TL;DR
This paper proves that the Yao graph with six cones, Y_6, functions as a spanner, ensuring efficient network connectivity among planar points with bounded stretch factor.
Contribution
The paper establishes that Y_6 is a spanner, providing a rigorous proof of its spanning properties in planar point sets.
Findings
Y_6 is a spanner for planar points.
Y_6 guarantees bounded stretch factor.
The proof confirms Y_6's efficiency in geometric networks.
Abstract
We prove that Y_6 is a spanner. Y_6 is the Yao graph on a set of planar points, which has an edge from each point x to a closest point y within each of the six angular cones of 60 deg surrounding x.
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Taxonomy
TopicsComputational Geometry and Mesh Generation · Advanced Graph Theory Research · graph theory and CDMA systems