M. Naor and O. Reingold, Synthesizers and their applications Proc. 36th IEEE Symposium on Foundations of Computer Science, 1995, pp. 170-- 181.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....(v; k; 1) BIBDs with k = 2; 3; 4 and 5 yield (n; m) quorum systems that are uniform of rank (roughly) c p n, where c 1:41; 1:23; 1:15 and 1:12, respectively. Various other constructions for (n; m) quorum systems that are uniform of rank c p n can be found in the literature; see, for example, [1, 2, 7, 9, 10, 12]. Most of these constructions have c = 2 or 1:41 (except for the finite projective plane construction from [10] and the difference cover construction from [9] which have c 1) 2 Attributes of quorum systems We discuss several figures of merit for quorum systems in this section, including ....

....L(pA ; Q) the load of the system (under the probability distribution p A ) measures the fraction of time that the busiest element in X is used under the probability distribution p A . In general, we choose the probability distribution p A so as to minimize the load. Therefore, Naor and Wool ([12]) defined the quantity L(Q) min p A L(pA ; Q) where the minimum is computed over all probability distributions p A . Another desirable property, especially when the elements in the system are all similar , is to balance the loads. The balancing ratio of the system (under the probability ....

M. Naor and A. Wool. The load, capacity and availiability of quorum systems. 35th IEEE Symposium on the Foundations of Computer Science, 1994, pp. 214--225.

....that are uniform of rank (roughly) c p n, where c 1:41; 1:23; 1:15 and 1:12, respectively. Note that by Theorem 2. 4 below, p n is the best possible) Various other constructions for (n; m) quorum systems that are uniform of rank c p n can be found in the literature; see, for example, [1, 2, 7, 9, 10, 12]. Most of these constructions have c = 2 or 1:41 (except for the finite projective plane construction from [10] and the difference cover construction from [9] which have c 1) 2 Attributes of quorum systems We discuss several measures of merit for quorum systems in this section, including ....

....L(pA ; Q) the load of the system (under the probability distribution p A ) measures the fraction of time that the busiest element in X is used under the probability distribution p A . In general, we choose the probability distribution p A so as to minimize the load. Therefore, Naor and Wool ([12]) defined the quantity L(Q) min p A L(pA ; Q) where the minimum is computed over all probability distributions p A . Another desirable property, especially when the elements in the system are all similar , is to balance the loads. The balancing ratio of the system (under the probability ....

M. Naor and A. Wool. The load, capacity and availability of quorum systems. 35th IEEE Symposium on the Foundations of Computer Science, 1994, pp. 214--225.

....learning finite automata with an evaluator is related to the noisy parity problem, but it is not clear whether hardness based on standard cryptographic assumptions can be shown or what is the status of learning such distributions with a generator. The recent construction of synthesizers in NC 1 [24] seems related, but we have not been able to use it. Acknowledgments I would like to thank Ronitt Rubinfeld for introducing me to this area and Oded Goldreich and Dan Roth for several useful discussions and suggestions. ....

M. Naor and O. Reingold, Synthesizers and their applications Proc. 36th IEEE Symposium on Foundations of Computer Science, 1995, pp. 170-- 181.

....as a function of its immediate neighborhood only. In particular for graphs with degree bounded by some constant, the best known bound on c 0 is c 0 = O(log log c) obtained by a nonconstructive solution of Szegedy and Vishwanathan [32] By applying a construction of certain set systems in [25, 27], we obtain a constructive color reduction method, closely related to the one of [32] also having c 0 = O(log log c) The solutions are not restricted to constant degree graphs. In Section 8 we discuss how c 0 depends on both c and the degree. 1.1 Related work We now survey several lines ....

.... From a d wise ffl bias probability space with m random variables we can get a d intersection independent collection: ffl k = size of probability space ffl points of probability space = elements of ground set B = f1; kg ffl S i = fall points such that X i = 1g Recently Naor et al. [27] showed a better construction for d intersection independent collections which is of size d O(logd) 2 d log m. The disadvantage of their construction is that it is a global one, in the sense that all the sets must be constructed together by a sequential algorithm of complexity similar to the ....

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M. Naor, L. J. Schulman, and A. Srinivasan, Splitters and near-optimal derandomization, Proc. 36th IEEE Symposium on Foundations of Computer Science, 1995, pp. 182-- 191.

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