Download PDF by Nathan J. Muller: Bluetooth Demystified

By Nathan J. Muller

Bluetooth is a instant networking commonplace that enables seamless verbal exchange of voice, electronic mail and such like. This consultant to Bluetooth is helping to determine if it truly is correct in your services. It info the strengths and weaknesses of Bluetooth and has insurance of functions and items.

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Extra info for Bluetooth Demystified

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Some empirical and special-case analysis is shown in [164] that the space used is closer to O(1/ε). Note There is a strong relationship between the (φ, ε)-quantiles and (φ, ε)heavy hitters problems. • Using (φ, ε/2)-quantiles will retrieve the (φ, ε)-heavy hitters. • Consider a partition of the universe 1 · · · N into log N problems, ith of which comprises N/2i disjoint intervals of size 2i – called dyadic intervals – covering [1, N ]. Use (φ/ log N, ε/ log N )-heavy hitters in each of these subproblems.

Combining the two steps: Theorem 10. [61] There exists a randomized O(1/ε2 ) log N log(1/δ)) space algorithm that with probability at least 1 − δ, returns an estimate for any A−1 [i] correct to ±ε. The sampling procedure above can be extended to the turnstile case too: the crux is in maintaining the unique element that maps to 0 under the hash function at any given time even if at times earlier, many items were mapped to 0 but subsequently removed. Independently, solutions have been proposed for this in [95] and [61].

Log2 N } such that Pr[f (i) = j] = 2−j . Any update j to item i sets c[f (i)] to 1. At any point, an unbiased estimate for the number of distinct items is given by 2k(c) , where k(c) is the lowest index of a counter c[j] that is zero (k = min{j | c[j] = 0}). Intuitively this procedure works because if the probability that any item is mapped onto counter j is 2−j , then if there are D distinct items, we expect D/2 to be mapped to c[1], D/4 to be mapped to c[2], and so on until there are none in c[log2 D].

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Bluetooth Demystified by Nathan J. Muller

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