Vertex removal in two-dimensional Delaunay triangulation: Speed-up by low degrees optimization

Abstract

The theoretical complexity of vertex removal in a Delaunay triangulation is often given in terms of the degree d of the removed point, with usual results O ( d ) , O ( d log d ) , or O ( d 2 ) . In fact, the asymptotic complexity is of poor interest since d is usually quite small. In this paper we carefully design code for small degrees 3 ⩽ d ⩽ 7 , it improves the global behavior of the removal for random points by more than 45%.