An Exact Exponential Time Algorithm for Power Dominating Set

Binkele-Raible, Daniel; Fernau, Henning

doi:10.1007/s00453-011-9533-2

Cited by 13 publications

(3 citation statements)

References 21 publications

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“…Liao and Lee [10] showed a different NP-completeness proof for the PDS problem in split graphs as well as introduced a polynomial-time algorithm for solving PDS optimally on interval graphs. As shown by Binkele-Raible and Fernau, the PDS problem continues to be NP-hard on cubic graphs [11]. Guo et al [6] also presented valid orientations to optimally address PDS on undirected graphs having bounded tree-width.…”

Section: Power Domination and Related Workmentioning

confidence: 99%

Recovery of Structural Controllability into Critical Infrastructures under Malicious Attacks

Alwasel¹

2020

IJACSA

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The problem of controllability of networks can be seen in critical infrastructure systems which are increasingly susceptible to random failures and/or malicious attacks. The ability to recover controllability quickly following an attack can be considered a major problem in control systems. If this is not ensured, it can enable the attacker to create more disruptions as well as, like the electric power networks case, violate real-time restrictions and result in the control of the network degrading and its observability reducing significantly. Thus, the present paper examines structural controllability problem that has been in focus through the equivalent problem of the Power Dominating Set (PDS) introduced in the context of electrical power network control. However, the controllability optimisation problem can be seen as computationally infeasible regarding large complex networks because such problems are considered NPhard and as having low approximability. Hence, the ability of structural controllability recoverability will be explored as per the PDS formulation, especially following perturbations in which an attacker with sufficient knowledge of the network topology is only able to completely violate the current driver control nodes of the original control network leading to a degradation of controllability of dependent nodes. The results highlight that the use of directed Laplacian matrix can be a useful approach for analysing structural controllability of a network. The simulation results show also that an increase of a connectivity probability of the distribution of links in Directed ER networks can minimise the number of driver control nodes which is highly desirable while monitoring the entire network.

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Section: Power Domination and Related Workmentioning

confidence: 99%

Recovery of Structural Controllability into Critical Infrastructures under Malicious Attacks

Alwasel¹

2020

IJACSA

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“…Current research on the PDSP mostly focuses on its theoretical aspects. It has been shown that the PDSP is NP‐hard even on specific types of graphs like cubic graphs (Binkele‐Raible & Fernau, 2012). Another direction of research has been in finding the optimal size or bounds for specific graphs like grid graphs (Dorfling & Henning, 2006; Pai, Chang, & Wang, 2007), hyper cubes (Dean, Ilic, Ramirez, Shen, & Tian, 2011), generalised Petersen graphs (Koh & Soh, 2016; Lai, Chien, Chou, & Kao, 2012), cylinders (Koh & Soh, 2016), circular‐arc graphs (Liao & Lee, 2013), and tori (Koh & Soh, 2016).…”

Section: Introductionmentioning

confidence: 99%

“…Only a small amount of published research is dedicated to solving the PDSP on general graphs. In (Binkele‐Raible & Fernau, 2012; Raible & Fernau, 2008) a method based on reference search trees is developed for finding optimal solutions having a computational complexity of

scriptO ((), {1.7548}^{n})

. Optimal solutions for the PDSP and the CPDSP have also been found using integer linear programs (ILP; Brimkov et al, 2017; Fan & Watson, 2012; Aazami & Stilp, 2009).…”

Section: Introductionmentioning

confidence: 99%

The fixed set search applied to the power dominating set problem

Jovanović

Voß

2020

Expert Systems

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In this article, we focus on solving the power dominating set problem and its connected version. These problems are frequently used for finding optimal placements of phasor measurement units in power systems. We present an improved integer linear program (ILP) for both problems. In addition, a greedy constructive algorithm and a local search are developed. A greedy randomised adaptive search procedure (GRASP) algorithm is created to find near optimal solutions for large scale problem instances. The performance of the GRASP is further enhanced by extending it to the novel fixed set search (FSS) metaheuristic. Our computational results show that the proposed ILP has a significantly lower computational cost than existing ILPs for both versions of the problem. The proposed FSS algorithm manages to find all the optimal solutions that have been acquired using the ILP. In the last group of tests, it is shown that the FSS can significantly outperform the GRASP in both solution quality and computational cost.

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Profit Parameterizations of Dominating Set

Fernau

Stege

2019

Algorithmic Aspects in Information and Management

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An Exact Exponential Time Algorithm for Power Dominating Set

Cited by 13 publications

References 21 publications

Recovery of Structural Controllability into Critical Infrastructures under Malicious Attacks

Recovery of Structural Controllability into Critical Infrastructures under Malicious Attacks

The fixed set search applied to the power dominating set problem

Profit Parameterizations of Dominating Set

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