Summary: Approximating Minimum Independent Dominating Sets in
Johann L. Hurink, Tim Nieberg
University of Twente
Faculty of Electrical Engineering, Mathematics & Computer Science
Postbus 217, NL-7500 AE Enschede
We present the first polynomial-time approximation scheme (PTAS) for the Mini-
mum 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
The presented approach yields a robust algorithm, that is, the algorithm accepts
any undirected graph as input, and returns a (1+)-approximate minimum dominating
set, or a certificate showing that the input graph does not reflect a wireless network.
Keywords: Minimum Independent Dominating Set, Minimum Maximal Indepen-