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Erschienen in:
2005 | OriginalPaper | Buchkapitel
Exact (Exponential) Algorithms for the Dominating Set Problem
verfasst von : Fedor V. Fomin, Dieter Kratsch, Gerhard J. Woeginger
Erschienen in: Graph-Theoretic Concepts in Computer Science
Verlag: Springer Berlin Heidelberg
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We design fast exact algorithms for the problem of computing a minimum dominating set in undirected graphs. Since this problem is NP-hard, it comes with no big surprise that all our time complexities are exponential in the number
n
of vertices. The contribution of this paper are ‘nice’ exponential time complexities that are bounded by functions of the form
c
n
with reasonably small constants
c
<2: For arbitrary graphs we get a time complexity of 1.93782
n
. And for the special cases of split graphs, bipartite graphs, and graphs of maximum degree three, we reach time complexities of 1.41422
n
, 1.73206
n
, and 1.51433
n
, respectively.