Abstract
We initiate the study of spanners under the Hausdorff and Fréchet distances. Let S be a set of points in Rd 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 ε1-Hausdorff-spanner of S and an ε2-Fréchet-spanner of S, where ε1 and ε2 are constants, such that neither of them is a t-spanner.
Original language | English |
---|---|
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