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arXiv · 1803.02979

Routing on the Visibility Graph

Prosenjit Bose·Matias Korman·André van Renssen·Sander Verdonschot
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Abstract

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.

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Prosenjit Bose, Matias Korman, André van Renssen, Sander Verdonschot. 2019-01-02. Routing on the Visibility Graph. https://doi.org/10.20382/jocg.v9i1a15

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