A Quadratic Time Algorithm for the Minmax Length Triangulation

Abstract

It is shown that a triangulation of a set of n points in the plane that minimizes the maximum edge length can be computed in time $O(n^2 )$. The algorithm is reasonably easy to implement and is based on the theorem that there is a triangulation with minmax edge length that contains the relative neighborhood graph of the points as a subgraph. With minor modifications the algorithm works for arbitrary normed metrics.