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 -proces
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...
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 ...
Evaluating these circuits is known to be a P-complete problem and thus, in the worst case, believed to be impossible to perform, even given a massively parallel computer, in time much less than the depth of the circuit. Nonetheless, it is found that for some ensembles of random circuits,...
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/...
We present a technique for analyzing the number of cache misses incurred by multithreaded cache oblivious algorithms on an idealized parallel machine in which each processor has a private cache. We specialize this technique to computations executed by the Cilk work-stealing scheduler on a machine ...
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 ...
For modular multiplication in finite field arithmetic, a variety of multipliers have been suggested. Mastrovito multiplier performs parallel multiplication [5]. Multipliers based on the first LSB and MSB algorithms are used to perform the multiplication starting from the operand’s least significant and...