2026-08-11T03:24:37Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:11519 2024-03-06T10:48:12Z ddc:004 open_access

Approximating the Geometric Edit Distance Fox, Kyle Li, Xinyi Geometric edit distance Approximation Randomized algorithms 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^2n) time O(sqrt n)-approximation algorithm. Then, we generalize our result to give a randomized alpha-approximation algorithm for any alpha in [1, sqrt n], running in time O~(n^2/alpha^2). Both algorithms are Monte Carlo and return approximately optimal solutions with high probability. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Kyle Fox and Xinyi Li 2019 Is Part Of LIPIcs, Volume 149, 30th International Symposium on Algorithms and Computation (ISAAC 2019) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.ISAAC.2019.23 urn:nbn:de:0030-drops-115195 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2019.23 eng https://creativecommons.org/licenses/by/3.0/legalcode