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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 method...
Consider a flow network, i.e., a directed graph where each arc has a nonnegative capacity value and an associated length, together with nonempty supply intervals for the sources and nonempty demand intervals for the sinks. The Maximum Min‐Cost‐Flow Problem (MaxMCF) is to find fixed supply and demand values within these intervals such that the optimal objective value of the induced Min‐Cost‐Flow Problem...
Obtaining high‐quality solutions to the minimum label spanning tree problem is of crucial importance to efficient communication network design, since such solutions can reduce both the construction cost and the complexity of the ultimate architecture. However, the corresponding optimization task was shown to be hard even for complete graphs. As a consequence, no computationally efficient method for...
In the multi‐vehicle covering tour problem with speed optimization, we aim to construct a set of maximal coverage routes for a fleet of vehicles that serve (observe) a set of secondary sites, given a fixed time schedule and coverage requirements. We develop an exact solution approach using a branch‐and‐price framework with a label‐correcting algorithm and a set of innovative dominance rules to solve...
In the Steiner forest problem, we are given a set of terminal pairs and need to find the minimum cost subgraph that connects each of the terminal pairs together. Motivated by the recent work on greedy approximation algorithms for the Steiner forest, we provide efficient implementations of existing approximation algorithms and conduct a thorough experimental study to characterize their performance...
Various models to quantify the reliability of a network have been studied where certain components of the graph may fail at random and the probability that the remaining graph is connected is the proxy for reliability. We introduce a strengthening of one of these models by considering the probability that the remaining graph is cop‐win. A graph is cop‐win if one cop can win the game Cops and Robber...
Given an undirected graph with positive weights on the edges we study a parametric biobjective graph clustering problem. We remove a subset of edges to break the graph into smaller pieces, that is, connected components, or clusters. We seek to maximize the number of clusters while minimizing the weight of the removed edges. We identify nested solutions that lie on the concave envelope of the efficient...
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