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Approximating the Minimum Independent Dominating Set in Perturbed Graphs

  • Weitian Tong
  • Randy Goebel
  • Guohui Lin
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7936)

Abstract

We investigate the minimum independent dominating set in perturbed graphs \({\mathfrak g}(G, p)\) of input graph G = (V, E), obtained by negating the existence of edges independently with a probability p > 0. The minimum independent dominating set (MIDS) problem does not admit a polynomial running time approximation algorithm with worst-case performance ratio of n 1 − ε for any ε > 0. We prove that the size of the minimum independent dominating set in \({\mathfrak g}(G, p)\), denoted as \(i({\mathfrak g}(G, p))\), is asymptotically almost surely in Θ(log|V|). Furthermore, we show that the probability of \(i({\mathfrak g}(G, p)) \ge \sqrt{\frac{4|V|}{p}}\) is no more than 2− |V|, and present a simple greedy algorithm of proven worst-case performance ratio \(\sqrt{\frac{4|V|}{p}}\) and with polynomial expected running time.

Keywords

Independent set independent dominating set dominating set approximation algorithm perturbed graph smooth analysis 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Weitian Tong
    • 1
  • Randy Goebel
    • 1
  • Guohui Lin
    • 1
  1. 1.Department of Computing ScienceUniversity of AlbertaEdmontonCanada

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