Approximating the Geometric Edit Distance

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(n log(2) n) time O(root n)-approximation algorithm. Then, we generalize our result to give a randomized alpha-approximation algorithm for any alpha is an element of[root log n, root n/log n] running in time O (n(2)/alpha(2) log n). Both algorithms are Monte Carlo and return approximately optimal solutions with high probability.