A unified approach to domination problems on interval graphs
Information Processing Letters
Minimum cuts for circular-arc graphs
SIAM Journal on Computing
Linear time algorithms on circular-arc graphs
Information Processing Letters
Domination in Graphs Applied to Electric Power Networks
SIAM Journal on Discrete Mathematics
Lower bounds for algebraic computation trees
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
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
Generalized power domination of graphs
Discrete Applied Mathematics
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To monitor an electric power system by placing as few phase measurement units (PMUs) as possible is closely related to the famous vertex cover problem and domination problem in graph theory. A set S is a power dominating set (PDS) of a graph G=(V,E), if every vertex and every edge in the system is observed following the observation rules of power system monitoring. The minimum cardinality of a PDS of a graph G is the power domination number γp(G). We show that the problem of finding the power domination number for split graphs, a subclass of chordal graphs, is NP-complete. In addition, we present a linear time algorithm for finding γp(G) of an interval graph G, if the interval ordering of the graph is provided, and show that the algorithm with O(nlog n) time complexity, is asymptotically optimal, if the interval ordering is not given, where n is the number of intervals. We also show that the same results hold for the class of proper circular-arc graphs.