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We develop a minimum set cover based metaheuristic based approach to solve this problem in a scalable manner.
The problem of sensor network design is converted to a minimum set cover problem on the bipartite graph, and is solved using a greedy heuristic algorithm.
This paper investigates the relations between common formulations for reserve selection, including minimum set cover, maximum coverage and maximal utility planning.
In the first approach, we transform the MTC problem to a minimum set cover (MSC) problem and use the greedy algorithm that exploits the submodularity property of the MSC problem to compute the solution to the MTC problem.
Directed paths between vulnerable nodes and potential sensor nodes are used to construct a bipartite graph, and the sensor network design problem is formulated as a minimum set cover problem.
To address this problem, we formulate a mathematical program with constraints involving the mixed strategy Nash equilibria of an operator-attacker game, and present a solution approach based on two combinatorial optimization problems, formulated as minimum set cover and maximum set packing problems.
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We show that Find-Minimal-Pathway is NP-hard [ 40] by a reduction from the Minimum-Set-Cover problem.
In Minimum-Set-Cover, we seek the minimal subset ⊆ such that every element in belongs to at least one member in.
A solution to Minimum-Set-Cover can be reconstructed in polynomial time from the solution to Find-Minimal-Pathway by assigning C i ∈ for each r i ∈ P. As Minimum-Set-Cover is NP-complete [ 40], it follows that Find-Minimal-Pathway is NP-hard.
Their result is the first improvement over the log n2 = 2 log n approximation ratio that can essentially be achieved by a standard reduction of Minimum Test Collection to Set Cover followed by a run of the classical set covering greedy algorithm.
It also makes it possible to define the minimum set of lines that cover the entire donor genome, according to the same parameters.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com