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...
Let S be an ordered set of disjoint unit spheres in R3 . We show that if every subset of at most six spheres from S admits a line transversal respecting the ordering, then the ent...
We present a near linear time algorithm for constructing hierarchical nets in finite metric spaces with constant doubling dimension. This data-structure is then applied to obtain...