# Approximating minimum independent dominating sets in wireless networks

Johann L. Hurink, Tim Nieberg

Research output: Book/ReportReportProfessional

## Abstract

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.
Original language English Enschede University of Twente, Department of Applied Mathematics 12 Published - 15 Feb 2007

### Publication series

Name Memorandum Department of Applied Mathematics, University of Twente 1824 1874-4850

## Keywords

• Approximation algorithms
• PTAS
• Minimum independent dominating set
• Minimum maximal independent set

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