We present the first polynomial-time approximation scheme (PTAS) for the Minimum Independent Dominating Set problem in graphs of polynomially bounded growth. Graphs of bounded growth are used to characterize wireless communication networks, and this class of graph includes many models known from the literature, e.g. (Quasi) Unit Disk Graphs. An independent dominating set is a dominating set in a graph that is also independent. It thus combines the advantages of both structures, and there are many applications that rely on these two structures e.g. in the area of wireless ad hoc networks. The presented approach yields a robust algorithm, that is, the algorithm accepts any undirected graph as input, and returns a $(1+\varepsilon )$-approximate minimum dominating set, or a certificate showing that the input graph does not reflect a wireless network.
|Place of Publication||Enschede|
|Publisher||University of Twente, Department of Applied Mathematics|
|Number of pages||12|
|Publication status||Published - 15 Feb 2007|
|Name||Memorandum Department of Applied Mathematics, University of Twente 1824|
Hurink, J. L., & Nieberg, T. (2007). Approximating minimum independent dominating sets in wireless networks. (Memorandum Department of Applied Mathematics, University of Twente 1824; No. 2/1824). Enschede: University of Twente, Department of Applied Mathematics.