Routing on the Visibility Graph

@article{Bose2017RoutingOT,
  title={Routing on the Visibility Graph},
  author={Prosenjit Bose and Matias Korman and Andr{\'e} van Renssen and Sander Verdonschot},
  journal={ArXiv},
  year={2017},
  volume={abs/1803.02979}
}
We consider the problem of routing on a network in the presence of line segment constraints (i.e., obstacles that edges in our network are not allowed to cross). Let $P$ be a set of $n$ points in the plane and let $S$ be a set of non-crossing line segments whose endpoints are in $P$. We present two deterministic 1-local $O(1)$-memory routing algorithms that are guaranteed to find a path of at most linear size between any pair of vertices of the \emph{visibility graph} of $P$ with respect to a… 
Constrained Routing Between Non-Visible Vertices
TLDR
This work presents the first 1-local O(1)-memory routing algorithm on the visibility graph of P with respect to a set of constraints S and shows that when routing on any triangulation T of P such that \(S\subseteq T\), no o(n)-competitive routing algorithm exists when only considering the triangles intersected by the line segment from the source to the target.
Bounded-Degree Spanners in the Presence of Polygonal Obstacles
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