KAIST Discrete Math Seminar

Given a planar subdivision with n vertices, each face having a cone of possible directions of travel, our goal is to decide which vertices of the subdivision can be reached from a given starting point s. We give an O(n log n)-time algorithm for this problem, as well as an Ω(n log n) lower bound in the algebraic computation tree model. We prove that the generalization where two cones of directions per face are allowed is NP-hard.

We show that the Gromov hyperbolicity of a discrete metric space at a fixed base-point cannot be computed in O(n^2.05) time, unless there exists a faster algorithm for (max,min) matrix multiplication algorithm than is currently known.