## Abstract

Given a curve P with points in R^{d} in a streaming fashion, and parameters ε > 0 and k, we construct a distance oracle that uses O(^{1}_{ε})^{kd} log ε^{−}^{1} space, and given a query curve Q with k points in R^{d}, returns in Õ(kd) time a 1 + ε approximation of the discrete Fréchet distance between Q and P. In addition, we construct simplifications in the streaming model, oracle for distance queries to a sub-curve (in the static setting), and introduce the zoom-in problem. Our algorithms work in any dimension d, and therefore we generalize some useful tools and algorithms for curves under the discrete Fréchet distance to work efficiently in high dimensions.

Original language | English |
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Title of host publication | ACM-SIAM Symposium on Discrete Algorithms, SODA 2021 |

Editors | Daniel Marx |

Publisher | Association for Computing Machinery |

Pages | 1150-1170 |

Number of pages | 21 |

ISBN (Electronic) | 9781611976465 |

State | Published - 2021 |

Externally published | Yes |

Event | 32nd Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2021 - Alexandria, Virtual, United States Duration: 10 Jan 2021 → 13 Jan 2021 |

### Publication series

Name | Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms |
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### Conference

Conference | 32nd Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2021 |
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Country/Territory | United States |

City | Alexandria, Virtual |

Period | 10/01/21 → 13/01/21 |

### Bibliographical note

Publisher Copyright:Copyright © 2021 by SIAM