Domination in Graphs Applied to Electric Power Networks

Haynes, Teresa W.; Hedetniemi, Stephen T.; Henning, Michael A.

doi:10.1137/s0895480100375831

Cited by 299 publications

(332 citation statements)

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“…We have considered the power domination problem, which is related to the domination problem in graph theory [16], and presented linear time algorithms to solve the power domination problem for both interval graphs and circular-arc graphs, provided that the given endpoints of the corresponding interval representation and circular-arc representation have been sorted. The problem is relevant to many fields.…”

Section: Discussionmentioning

confidence: 99%

“…Haynes et al [16] considered the power domination problem as a variation of the domination problem and studied the relationship between them. They provided NP-completeness proofs for bipartite graphs and chordal graphs, and proposed a linear time algorithm for the power domination problem in trees.…”

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

confidence: 99%

“…The power system observation problem can be transformed into a graph-theoretic problem as follows [16]. Let G = (V, E) be a graph representation of an electric power system, where a vertex represents an electric node (a substation bus that connects transmission branches, loads, and generators) and an edge represents a transmission branch that connects two electric nodes.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Discussionmentioning

confidence: 99%

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

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Power Domination in Circular-Arc Graphs

Liao

Lee

2011

Algorithmica

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“…Complete Observability [7] of the system should be achieved with minimum number of PMUs used. Then the PMUs are said to be optimally located.…”

Section: Optimal Allocation Of Pmu's 31 Optimality and Node To Node mentioning

confidence: 99%

“…In 2002, Haynes et al [7], mathematically proved that, for a tree having k vertices of degree at least 3, the "power dominating number" has been minimized where n is the total number of vertices. Above equations give the upper and lower bounds for the power dominating number [9].…”

Section: Dominant Setmentioning

confidence: 99%

Fast Initial State Assessment for State Estimator using Optimally Located Phasor Measurement Units

Gayatri¹,

Sarma²,

Charan³

2012

IJCA

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Complex power systems need better observability and visualization capabilities to handle critical situations effectively. Synchro-phasor measurements provide intra second visibility to power system dynamics and enable faster control actions. A Phasor Measurement Unit (PMU) measures the voltage and current phasors (angle and magnitude) at a bus in a power system. In the literature, many methods have been reported for determining a measurement set for the allocation of PMU"s. Most of these methods use conventional optimization techniques involving more mathematical equations, which are generally time-consuming from a computation point of view, especially for large systems under emergency conditions. The operator has to take instantaneous measurements for the quick state estimation. In this paper a simplified approach has been proposed for placing the measuring devices (PMU"s) which involves graph theoretical approach only .A linear algorithm is used to minimize the number of PMUs to monitor the entire system by modeling the system with topological observation theory. A relationship was developed between phasors where PMU"s are located and unknown phasors of the system. The results can be used as initial assessment for the state estimator. The algorithm was tested on IEEE-14 Bus System. General TermsPhasor Measurement Units, Graph Theory

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Domination Problems

Shen¹

2011

Wiley Encyclopedia of Operations Research and Management Science

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In this article, we focus on dominating set problems in graphs. We review the literature that analyzes domination from different aspects, including bounds for the domination number, the algorithmic complexity, and valid inequality chains associated with each domination variant. In particular, we discuss the relationship between domination, independence, and irredundance, and reveal the well‐known domination chain and its properties. As many domination‐related problems can be solved in polynomial time for certain types of graphs (e.g., trees), we summarize start‐of‐the‐art results of polynomial algorithms regarding the domination‐related parameters of graphs. We also describe applications such as wireless ad hoc networks, social networks, and broadcast domination in which domination or its variants can be suitably implemented, as well as associated approximation algorithms, in order to emphasize the importance of the domination in graphs from a practical perspective.

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Domination in Graphs Applied to Electric Power Networks

Cited by 299 publications

References 1 publication

Power Domination in Circular-Arc Graphs

Power Domination in Circular-Arc Graphs

Fast Initial State Assessment for State Estimator using Optimally Located Phasor Measurement Units

Domination Problems

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