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Coverage and distinguishability requirements for Traffic Flow Monitoring Systems

Traffic flow monitoring systems aim to measure and monitor vehicle trajectories in smart cities. Their critical applications include vehicle theft prevention, vehicle localization, and traffic congestion solution. This paper studies an RoadSide Unit (RSU) placement problem in traffic flow monitoring systems. Given some traffic flows on streets, the objective is to place a minimum number of RSUs to cover and distinguish all traffic flows. A traffic flow is covered and distinguishable, if the set of its passing RSUs is non-empty and unique among all traffic flows. The RSU placement problem is NP-hard, monotonic, and non-submodular. It is a non-trivial extension of the traditional set cover problem that is submodular. We show that, to cover and distinguish an arbitrary pair of traffic flows (f and f'), two RSUs should be placed on streets from two different subsets of f\f', f'\f, and f ∩ f'. Three bounded RSU placement algorithms are proposed. Their approximation ratios are n ln n(n-1)/2 , n+1/2 ln 3n(n-1)/2, and ln n(n+1)/2, respectively. Here, ri is the number of given traffic flows. Extensive real data-driven experiments demonstrate the efficiency and effectiveness of the proposed algorithms.