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Line-Constrained L∞ One-Center Problem on Uncertain Points

Problems on uncertain data have attracted significant attention due to the imprecise nature of the measurement. In this paper, we consider the (weighted) L∞ one-center problem on uncertain data with an addition constraint that requires the sought center to be on a line. Given are a set of n (weighted) uncertain points and a line L. Each uncertain point has m possible locations in the plane associated with probabilities. The L∞ one-center aims to compute a point q* on L to minimize the maximum of the expected L∞ distances of all uncertain points to q*. We propose an algorithm to solve this problem in O(mn) time, which is optimal since the input is O(mn).