Minimum Dominating Set Approximation in Graphs of Bounded Arboricity

11 years 5 months ago
Minimum Dominating Set Approximation in Graphs of Bounded Arboricity
Abstract. Since in general it is NP-hard to solve the minimum dominating set problem even approximatively, a lot of work has been dedicated to central and distributed approximation algorithms on restricted graph classes. In this paper, we compromise between generality and efficiency by considering the problem on graphs of small arboricity a. These family includes, but is not limited to, graphs excluding fixed minors, such as planar graphs, graphs of (locally) bounded treewidth, or bounded genus. We give two viable distributed algorithms. Our first algorithm employs a forest decomposition, achieving a factor O(a2 ) approximation in randomized time O(log n). This algorithm can be transformed into a deterministic central routine computing a linear-time constant approximation on a graph of bounded arboricity, without a priori knowledge on a. The second algorithm exhibits an approximation ratio of O(a log ∆), where ∆ is the maximum degree, but in turn is uniform and deterministic, and...
Christoph Lenzen, Roger Wattenhofer
Added 31 Jan 2011
Updated 31 Jan 2011
Type Journal
Year 2010
Where WDAG
Authors Christoph Lenzen, Roger Wattenhofer
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