dynamic fail-stop errors. The efficient algorithmic approaches to multiprocessor fault-tolerance presented in this monograph make a contribution towards bridging the gap between the abstract models of parallel computation and realizable parallel architectures. Fault-Tolerant Parallel Computation presents the state of the art in algorithmic approaches to fault-tolerance in efficient parallel algorithms. The monograph synthesizes work that was presented in recent symposia and published in refereed journals by the authors and other leading researchers. This is the first text that takes the reader on the grand tour of this new field summarizing major results and identifying hard open problems. This monograph will be of interest to academic and industrial researchers and graduate students working in the areas of fault-tolerance, algorithms and parallel computation and may also be used as a text in a graduate course on parallel algorithmic techniques and fault-tolerance.

This book constitutes the refereed proceedings of the 16th Annual Symposium on Theoretical Aspects of Computer Science, STACS 99, held in Trier, Germany in March 1999. The 51 revised full papers presented were selected from a total of 146 submissions. Also included are three invited papers. The volume is divided in topical sections on complexity, parallel algorithms, computational geometry, algorithms and data structures, automata and formal languages, verification, algorithmic learning, and logic in computer science.