Nearest Neighbour Graph and Locally Minimal Triangulation

Abstract

Nearest neighbour graph (NNG) is a useful tool namely for collision detection tests. It is well known that NNG, when considered as an undirected graph, is a subgraph of Delaunay triangulation (DT) and this relation can be used for efficient NNG computation. This paper concentrates on relation of NNG to the locally minimal triangulation (LMT) and shows that, although NNG can be proved not to be a LMT subgraph, in most cases LMT contains all or nearly all NNG edges. This fact can also be used for NNG computation, namely in kinetic problems, because LMT computation is easier.