Reachability in a Planar Subdivision with Direction Constraints

Authors Daniel Binham, Pedro Machado Manhaes de Castro, Antoine Vigneron

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Daniel Binham
Pedro Machado Manhaes de Castro
Antoine Vigneron

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Daniel Binham, Pedro Machado Manhaes de Castro, and Antoine Vigneron. Reachability in a Planar Subdivision with Direction Constraints. In 33rd International Symposium on Computational Geometry (SoCG 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 77, pp. 17:1-17:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)


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 Omega(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.
  • Design and analysis of geometric algorithms
  • Path planning
  • Reachability


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