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6 papers · 2 filters
Competitive Local Routing with Constraints
Prosenjit Bose, Rolf Fagerberg, André van Renssen +1
Let be a set of vertices in the plane and a set of non-crossing line segments between vertices in , called constraints. Two vertices are visible if the straight line…
Higher-Order Triangular-Distance Delaunay Graphs: Graph-Theoretical Properties
Ahmad Biniaz, Anil Maheshwari, Michiel Smid
We consider an extension of the triangular-distance Delaunay graphs (TD-Delaunay) on a set of points in the plane. In TD-Delaunay, the convex distance is defined by a fixed-ori…
Continuous Yao Graphs
Luis Barba, Prosenjit Bose, Jean-Lou De Carufel +5
In this paper, we introduce a variation of the well-studied Yao graphs. Given a set of points and an angle , we define the continuous Yao grap…
Theta-3 is connected
Oswin Aichholzer, Sang Won Bae, Luis Barba +5
In this paper, we show that the -graph with three cones is connected. We also provide an alternative proof of the connectivity of the Yao graph with three cones.
Towards Tight Bounds on Theta-Graphs
Prosenjit Bose, Jean-Lou De Carufel, Pat Morin +2
We present improved upper and lower bounds on the spanning ratio of -graphs with at least six cones. Given a set of points in the plane, a -graph partitions the plane around…
Spanning Properties of Yao and -Graphs in the Presence of Constraints
Prosenjit Bose, André van Renssen
We present improved upper bounds on the spanning ratio of constrained -graphs with at least 6 cones and constrained Yao-graphs with 5 or at least 7 cones. Given a set of points…