Approximation Algorithms and Hardness for Domination with Propagation

Aazami, Ashkan; Stilp, Michael D.

doi:10.1007/978-3-540-74208-1_1

Cited by 29 publications

(62 citation statements)

References 16 publications

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“…In this paper we continue the study of the power domination in graphs started in [3,13] and which is now well-studied in the literature (see, for example, [1,2,3,5,6,7,8,9,11,12,13,14,15,16]).…”

Section: Introductionmentioning

confidence: 87%

“…Power domination is now well-studied in graph theory. From the algorithmic and complexity point of view, the power domination problem is known to be NP-complete [1,2,7,8,9], and approximation algorithms were given, for example, in [2]. On the other hand, linear-time algorithms for the power domination problem were given for trees [9], for interval graphs [12], and for block graphs [14].…”

Section: Introductionmentioning

confidence: 99%

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Generalized Power Domination in Regular Graphs

Dorbec¹,

Henning²,

Löwenstein³

et al. 2013

SIAM J. Discrete Math.

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Section: Introductionmentioning

confidence: 87%

Section: Introductionmentioning

confidence: 99%

Generalized Power Domination in Regular Graphs

Dorbec¹,

Henning²,

Löwenstein³

et al. 2013

SIAM J. Discrete Math.

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“…The PDS has been extensively studied in the literature: for example, it is NP ‐complete even for bipartite and chordal graphs, but polynomial for trees ; it is NP ‐complete for planar bipartite graphs, but polynomial for grids ; and there is an

O (\sqrt{n})

‐approximation algorithm for planar graphs of n vertices, but it is NP ‐hard to approximate (on general graphs) within a factor

2^{\log^{1 - ε} n}

. By inclusion from the PDS, the PMUP is also NP ‐complete.…”

Section: Introductionmentioning

confidence: 99%

The power edge set problem

et al. 2016

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The automated real time control of an electrical network is achieved through the estimation of its state using phasor measurement units. Given an undirected graph representing the network, we study the problem of finding the minimum number of phasor measurement units to place on the edges such that the graph is fully observed. This problem is also known as the Power Edge Set problem, a variant of the Power Dominating Set problem. It is naturally modeled using an iteration-indexed binary linear program, whose size turns out to be too large for practical purposes. We use a fixed-point argument to remove the iteration indices and obtain a more compact bilevel formulation. We then reformulate the latter to a single-level mixed-integer linear program, which performs better than the natural formulation. Lastly, we provide an algorithm that solves the bilevel program directly and much faster than a commercial solver can solve the previous models. We also discuss robust variants and extensions of the problem.

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“…The running time of their algorithm is

O (c^{k^{2}} \cdot n)

, where c is a constant. Aazami and Stilp gave an

O (\sqrt{n})

‐approximation algorithm for planar graphs and showed that their methods cannot improve on this approximation guarantee. Zhao et al.…”

Section: Introductionmentioning

confidence: 99%

Minimum Power Dominating Sets of Random Cubic Graphs

Kang

Wormald

2016

Journal of Graph Theory

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We present two heuristics for finding a small power dominating set of cubic graphs. We analyze the performance of these heuristics on random cubic graphs using differential equations. In this way, we prove that the proportion of vertices in a minimum power dominating set of a random cubic graph is asymptotically almost surely at most 0.067801. We also provide a corresponding lower bound of 1/29.7≈0.03367 using known results on bisection width.

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Approximation Algorithms and Hardness for Domination with Propagation

Cited by 29 publications

References 16 publications

Generalized Power Domination in Regular Graphs

Generalized Power Domination in Regular Graphs

The power edge set problem

Minimum Power Dominating Sets of Random Cubic Graphs

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