
Domination Cover Number of Graphs
A set D ⊆ V for the graph G=(V, E) is called a dominating set if any ver...
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Decremental Optimization of Dominating Sets Under Reachability Constraints
Given a dominating set, how much smaller a dominating set can we find th...
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Maximum matchings and minimum dominating sets in Apollonian networks and extended Tower of Hanoi graphs
The Apollonian networks display the remarkable powerlaw and smallworld...
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A LinearTime Algorithm for Minimum kHop Dominating Set of a Cactus Graph
Given a graph G=(V,E) and an integer k ≥ 1, a khop dominating set D of ...
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Asymptotic growth rate of square grids dominating sets: a symbolic dynamics approach
In this text, we prove the existence of an asymptotic growth rate of the...
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Intensive use of computing resources for dominations in grids and other combinatorial problems
Our goal is to prove new results in graph theory and combinatorics thank...
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An Extremal Optimization approach to parallel resonance constrained capacitor placement problem
Installation of capacitors in distribution networks is one of the most u...
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Optimal Sensor Placement in Power Grids: Power Domination, Set Covering, and the Neighborhoods of Zero Forcing Forts
To monitor electrical activity throughout the power grid and mitigate outages, sensors known as phasor measurement units can installed. Due to implementation costs, it is desirable to minimize the number of sensors deployed while ensuring that the grid can be effectively monitored. This optimization problem motivates the graph theoretic power dominating set problem. In this paper, we propose a novel integer program for identifying minimum power dominating sets by formulating a set cover problem. This problem's constraints correspond to neighborhoods of zero forcing forts; we study their structural properties and show they can be separated, allowing the proposed model to be solved via row generation. The proposed and existing methods are compared in several computational experiments in which the proposed method consistently exhibits an order of magnitude improvement in runtime performance.
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