Approximating the Geometric Edit Distance

10/02/2019

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by   Kyle Fox, et al.

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Edit distance is a measurement of similarity between two sequences such as strings, point sequences, or polygonal curves. Many matching problems from a variety of areas, such as signal analysis, bioinformatics, etc., need to be solved in a geometric space. Therefore, the geometric edit distance (GED) has been studied. In this paper, we describe the first strictly sublinear approximate near-linear time algorithm for computing the GED of two point sequences in constant dimensional Euclidean space. Specifically, we present a randomized (O(nlog^2n)) time (O(√(n)))-approximation algorithm. Then, we generalize our result to give a randomized α-approximation algorithm for any α∈ [1, √(n)], running in time Õ(n^2/α^2). Both algorithms are Monte Carlo and return approximately optimal solutions with high probability.