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S. Gaspers, M. Liedloff:
"A Branch-and-Reduce Algorithm for Finding a Minimum Independent Dominating Set";
Discrete Mathematics & Theoretical Computer Science, Vol. 14 (2012), No. 1; S. 29 - 42.

An independent dominating set D of a graph G = (V, E) is a subset of vertices such that every vertex in V \ D has at least one neighbor in D and D is an independent set, i.e. no two vertices of D are adjacent in G. Finding a minimum independent dominating set in a graph is an NP-hard problem. Whereas it is hard to cope with this problem using parameterized and approximation algorithms, there is a simple exact O(1.4423n )-time algorithm solving the problem by enumerating all maximal independent sets. In this paper we improve the latter result, providing the first non-trivial algorithm computing a minimum independent dominating set of a graph in time O(1.3569n ). Furthermore, we give a lower bound of Ω(1.3247n ) on the worst-case running time of this algorithm, showing that the running time analysis is almost tight.

Exponential time algorithms, minimum independent dominating set, minimum maximal independent set

Projektleitung Stefan Szeider:
The Parameterized Complexity of Reasoning Problems