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 variety areas, signal analysis, bioinformatics, etc., need to be solved in geometric space. Therefore, the edit (GED) has been studied. In this paper, we describe first strictly sublinear approximate near-linear time algorithm for computing GED constant dimensional Euclidean Specifically, present randomized $$O(n\log ^2n)$$ $$O(\sqrt{n})$$ -approximation algorithm. Then, generalize our result give $$\alpha $$ any \in [\sqrt{\log n}, \sqrt{n/\log n}]$$ , running $$O(n^2/\alpha ^2 \log n)$$ . Both algorithms are Monte Carlo and return approximately optimal solutions with high probability.