Polynomial-time data reduction for dominating set
Journal of the ACM (JACM)
Parameterized power domination complexity
Information Processing Letters
Power domination in block graphs
Theoretical Computer Science
A note on power domination in grid graphs
Discrete Applied Mathematics
Approximating the minimum weight weak vertex cover
Theoretical Computer Science - Computing and combinatorics
Computational Study on Dominating Set Problem of Planar Graphs
COCOA 2008 Proceedings of the 2nd international conference on Combinatorial Optimization and Applications
Approximation Algorithms and Hardness for Domination with Propagation
APPROX '07/RANDOM '07 Proceedings of the 10th International Workshop on Approximation and the 11th International Workshop on Randomization, and Combinatorial Optimization. Algorithms and Techniques
Computational study on planar dominating set problem
Theoretical Computer Science
Note: A note on power domination in grid graphs
Discrete Applied Mathematics
Parameterized power domination complexity
Information Processing Letters
Restricted power domination and fault-tolerant power domination on grids
Discrete Applied Mathematics
Approximation algorithms for the capacitated domination problem
FAW'10 Proceedings of the 4th international conference on Frontiers in algorithmics
On the power domination number of the generalized Petersen graphs
Journal of Combinatorial Optimization
Power domination problem in graphs
COCOON'05 Proceedings of the 11th annual international conference on Computing and Combinatorics
Improved algorithms and complexity results for power domination in graphs
FCT'05 Proceedings of the 15th international conference on Fundamentals of Computation Theory
Discrete Applied Mathematics
On the impact of PMU placement on observability and cross-validation
Proceedings of the 3rd International Conference on Future Energy Systems: Where Energy, Computing and Communication Meet
Generalized power domination of graphs
Discrete Applied Mathematics
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The problem of monitoring an electric power system by placing as few measurement devices in the system as possible is closely related to the well-known vertex covering and dominating set problems in graphs. We consider the graph theoretical representation of this problem as a variation of the dominating set problem and define a set S to be a power dominating set of a graph if every vertex and every edge in the system is monitored by the set S (following a set of rules for power system monitoring). The minimum cardinality of a power dominating set of a graph G is the power domination number $\gamma_P(G)$. We show that the power dominating set (PDS) problem is NP-complete even when restricted to bipartite graphs or chordal graphs. On the other hand, we give a linear algorithm to solve the PDS for trees. In addition, we investigate theoretical properties of $\gamma_P(T)$ in trees T.