Power domination with bounded time constraints

Chung-Shou Liao ()
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Chung-Shou Liao: National Tsing Hua University

Journal of Combinatorial Optimization, 2016, vol. 31, issue 2, No 16, 725-742

Abstract: Abstract Based on the power observation rules, the problem of monitoring a power utility network can be transformed into the graph-theoretic power domination problem, which is an extension of the well-known domination problem. A set $$S$$ S is a power dominating set (PDS) of a graph $$G=(V,E)$$ G = ( V , E ) if every vertex $$v$$ v in $$V$$ V can be observed under the following two observation rules: (1) $$v$$ v is dominated by $$S$$ S , i.e., $$v \in S$$ v ∈ S or $$v$$ v has a neighbor in $$S$$ S ; and (2) one of $$v$$ v ’s neighbors, say $$u$$ u , and all of $$u$$ u ’s neighbors, except $$v$$ v , can be observed. The power domination problem involves finding a PDS with the minimum cardinality in a graph. Similar to message passing protocols, a PDS can be considered as a dominating set with propagation that applies the second rule iteratively. This study investigates a generalized power domination problem, which limits the number of propagation iterations to a given positive integer; that is, the second rule is applied synchronously with a bounded time constraint. To solve the problem in block graphs, we propose a linear time algorithm that uses a labeling approach. In addition, based on the concept of time constraints, we provide the first nontrivial lower bound for the power domination problem.

Keywords: Algorithm; Domination; Power domination; Time constraint (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (5)

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DOI: 10.1007/s10878-014-9785-2

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