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null (Ed.)We study an online hypergraph matching problem with delays, motivated by ridesharing applications. In this model, users enter a marketplace sequentially, and are willing to wait up to $d$ timesteps to be matched, after which they will leave the system in favor of an outside option. A platform can match groups of up to $k$ users together, indicating that they will share a ride. Each group of users yields a match value depending on how compatible they are with one another. As an example, in ridesharing, $k$ is the capacity of the service vehicles, and $d$ is the amount of time a user is willing to wait for a driver to be matched to them. We present results for both the utility maximization and cost minimization variants of the problem. In the utility maximization setting, the optimal competitive ratio is $\frac{1}{d}$ whenever $k \geq 3$, and is achievable in polynomialtime for any fixed $k$. In the cost minimization variation, when $k = 2$, the optimal competitive ratio for deterministic algorithms is $\frac{3}{2}$ and is achieved by a polynomialtime thresholding algorithm. When $k>2$, we show that a polynomialtime randomized batching algorithm is $(2  \frac{1}{d}) \log k$competitive, and it is NPhard to achieve a competitive ratio better than $\log k  O (\log \log k)$.more » « less

null (Ed.)This paper presents an algorithmic framework to optimize the operation of an Autonomous MobilityonDemand system whereby a centrally controlled fleet of electric selfdriving vehicles provides ondemand mobility. In particular, we first present a mixedinteger linear program that captures the joint vehicle coordination and charge scheduling problem, accounting for the battery level of the single vehicles and the energy availability in the power grid. Second, we devise a heuristic algorithm to compute nearoptimal solutions in polynomial time. Finally, we apply our algorithm to realistic case studies for Newport Beach, CA. Our results validate the near optimality of our method with respect to the global optimum, whilst suggesting that through vehicletogrid operation we can enable a 100% penetration of renewable energy sources and still provide a highquality mobility service.more » « less

null (Ed.)This paper presents an algorithmic framework to optimize the operation of an Autonomous MobilityonDemand system whereby a centrally controlled fleet of electric selfdriving vehicles provides ondemand mobility. In particular, we first present a mixedinteger linear program that captures the joint vehicle coordination and charge scheduling problem, accounting for the battery level of the single vehicles and the energy availability in the power grid. Second, we devise a heuristic algorithm to compute nearoptimal solutions in polynomial time. Finally, we apply our algorithm to realistic case studies for Newport Beach, CA. Our results validate the near optimality of our method with respect to the global optimum, whilst suggesting that through vehicletogrid operation we can enable a 100% penetration of renewable energy sources and still provide a highquality mobility service.more » « less