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.
The inequality here follows usingz 1 = 1 e −ε,z 2 = 1 e , andr= E[|L∩U1|] k
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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.