## Abstract

We initiate the study of spanners under the Hausdorff and Fréchet distances. Let S be a set of points in R^{d} and ε a non-negative real number. A subgraph H of the Euclidean graph over S is an ε-Hausdorff-spanner (resp., an ε-Fréchet-spanner) of S, if for any two points u,v∈S there exists a path P(u,v) in H between u and v, such that the Hausdorff distance (resp., the Fréchet distance) between P(u,v) and uv‾ is at most ε. We show that any t-spanner of a planar point-set S is a [Formula presented]}-Fréchet spanner. We also prove that for any t>1, there exist a set of points S and an ε_{1}-Hausdorff-spanner of S and an ε_{2}-Fréchet-spanner of S, where ε_{1} and ε_{2} are constants, such that neither of them is a t-spanner.

Original language | English |
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Article number | 106513 |

Journal | Information Processing Letters |

Volume | 187 |

DOIs | |

State | Published - 1 Jan 2025 |

## Keywords

- Computational geometry
- Fréchet distance
- Geometric spanners

## ASJC Scopus subject areas

- Theoretical Computer Science
- Signal Processing
- Information Systems
- Computer Science Applications