Edge-skeletons in arrangements with applications

An edge-skeleton in an arrangementA(H) of a finite set of planes inE 3 is a connected collection of edges inA(H). We give a method that constructs a skeleton inO(√n logn) time per edge. This method implies new and more efficient algorithms for a number of structures in computational geometry including order-k power diagrams inE 2 and space cutting trees inE 3. We also give a novel method for handling special cases which has the potential to substantially decrease the amount of effort needed to implement geometric algorithms.