Approximating the Geometric Edit Distance

Kyle Fox, Xinyi Li, Michael Wagner
2019 International Symposium on Algorithms and Computation  
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
more » ... nal Euclidean space. Specifically, we present a randomized O(n log 2 n) time O( √ n)-approximation algorithm. Then, we generalize our result to give a randomized α-approximation algorithm for any α ∈ [1, √ n], running in timeÕ(n 2 /α 2 ). Both algorithms are Monte Carlo and return approximately optimal solutions with high probability. Experimental comparison of representation methods and distance measures for time series data. Data Mining and Knowledge Discovery, 26(2):275-309, 2013.
doi:10.4230/lipics.isaac.2019.23 dblp:conf/isaac/FoxL19 fatcat:tr7v27tcqvhqjporsle6pogdtu