Introduces the k-robotaxi placement problem on metric spaces, gives a randomized 2-approximation by independent sampling from demand, proves inapproximability via max-coverage reduction, provides exact DP on trees, and shows variance-reduced random placement works well empirically.
Bertsimas.Probabilistic combinatorial optimization problems
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The Robotaxi Placement Problem: Minimizing Expected ETA for Stochastic Demand
Introduces the k-robotaxi placement problem on metric spaces, gives a randomized 2-approximation by independent sampling from demand, proves inapproximability via max-coverage reduction, provides exact DP on trees, and shows variance-reduced random placement works well empirically.