Approximating the Geometric Edit Distance

Authors Kyle Fox, Xinyi Li

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Author Details

Kyle Fox
  • The University of Texas at Dallas, USA
Xinyi Li
  • The University of Texas at Dallas, USA


The authors would like to thank Anne Driemel and Benjamin Raichel for helpful discussions.

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Kyle Fox and Xinyi Li. Approximating the Geometric Edit Distance. In 30th International Symposium on Algorithms and Computation (ISAAC 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 149, pp. 23:1-23:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Approximation algorithms analysis
  • Theory of computation → Computational geometry
  • Geometric edit distance
  • Approximation
  • Randomized algorithms


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