• DOI:10.20382/jocg.v9i1a15
• Corpus ID: 3750150

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}
}

• P. Bose, Matias Korman, +1 author S. Verdonschot
• Published 8 March 2018
• Computer Science
• ArXiv

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 set of constraints $S$ (i.e., the algorithms never look beyond the direct neighbours of the current location and store only a constant amount of additional information). Contrary to {\em all} existing deterministic local routing algorithms, our routing algorithms do not route on a plane subgraph of the visibility graph. Additionally, we provide lower bounds on the routing ratio of any deterministic local routing algorithm on the visibility graph.