The paper presents a new method of investigating topological properties of three-dimensional manifolds by means of computers. Manifolds are represented as finite cell complexes. Th...
This paper addresses the complexity of computing the smallest-radius infinite cylinder that encloses an input set of n points in 3-space. We show that the problem can be solved in...
We present algorithms for constructing a hierarchy of increasingly coarse Morse complexes that decompose a piecewise linear 2-manifold. While Morse complexes are defined only in t...
Given a simple polygon in the plane with two distinguished vertices, s and g, is it possible for two guards to simultaneously walk along the two boundary chains from s to g in suc...
We initiate the study of exact geometric algorithms that require limited storage and make only a small number of passes over the input. Fundamental problems such as lowdimensional...