Keywords and Synonyms
Connected dominating set
Problem Definition
The dominating set problem is a classical NP-hard optimization problem which fits into the broader class of covering problems. Hundreds of papers have been written on this problem that has a natural motivation in facility location.
Definition 1
For a given undirected, simple graph \( { G=(V,E) } \) a subset of vertices \( { D\subseteq V } \) is called a dominating set if every vertex \( { u\in V-D } \) has a neighbor in D. The minimum dominating set (MDS) problem is to find a minimum dominating set of G, i. e. a dominating set of G of minimum cardinality.
Problem 1 (MDS)
Input: Undirected simple graph \( { G=(V,E) } \).
Output: A minimum dominating set D of G.
Various modifications of the dominating set problem are of interest, some of them obtained by putting additional constraints on the dominating set such as, for example, requesting it to be an independent set or to be connected. In graph theory there is a huge...
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Kratsch, D. (2008). Exact Algorithms for Dominating Set. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-30162-4_132
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