CDS in Disk-Intersection Graphs

Ding-Zhu Du and Peng-Jun Wan
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Ding-Zhu Du: University of Texas, Dallas
Peng-Jun Wan: Illinois Institute of Technology

Chapter Chapter 9 in Connected Dominating Set: Theory and Applications, 2013, pp 151-159 from Springer

Abstract: Abstract Consider a finite set V of nodes in the plane and a radius function $$r : V \rightarrow {\rm IR}^{+}$$ . The disk-intersection graph (DIG) of V with the radius function r, denoted by $${G}_{r}\left (V \right )$$ , is the undirected graph on V in which u and v are adjacent if and only if the disk centered at u of radius $$r\left (u\right )$$ and the disk centered at v of radius $$r\left (v\right )$$ intersect, or equivalently, $$\left \Vert uv\right \Vert \leq r\left (u\right ) + r\left (v\right ).$$ If $$r\left (v\right ) = 1/2$$ for all v ∈ V, then $${G}_{r}\left (V \right )$$ is exactly the unit disk graph (UDG) of V.

Keywords: Unit Disk Graph (UDG); Radius Function; Voronoi Cell; Polynomial Time Approximation Scheme (PTAS); Connected Domination Number (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1007/978-1-4614-5242-3_9

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