# Continuous Yao Graphs

Luis Barba,
Prosenjit Bose,
Jean-Lou De Carufel,
Mirel Damian,
Rolf Fagerberg,
André van Renssen,
Perouz Taslakian,
Sander Verdonschot

August 2014

### Abstract

In this paper, we introduce a variation of the well-studied Yao graphs. Given a set of points $S⊂ ℝ^2$ and an angle $0 < Θ łeq 2π$, we define the emphcontinuous Yao graph $y̧ao$ with vertex set $S$ and angle $Θ$ as follows. For each $p,qın S$, we add an edge from $p$ to $q$ in $a̧o$ if there exists a cone with apex $p$ and aperture $Θ$ such that $q$ is the closest point to $p$ inside this cone.

Publication

*Proceedings of the 25th Canadian Conference on Computational Geometry (CCCG 2014)*