Power domination in block graphs

Xu, Guangjun; Kang, Lei; Zhao, Min

doi:10.1016/j.tcs.2006.04.011

Cited by 55 publications

(33 citation statements)

References 6 publications

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“…The authors of [11] achieve this by transforming PDS into an orientation problem on undirected graphs. The problem was also studied in the context of special graph classes like interval graphs (Liao and Lee [14]) and block graphs (Xu et al [24]) where linear time algorithms where obtained. Aazami and Stilp [1] raised the approximation lower bound to (2 log 1− n ) and gave an O( √ n)-approximation for planar graphs.…”

Section: Discussion Of Related Resultsmentioning

confidence: 99%

An Exact Exponential Time Algorithm for Power Dominating Set

Binkele-Raible

Fernau

2011

Algorithmica

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The POWER DOMINATING SET problem is an extension of the well-known domination problem on graphs in a way that we enrich it by a second propagation rule: given a graph G(V , E), a set P ⊆ V is a power dominating set if every vertex is observed after the exhaustive application of the following two rules. First, a vertex is observed if v ∈ P or it has a neighbor in P . Secondly, if an observed vertex has exactly one unobserved neighbor u, then also u will be observed, as well. We show that POWER DOMINATING SET remains N P-hard on cubic graphs. We design an algorithm solving this problem in time O * (1.7548 n ) on general graphs, using polynomial space only. To achieve this, we introduce so-called reference search trees that can be seen as a compact representation of usual search trees, providing non-local pointers in order to indicate pruned subtrees.

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Section: Discussion Of Related Resultsmentioning

confidence: 99%

An Exact Exponential Time Algorithm for Power Dominating Set

Binkele-Raible

Fernau

2011

Algorithmica

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“…Some special classes of graphs have also been considered from an algorithmic point of view [3,5,10,11,19,26,27,36]. Dorfling and Henning [11] and Pai et al [26] determined the power domination number in grid graphs.…”

Section: The Minimum Cardinality Of a Pds Of A Graph G Is Called The mentioning

confidence: 99%

“…Dorfling and Henning [11] and Pai et al [26] determined the power domination number in grid graphs. Atkins et al [3], Hon et al [19], and Xu et al [36] proposed linear time algorithms for the power domination problem in block graphs. A block graph is an intersection graph in which every maximal connected component (block) without a cut vertex is a clique.…”

Section: The Minimum Cardinality Of a Pds Of A Graph G Is Called The mentioning

confidence: 99%

Power Domination in Circular-Arc Graphs

Liao

Lee

2011

Algorithmica

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A set S ⊆ V is a power dominating set (PDS) of a graph G = (V, E) if every vertex and every edge in G can be observed based on the observation rules of power system monitoring. The power domination problem involves minimizing the cardinality of a PDS of a graph. We consider this combinatorial optimization problem and present a linear time algorithm for finding the minimum PDS of an interval graph if the interval ordering of the graph is provided. In addition, we show that the algorithm, which runs in Θ(n log n) time, where n is the number of intervals, is asymptotically optimal if the interval ordering is not given. We also show that the results hold for the class of circular-arc graphs.

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“…Several complexity results have been shown for PDS: NP-completeness proofs for bipartite, cographs (Haynes et al, 2002), and planar bipartite graphs (Brueni and Heath, 2005), and polynomial-time algorithms for trees, grids (Doring and Henning, 2006), block graphs (Xu et al, 2006), and bounded treewidth (Guo et al, 2005). Approximation algorithms and hardness results are presented in (Aazami and Stilp, 2007): O( √ n)-approximation for planar graphs and NP-hardness of approximability within a factor 2 log 1− n .…”

Section: Introductionmentioning

confidence: 99%

Complexity and inapproximability results for the Power Edge Set problem

et al. 2017

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We consider the single channel PMU placement problem called the Power Edge Set (PES) problem. In this variant of the PMU placement problem, (single channel) PMUs are placed on the edges of an electrical network. Such a PMU measures the current along the edge on which it is placed and the voltage at its two endpoints. The objective is to nd the minimum placement of PMUs in the network that ensures its full observability, namely measurement of all the voltages and currents. We prove that PES is NP-hard to approximate within a factor (1.12)-, for any > 0. On the positive side we prove that PES problem is solvable in polynomial time for trees and grids.Keywords PMU placement problem · Power Edge Set · NP-hardness · inapproximability This work was carried out as part of the SOGRID project (www.so-grid.com), co-funded by the French agency for Environment and Energy Management (ADEME) and developed in collaboration between participating academic and industrial partners.

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Power domination in block graphs

Cited by 55 publications

References 6 publications

An Exact Exponential Time Algorithm for Power Dominating Set

An Exact Exponential Time Algorithm for Power Dominating Set

Power Domination in Circular-Arc Graphs

Complexity and inapproximability results for the Power Edge Set problem

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