Reif, J. H. Probabilistic parallel prefix computation. Proc.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....n) time using O(n log n) EREW processors, each capable of performing the binary operation of the prefix computation in constant time. Some prefix operations can be performed even more e#ciently. Prefix maximum may be performed in O(log log n) time, using linear weak CRCW operations [60] Reif [58] showed that certain prefix computations can be performed in O(log log n) expected time, again with O(n) operations. The result is deterministic, but for the average case in which the inputs are drawn from a random distribution. It does not work for prefix addition, but it does for other ....

J.H. Reif, Probabilistic Parallel Prefix Computation. Manuscript.

....version of the knapsack evolutionary algorithm have demonstrated significantly better optimization performance than genetic algorithms. Parallel probabilistic algorithms have found diverse applications in computational biology [14] inference [6] simulation [16] sorting [15] prefix computation [11]. Research in theory of probabilistic algorithms [12, Ch. VII] has been concentrated on algorithms that solve problems exactly for poly logarithmic expected running time. Probabilistic algorithms from this class have been proposed for a variety of problems, such as parallel prefixes, sorting, ....

Reif J. H. Probabilistic Parallel Prefix Computation, Computers and Mathematics with Applications, 26, No 1, 1993, 101-110.

....problems. In particular, we show that for a given circuit C and a bound t the question 9x timeC (x) t is NP complete. This also holds for logarithmic depth bounded circuits. The time of a circuit depends on the input. This way it is possible to investigate the average behavior of circuits. In [Reif93] a circuit for addition of n bit numbers (ADDn ) is presented which is expected log log n time bounded with respect to the uniform distribution. Broader classes of distributions are investigated in [JRS93] Here special depth bounded distribution generating circuits with coin tossed inputs are ....

....arbitrary additive constant in polynomial time. Such a approximation rate is extraordinary, since normally approximation rate is measured by a factor. 5 Conclusion Recent research in average compexity theory of circuit was directed towards the classification of Boolean functions. First results [JRS93, Reif93] analyzed upper and lower bounds for basic functions. Later more sophisticated analysis was done to find more general bounds for the expected time [JRSW93, JRS95] Even for simple functions these analyses turned out to be quite complicated. For many functions this approach seems hopeless. For a ....

J. Reif, Probabilistic Parallel Prefix Computation, Comp. Math. Applic. 26, 1993, 101-110.

....there is an exponential speedup from the worst case to the average case. On the other hand, for functions like PARITY or MAJORITY no speedup is possible. Expected case upper bounds of order O(llog n) for the addition and other prefix problems have also been obtained by Reif for a different model [Rei93]. He observed that circuit depth O(llog n) ist sufficient if one allows a small portion of input vectors for which a wrong result will be obtained. The aim of this paper is to study the relation between the average case complexity of the parallel prefix problem and the underlying semigroup in ....

J. Reif, Probabilistic Parallel Prefix Computation, Comp. Math. Applic. 26, 1993, 101-110.

....the literature. Expected case upper bounds of order O(log log n) supported by DFG Research Grant Re 672 2 y Institut fur Theoretische Informatik, Wallstra e 40, 23560 Lubeck, Germany email: jakoby informatik.mu luebeck.de for the addition and other prefix problems have also been obtained in [Reif93] and [JRSW94] Reif has observed that circuit depth O(log log n) is sufficient if one allows a small portion of input vectors for which a wrong result may be obtained. He has also introduced a circuit that supervises these errors and corrects them but this requires one gate of unbounded fanin ....

J. Reif, Probabilistic Parallel Prefix Computation, Comp. Math. Applic. 26, 1993, 101-110.

.... delay for addition and similar prefix problems by circuits of linear size [JRSW93] as it was obtained by Ladner Fischer for the worst case [LaFi80] Expected case upper bounds of order O(llog n) for the addition and other prefix problems have also been obtained by Reif for a different model [Reif93]. He observed that circuit depth O(llog n) is sufficient if one allows a small portion of input vectors for which a wrong result will be obtained. Conbining such a circuit with a worst case circuit of depth O(log n) that is always correct and using one gate of unbounded fanin a circuit with ....

J. Reif, Probabilistic Parallel Prefix Computation, Comp. Math. Applic. 26, 1993, 101-110.

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Reif, J. H. Probabilistic parallel prefix computation. Proc.

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. J. Reif. Probabilistic parallel prefix computation. Proc. of

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. J. H. Reif. Probabilistic parallel prefix computation, Proc. of 1984.

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. J. H. Reif. Probabilistic parallel prefix computation, Proc. of 1984.

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