Geodesic Spanners for Points on a Polyhedral Terrain

TL;DR

This paper demonstrates the existence of a geodesic spanner with nearly linear edges for points on a polyhedral terrain, improving efficiency in geometric network design.

Contribution

It introduces a new construction of geodesic spanners with almost linear size specifically for points on polyhedral terrains.

Findings

Existence of a geodesic spanner with nearly linear edges

Efficient geometric network design on terrains

Improved bounds over previous spanner constructions

Abstract

We show that there exists a geodesic spanner with almost linear number of edges.