Asymptotically Optimal Algorithms for Running Max and Min Filters on Random Inputs - 2018


Given a d-dimensional array of size n d and an integer p, the running max (or min) filter is the set of maximum (or minimum) components inside a d-dimensional sliding window of edge length p inside the array. This problem is useful in several Signal Processing applications like pattern analysis, adaptive Signal Processing, and morphological analysis. This best algorithm for computing the one-dimensional (one-D) max (or min) filter, due to the work of [H. Yuan and M. J. Atallah, “Running max/min filters using 1+o(1) comparisons per sample,” IEEE Trans. Pattern Anal. Mach. Intell., vol. thirty three, no. twelve, pp. 254four-2548, Dec. 2011], uses one+o(one) comparisons per sample in the worst case. As an immediate consequence, the d-dimensional max (or min) filter (max and min filters, respectively) can be computed in d+o(one) (2nd+o(1), respectively) comparisons per sample. In this Project, we have a tendency to 1st gift an algorithm for computing d-dimensional max and min filters simultaneously on i.i.d. inputs that uses one.5+o(one) expected comparisons per sample. This is the primary algorithm (on i.i.d. inputs) that takes out the dependence on d within the dominating term, with respect to n and p, of the (expected) number of comparisons required. It's conjointly asymptotically optimal (when d could be a mounted constant as n ? 8 and p ? eight). We also take into account the dynamic version of the matter of d-dimensional max and min filters simultaneously on i.i.d. inputs where we wish to keep up the filters when changes within the input array. We style a linear-sized information structure that stores precomputed data for efficient update using O(p d-one log2 p) expected comparisons per update.

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