The technique of randomization has been employed to solve numerous prob lems of computing both sequentially and in parallel. Examples of randomized algorithms that are asymptotically better than their deterministic counterparts in solving various fundamental problems abound. Randomized algorithms have the advantages of simplicity and better performance both in theory and often is a collection of articles written by renowned experts in practice. This book in the area of randomized parallel computing. A brief introduction to randomized algorithms In the analysis of algorithms, at least three different measures of performance can be used: the best case, the worst case, and the average case. Often, the average case run time of an algorithm is much smaller than the worst case. 2 For instance, the worst case run time of Hoare's quicksort is O(n ), whereas its average case run time is only O(nlogn). The average case analysis is conducted with an assumption on the input space. The assumption made to arrive at the O(n logn) average run time for quicksort is that each input permutation is equally likely. Clearly, any average case analysis is only as good as how valid the assumption made on the input space is. Randomized algorithms achieve superior performances without making any assumptions on the inputs by making coin flips within the algorithm. Any analysis done of randomized algorithms will be valid for all possible inputs.

Transformational programming and parallel computation are two emerging fields that may ultimately depend on each other for success. Perhaps because ad hoc programming on sequential machines is so straightforward, sequential programming methodology has had little impact outside the academic community, and transformational methodology has had little impact at all. However, because ad hoc programming for parallel machines is so hard, and because progress in software construction has lagged behind architectural advances for such machines, there is a much greater need to develop parallel programming and transformational methodologies.Parallel Algorithm Derivation and Program Transformation stimulates the investigation of formal ways to overcome problems of parallel computation, with respect to both software development and algorithm design. It represents perspectives from two different communities: transformational programming and parallel algorithm design, to discuss programming, transformational, and compiler methodologies for parallel architectures, and algorithmic paradigms, techniques, and tools for parallel machine models.Parallel Algorithm Derivation and Program Transformation is an excellent reference for graduate students and researchers in parallel programming and transformational methodology. Each chapter contains a few initial sections in the style of a first-year, graduate textbook with many illustrative examples. The book may also be used as the text for a graduate seminar course or as a reference book for courses in software engineering, parallel programming or formal methods in program development.

Transformational programming and parallel computation are two emerging fields that may ultimately depend on each other for success. Perhaps because ad hoc programming on sequential machines is so straightforward, sequential programming methodology has had little impact outside the academic community, and transformational methodology has had little impact at all. However, because ad hoc programming for parallel machines is so hard, and because progress in software construction has lagged behind architectural advances for such machines, there is a much greater need to develop parallel programming and transformational methodologies. Parallel Algorithm Derivation and Program Transformation stimulates the investigation of formal ways to overcome problems of parallel computation, with respect to both software development and algorithm design. It represents perspectives from two different communities: transformational programming and parallel algorithm design, to discuss programming, transformational, and compiler methodologies for parallel architectures, and algorithmic paradigms, techniques, and tools for parallel machine models.Parallel Algorithm Derivation and Program Transformation is an excellent reference for graduate students and researchers in parallel programming and transformational methodology. Each chapter contains a few initial sections in the style of a first-year, graduate textbook with many illustrative examples. The book may also be used as the text for a graduate seminar course or as a reference book for courses in software engineering, parallel programming or formal methods in program development.