RECENT RESULTS ON THE GEOMETRIC DILATION PROBLEM IN NORMED PLANES
Keywords:
arc length, area-halving distance, Birkhoff orthogonality, convex curve, geometric dilation, halving distance, halving pair, isosceles orthogonality, midpoint curve, Minkowski plane, normed plane, Zindler curve
Abstract
Let G be a planar simple graph. For any two points p, q ∈ G, the ratio of the distance between p and q on the graph G to the distance between these two points is called the detour between p and q. The worst-case detour δ(G) of a graph G is called the geometric dilation of G. The geometric dilation problem in the Euclidean plane asks for a simple planar graph with smallest geometric dilation to embed a given finite set S. In this paper we discuss recent results concerning the extension of the geometric dilation problem from the Euclidean plane to general normed (or Minkowski) planes.
Published
2019-07-12
Section
Articles
