Spanners under the Hausdorff and Fréchet distances

Tsuri Farhana, Matthew J. Katz

Research output: Contribution to journalArticlepeer-review

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 languageAmerican English
Article number106513
JournalInformation Processing Letters
Volume187
DOIs
StatePublished - 1 Jan 2025

Keywords

  • Computational geometry
  • Fréchet distance
  • Geometric spanners

All Science Journal Classification (ASJC) codes

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

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