M. Dietzfelbinger, M. Kuty/lowski, and R. Reischuk, "Exact Time Bounds for Computing Boolean Functions without Simultaneous Writes", Proc. Second Annual ACM Symposium on Parallel Algorithms and Architectures, 1990, pages 125-135.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... every previously studied concurrent read concurrentwrite (CRCW) PRAM can easily compute the OR of n Boolean variables in constant time using n processors, whereas Omega (log n) steps are necessary for the concurrent read exclusive write (CREW) PRAM, even with an unbounded number of processors [2, 3]. It is unknown whether the ROBUST PRAM can compute OR any faster than the CREW PRAM. More generally, it is not known whether this very weak form of concurrent write is useful for deterministically computing any function over a complete domain. We address the question of the relative power of the ....

..... In Section 4, we present a new randomized ROBUST PRAM algorithm that uses only O(log n) time and n= log n) processors and has error probability 2 GammaO(2 (log n) 4 ) In contrast, even with an unlimited number of processors, the randomized CREW PRAM requires Omega (log n) steps [3]. Together with our lower bounds, these results prove a separation between the deterministic and randomized ROBUST PRAM. For the CREW PRAM, no such separation exists, since randomization provides no more than a factor of 8 in speedup over the deterministic model [3] Throughout this paper, we use ....

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M. Dietzfelbinger, M. Kuty/lowski, and R. Reischuk, "Exact Time Bounds for Computing Boolean Functions without Simultaneous Writes", Proc. Second Annual ACM Symposium on Parallel Algorithms and Architectures, 1990, pages 125-135.

....n) 2 ) steps using O(n= log n) 2 ) processors with o(1) probability of error. Thus, adding randomization increases the computational power of the ROBUST PRAM. This is in contrast to the situation for the CREW PRAM, where adding randomization can at best decrease time by a constant factor [3]. 1 Introduction A parallel random access machine (PRAM) that allows concurrent writes must specify how to resolve write conflicts when they occur. One method is to let an adversary determine what value appears [1] In other words, an algorithm must compute the correct answer no matter what ....

..... In Section 4, we present a new randomized ROBUST PRAM algorithm that uses only O( log n) 2 ) time and n= log n) 2 processors and has o(1) error probability. In contrast, even with randomization and an unlimited number of processors, the CREW PRAM requires Omega Gammaqui n) steps [3]. Together with our lower bounds, these results prove a separation between the deterministic and randomized ROBUST PRAM (and fixed adversary PRAMs) For the CREW PRAM, no such separation exists, since randomization provides no more than a factor of 8 in speedup over the deterministic model [3] ....

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M. Dietzfelbinger, M. Kuty/lowski, and R. Reischuk, "Exact Time Bounds for Computing Boolean Functions without Simultaneous Writes", Proceedings of the Second Annual ACM Symposium on Parallel Algorithms and Architectures, 1990, pages 125-135.

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