Results 1  10
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15
Experiments on Data Reduction for Optimal Domination in Networks
 in Proceedings International Network Optimization Conference (INOC 2003), Evry/Paris
, 2003
"... We present empirical results on computing optimal dominating sets in networks by means of data reduction through preprocessing rules. Thus, we demonstrate the usefulness of so far only theoretically considered reduction techniques for practically solving one of the most important network problems ..."
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Cited by 18 (13 self)
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We present empirical results on computing optimal dominating sets in networks by means of data reduction through preprocessing rules. Thus, we demonstrate the usefulness of so far only theoretically considered reduction techniques for practically solving one of the most important network problems in combinatorial optimization.
Tree decompositions of graphs: Saving memory in dynamic programming
 CTW 2004: CologneTwente Workshop on Graphs and Combinatorial Optimization, Villa Vigoni (CO
, 2004
"... We propose a simple and effective heuristic to save memory in dynamic programming on tree decompositions when solving graph optimization problems. The introduced “anchor technique ” is based on a treelike set covering problem. We substantiate our findings by experimental results. Our strategy has n ..."
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Cited by 9 (2 self)
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We propose a simple and effective heuristic to save memory in dynamic programming on tree decompositions when solving graph optimization problems. The introduced “anchor technique ” is based on a treelike set covering problem. We substantiate our findings by experimental results. Our strategy has negligible computational overhead concerning running time but achieves memory savings for nice tree decompositions and path decompositions between 60 % and 98%.
A practical comprehensive approach to PMU placement for full observability
 in Electrical and Computer Engineering. 2008, Virginia Polytechnic Institute and State
"... In recent years, the placement of phasor measurement units (PMUs) in electric transmission systems has gained much attention. Engineers and mathematicians have developed a variety of algorithms to determine the best locations for PMU installation. But often these placement algorithms are not practic ..."
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Cited by 3 (0 self)
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In recent years, the placement of phasor measurement units (PMUs) in electric transmission systems has gained much attention. Engineers and mathematicians have developed a variety of algorithms to determine the best locations for PMU installation. But often these placement algorithms are not practical for real systems and do not cover the whole process. This thesis presents a strategy that is practical and addresses three important topics: system preparation, placement algorithm, and installation scheduling. To be practical, a PMU strategy should strive for full observability, work well within the heterogeneous nature of power system topology, and enable system planners to adapt the strategy to meet their unique needs and system configuration. Practical considerations for the three placement topics are discussed, and a specific strategy based on these considerations is developed and demonstrated on real transmission system models.
Generalized power domination: propagation radius and Sierpiński graphs
, 2014
"... The recently introduced concept of kpower domination generalizes domination and power domination, the latter concept being used for monitoring an electric power system. The kpower domination problem is to determine a minimum size vertex subset S of a graph G such that after setting X = N [S], and ..."
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Cited by 2 (2 self)
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The recently introduced concept of kpower domination generalizes domination and power domination, the latter concept being used for monitoring an electric power system. The kpower domination problem is to determine a minimum size vertex subset S of a graph G such that after setting X = N [S], and iteratively adding to X vertices x that have a neighbour v in X such that at most k neighbours of v are not yet in X, we get X = V (G). In this paper the kpower domination number of Sierpiński graphs is determined. The propagation radius is introduced as a measure of the efficiency of power dominating sets. The propagation radius of Sierpiński graphs is obtained in most of the cases.
Domination in graphs with bounded propagation: algorithms, formulations and hardness results
, 2008
"... We introduce a hierarchy of problems between the Dominating Set problem and the Power Dominating Set (PDS) problem called the ℓround power dominating set (ℓround PDS, for short) problem. For ℓ = 1, this is the Dominating Set problem, and for ℓ ≥ n − 1, this is the PDS problem; here n denotes the n ..."
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We introduce a hierarchy of problems between the Dominating Set problem and the Power Dominating Set (PDS) problem called the ℓround power dominating set (ℓround PDS, for short) problem. For ℓ = 1, this is the Dominating Set problem, and for ℓ ≥ n − 1, this is the PDS problem; here n denotes the number of nodes in the input graph. In PDS the goal is to find a minimum size set of nodes S that power dominates all the nodes, where a node v is power dominated if (1) v is in S or it has a neighbor in S, or (2) v has a neighbor u such that u and all of its neighbors except v are power dominated. Note that rule (1) is the same as for the Dominating Set problem, and that rule (2) is a type of propagation rule that applies iteratively. The ℓround PDS problem has the same set of rules as PDS, except we apply rule (2) in “parallel ” in at most ℓ − 1 rounds. We prove that ℓround PDS cannot be approximated better than 2log1−ǫ n even for ℓ = 4 in general graphs. We provide a dynamic programming algorithm to solve ℓround PDS optimally in polynomial time on graphs of bounded treewidth. We present a PTAS (polynomial log n time approximation scheme) for ℓround PDS on planar graphs for ℓ = O( log log n). Finally, we give integer programming formulations for ℓround PDS. 1
Broadcast Domination
"... First of all, I would like to thank my supervisor Pinar Heggernes. She introduced me to Broadcast Domination and has been a great help and inspiration during the work on this thesis. I always felt welcome in her office, a place where the answers to most of my numerous questions could be found. I als ..."
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First of all, I would like to thank my supervisor Pinar Heggernes. She introduced me to Broadcast Domination and has been a great help and inspiration during the work on this thesis. I always felt welcome in her office, a place where the answers to most of my numerous questions could be found. I also want to thank the whole Algorithms research group. They welcomed me into the fold the moment I stepped into the faculty building. With their help, I could go on several trips that have played a key role in my academical development. Finally, thanks to my friends and family. You there for me, whether it is to go for a walk, play soccer, drown my sorrows in wine, make a delicious dinner, watch a movie
Power Domination in Honeycomb Meshes
"... The power domination problem is to find a minimum placement of phase measurement units (PMUs) for observing the whole electric power system represented by a graph G. The number of such a minimum placement of PMUs is called the power domination number of G and is denoted by γp(G). Finding γp(G) of a ..."
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The power domination problem is to find a minimum placement of phase measurement units (PMUs) for observing the whole electric power system represented by a graph G. The number of such a minimum placement of PMUs is called the power domination number of G and is denoted by γp(G). Finding γp(G) of an arbitrary graph is known to be NPcomplete. In this paper, we deal with the power domination problem on honeycomb meshes. For a tdimensional honeycomb mesh HMt, we show that γp(HMt) = d2t3 e. In particular, we present an O(t)time algorithm as the placement scheme.
unknown title
"... Abstract The power system monitoring problem asks for as few as possible measurementdevices to be put in an electric power system. The problem has a graph theory model involving power dominating sets in graphs. The power domination number flP (G) of G is the minimum cardinality of a power dominating ..."
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Abstract The power system monitoring problem asks for as few as possible measurementdevices to be put in an electric power system. The problem has a graph theory model involving power dominating sets in graphs. The power domination number flP (G) of G is the minimum cardinality of a power dominating set. Dorfling andHenning [2] determined the power domination number of the Cartesian product