Abstract
Broadcast domination was introduced by Erwin in 2002, and it is a variant of the standard dominating set problem, such that vertices can be assigned various domination powers. Broadcast domination assigns a power f(v) ≥ 0 to each vertex v of a given graph, such that every vertex of the graph is within distance f(v) from some vertex v having f(v) ≥ 1. The optimal broadcast domination problem seeks to minimize the sum of the powers assigned to the vertices of the graph. Since the presentation of this problem its computational complexity has been open, and the general belief has been that it might be \(\mathcal{NP}\)-hard. In this paper, we show that optimal broadcast domination is actually in \(\mathcal{P}\), and we give a polynomial time algorithm for solving the problem on arbitrary graphs, using a non standard approach.
This work is supported by the Research Council of Norway through the SPECTRUM project grant.
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Heggernes, P., Lokshtanov, D. (2005). Optimal Broadcast Domination of Arbitrary Graphs in Polynomial Time. In: Kratsch, D. (eds) Graph-Theoretic Concepts in Computer Science. WG 2005. Lecture Notes in Computer Science, vol 3787. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11604686_17
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DOI: https://doi.org/10.1007/11604686_17
Publisher Name: Springer, Berlin, Heidelberg
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