Reachability in a Planar Subdivision with Direction Constraints

Antoine Vigneron

School of Electrical and Computer Engineering, UNIST, Ulsan, South Korea

School of Electrical and Computer Engineering, UNIST, Ulsan, South Korea

2018/3/27 Tue 5PM

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.