Algorithms for Placing Monitors in a Flow Network
In the Flow Edge-Monitor Problem, we are given an undirected graph G=(V,E), an integer k>0 and some unknown circulation ψ on G. We want to find a set of k edges in G, so that if we place k monitors on those edges to measure the flow along them, the total number of edges for which the flow can be uniquely determined is maximized. In this paper, we first show that the Flow Edge-Monitor Problem is NP-hard. Then we study an algorithm called σ-Greedy that, in each step, places monitors on σ edges for which the number of edges where the flow is determined is maximized. We show that the approximation ratio of 1-Greedy is 3 and that the approximation ratio of 2-Greedy is 2.
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