Ajtai et al . showed that probabilistic algorithms can achieve a slightly better approximation factor of \ beta = 2 ^ { O ( n \ log \ log n / \ log n ) }.
22.
If we allow both bounded-error quantum and classical algorithms, then there is no speedup since a classical probabilistic algorithm can solve the problem with a constant number of queries with small probability of error.
23.
"' OptiY "'is a design environment providing modern optimization strategies and state of the art probabilistic algorithms for uncertainty, reliability, robustness, sensitivity analysis, data-mining and meta-modeling.
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Second, the paper you've cited shows a probabilistic algorithm for polynomial factorization which runs in time polynomial in n ( the degree of the polynomial ) and in log ( q ) ( over Z _ q ).
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Such problems cannot be approximated to any multiplicative factor by a bounded-error probabilistic algorithm unless NP = RP, because any multiplicative approximation would distinguish the values 0 and 1, effectively solving the decision version in bounded-error probabilistic polynomial time.
26.
A . Pandey, S . Kushwaha, P . Gupta and C . J . Hwang, A Weighted Probabilistic Algorithm for Cluster based Mobile Ad Hoc Networks , Proceedings of IASTED International conference on Wireless Networks & Emerging Technologies ( WNET 2003 ) held at Banff, Canada, July 2003.
27.
PCMOS-based system on a chip architectures were shown to be gains that are as high as a substantial multiplicative factor of 560 when compared to a competing energy-efficient CMOS based realization on applications based on probabilistic algorithms such as hyper-encryption, bayesian networks, random neural networks and probabilistic cellular automata.
28.
Especially, Absolute best-digit rational bounds / approximations for irrational numbers : Pre-and super-computer era ( permits use of irrational numbers in error-free computation in the best ( most accurate ) way; earlier entry of irrational numbers in error-free computation was not thought over ), Quasi-and pseudo-random number generators : their scope, Probabilistic algorithms ( allows deterministically exponential / intractable computational problems to be solved in polynomial-time ), Numerical analysis ( provides us appropriate algorithms for a given problem with the knowledge of quality and cost of the numerical solution ), Computational error and computational complexity including error in error-free computations ( any numerical computation must be accompanied by computational error and computational complexity and not the theoretical error and complexity ), The problem of error in error-free computations has not been explored earlier.
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