License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ISAAC.2019.23
URN: urn:nbn:de:0030-drops-115195
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2019/11519/
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Fox, Kyle ; Li, Xinyi

Approximating the Geometric Edit Distance

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LIPIcs-ISAAC-2019-23.pdf (0.6 MB)

Abstract

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.

BibTeX - Entry

@InProceedings{fox_et_al:LIPIcs:2019:11519,
  author =	{Kyle Fox and Xinyi Li},
  title =	{{Approximating the Geometric Edit Distance}},
  booktitle =	{30th International Symposium on Algorithms and Computation (ISAAC 2019)},
  pages =	{23:1--23:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-130-6},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{149},
  editor =	{Pinyan Lu and Guochuan Zhang},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2019/11519},
  URN =		{urn:nbn:de:0030-drops-115195},
  doi =		{10.4230/LIPIcs.ISAAC.2019.23},
  annote =	{Keywords: Geometric edit distance, Approximation, Randomized algorithms}
}

Keywords: Geometric edit distance, Approximation, Randomized algorithms
Collection: 30th International Symposium on Algorithms and Computation (ISAAC 2019)
Issue Date: 2019
Date of publication: 28.11.2019

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