Suppose we know W(e) and D(e) and our platform has P parallel threads Regardless of P, cannot finish sooner thanD(e)because of dependencies Regardless of D(e), cannot finish sooner than\frac{W(e)}{P}: every piece of work needs to be done So it is reasonable to use this estimate...
The complexity of serial algorithms is usually measured by the number of arithmetic operations. But the complexity of parallel algorithms is measured by the time, in which they can be implemented on a k -processor computer.doi:10.1007/978-3-662-11106-2_2Jozef Mikloško...
Recently, processor efficiency of the previous parallel algorithms for numerical matrix inversion has been substantially improved in (Pan and Reif, 1987), reaching optimum estimates up to within a logarithmic factor; that work, however, applies neither to the evaluation of the determinant and the ...
Types for Complexity of Parallel Computation in Pi-Calculus Patrick Baillot1 and Alexis Ghyselen1 Univ Lyon, CNRS, ENS de Lyon, Universite Claude-Bernard Lyon 1, LIP, F-69342, Lyon Cedex 07, France alexis.ghyselen@ens-lyon.fr Abstract. Type systems as a technique to analyse or control ...
They cover all important areas of research on algorithms and complexity such as algorithm design and analysis; sequential, parallel and distributed algorithms; data structures; computational and structural complexity; lower bounds and limitations of algorithms; randomized and approximation algorithms; ...
This chapter is an introduction to the area of parallel computation written in accordance with the guidelines for the CRC HANDBOOK ON ALGORITHMS AND THEORY OF COMPUTATION where it will appear. References to chapters refer to other chapters in this book. This research partially supported by National...
Namely we consider optimization algorithms interacting with a highly parallel gradient oracle, that is one that can answer poly(d) gradient queries in parallel. We show that in this case gradient descent is optimal only up to O(d~(1/2)) rounds of interactions with the oracle. The lower ...
Traditionally, the bulk of complexity theory has gone into the complexity of sequential computation, but parallel computation is getting more and more attention in both theory and practice. Parallel computing faces several additional issues such as the question of the amount of parallel processors requi...
Quadrant Interlocking splittingshared memory computerIn this paper the Quadrant Interlocking (QI) matrix splitting is shown to yield parallel iterative methods for the solution of linear equations with improved convergence rates for both synchronous and asynchronous versions of the algorithms.doi:10.1080/...
Treewidth was introduced by Robertson and Seymour [9], and it has proved to be a useful tool in the design of graph algorithms. Bodlaen- der and Hagerup [4] showed that there exists an optimal parallel algorithm on a E R E W PRAM using C9((log n) 2) time and O(n) space ...