A randomized online quantile summary in $O(\frac{1}{\varepsilon} \log \frac{1}{\varepsilon})$ words
نویسندگان
چکیده
A quantile summary is a data structure that approximates to ε-relative error the order statistics of a much larger underlying dataset. In this paper we develop a randomized online quantile summary for the cash register data input model and comparison data domain model that uses O( 1 ε log 1 ε ) words of memory. This improves upon the previous best upper bound of O( 1 ε log 1 ε ) by Agarwal et. al. (PODS 2012). Further, by a lower bound of Hung and Ting (FAW 2010) no deterministic summary for the comparison model can outperform our randomized summary in terms of space complexity. Lastly, our summary has the nice property that O( 1 ε log 1 ε ) words suffice to ensure that the success probability is 1 − e−poly(1/ε).
منابع مشابه
Efficient Approximation Algorithms for Point-set Diameter in Higher Dimensions
We study the problem of computing the diameter of a set of $n$ points in $d$-dimensional Euclidean space for a fixed dimension $d$, and propose a new $(1+varepsilon)$-approximation algorithm with $O(n+ 1/varepsilon^{d-1})$ time and $O(n)$ space, where $0 < varepsilonleqslant 1$. We also show that the proposed algorithm can be modified to a $(1+O(varepsilon))$-approximation algorithm with $O(n+...
متن کاملCharacterization of $(delta, varepsilon)$-double derivation on rings and algebras
This paper is an attempt to prove the following result:Let $n>1$ be an integer and let $mathcal{R}$ be a $n!$-torsion-free ring with the identity element. Suppose that $d, delta, varepsilon$ are additive mappings satisfyingbegin{equation}d(x^n) = sum^{n}_{j=1}x^{n-j}d(x)x^{j-1}+sum^{n-1}_{j=1}sum^{j}_{i=1}x^{n-1-j}Big(delta(x)x^{j-i}varepsilon(x)+varepsilon(x)x^{j-i}delta(x)Big)x^{i-1}quadend{e...
متن کاملA path following interior-point algorithm for semidefinite optimization problem based on new kernel function
In this paper, we deal to obtain some new complexity results for solving semidefinite optimization (SDO) problem by interior-point methods (IPMs). We define a new proximity function for the SDO by a new kernel function. Furthermore we formulate an algorithm for a primal dual interior-point method (IPM) for the SDO by using the proximity function and give its complexity analysis, and then we sho...
متن کاملDeterministic Approximate Counting of Depth-2 Circuits
We describe deterministic algorithms which for a given depth-2 circuit $F$ approximate the probability that on a random input $F$ outputs a specific value $\alpha$. Our approach gives an algorithm which for a given $GF[2]$ multivariate polynomial $p$ and given $\varepsilon >0$ approximates the number of zeros of $p$ within a multiplicative factor $1+ \varepsilon$. The algorithm runs in time $ex...
متن کاملA randomized online quantile summary in O(1/ɛ log 1/ɛ) words
A quantile summary is a data structure that approximates to ε-relative error the order statistics of a much larger underlying dataset. In this paper we develop a randomized online quantile summary for the cash register data input model and comparison data domain model that uses O( ε log 1 ε ) words of memory. This improves upon the previous best upper bound of O( ε log 3/2 1 ε ) by Agarwal et a...
متن کامل