Pi/2-Angle Yao Graphs are Spanners
Prosenjit Bose, Mirela Damian, Karim Douieb, Joseph O'Rourke, Ben, Seamone, Michiel Smid, Stefanie Wuhrer
TL;DR
This paper proves that the Yao graph Y4 functions as a spanner with bounded stretch factors in both L2 and Linf metrics, demonstrating its efficiency in geometric network design.
Contribution
The paper establishes that Yao graph Y4 is a spanner with specific stretch factors in L2 and Linf metrics, providing new insights into geometric spanner properties.
Findings
Yao graph Y4 is a spanner in L2 metric with stretch factor 8(29+23√2)
Yao graph Y4 is a planar spanner in Linf metric with stretch factor 8
Yao graph Y4 has desirable spanning properties in geometric networks
Abstract
We show that the Yao graph Y4 in the L2 metric is a spanner with stretch factor 8(29+23sqrt(2)). Enroute to this, we also show that the Yao graph Y4 in the Linf metric is a planar spanner with stretch factor 8.
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