Efficient One Sided Kolmogorov Approximation

Liat Cohen; Tal Grinshpoun; Gera Weiss

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arXiv · 2207.07916

Efficient One Sided Kolmogorov Approximation

Liat Cohen·Tal Grinshpoun·Gera Weiss

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Abstract

We present an efficient algorithm that, given a discrete random variable $X$ and a number $m$, computes a random variable whose support is of size at most $m$ and whose Kolmogorov distance from $X$ is minimal, also for the one-sided Kolmogorov approximation. We present some variants of the algorithm, analyse their correctness and computational complexity, and present a detailed empirical evaluation that shows how they performs in practice. The main application that we examine, which is our motivation for this work, is estimation of the probability missing deadlines in series-parallel schedules. Since exact computation of these probabilities is NP-hard, we propose to use the algorithms described in this paper to obtain an approximation.

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BibTeX RIS

Liat Cohen, Tal Grinshpoun, Gera Weiss. 2022-07-14. Efficient One Sided Kolmogorov Approximation. https://arxiv.org/abs/2207.07916

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