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On certain geometric properties of the Yao–Yao graphs

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Abstract

We show that, for any constant \(\rho > 1\), there exists an integer constant \(k\) such that the Yao–Yao graph with parameter \(k\) defined on a civilized unit disk graph is a geometric spanner of stretch factor \(\rho \). This improves the results of Wang and Li in several aspects, as described in the paper. This partially answers an open problem posed by Demaine, Mitchell and O’Rourke about the spanner properties of Yao–Yao graphs. We also show that the Yao–Yao graph with parameter \(k=4\) defined on the complete Euclidean graph is not plane.

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Authors and Affiliations

  1. School of Computing, DePaul University, 243 S. Wabash Avenue, Chicago, IL, 60604-2301, USA

    Iyad A. Kanj

  2. Department of Computer Science, Acopian Engineering Center, Lafayette College, Easton, PA, 18042, USA

    Ge Xia

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  1. Iyad A. Kanj
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  2. Ge Xia
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Correspondence to Ge Xia.

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Kanj, I.A., Xia, G. On certain geometric properties of the Yao–Yao graphs. J Comb Optim 27, 78–87 (2014). https://doi.org/10.1007/s10878-012-9570-z

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  • DOI: https://doi.org/10.1007/s10878-012-9570-z

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