Abstract
In the online car-sharing (a.k.a. ride-sharing) problem, we are given a set of m available car, and n requests arrive sequentially in T periods, in which each request consists of a pick-up location and a drop-off location. In each period, we must immediately and irrevocably assign free cars to serve arrived requests, such that two requests share one car. The goal is to find an online algorithm to process all requests while minimizing the total travel distance of cars.
We give the first algorithm for this problem under the adversarial model and the random arrival model. For the adversarial model, we give a \(2T+1/2\)-competitive algorithm, then we show this can be further improved to 2T-competitive by a carefully designed edge cost function. This almost matches the known \(2T-1\) lower bound in this model. For the random arrival model, our algorithm is \(3H_T-1/2+o(1)\)-competitive, where \(H_T\) is the T-th harmonic number. All the above three results are based on one single algorithm that runs in \(O(n^3)\) time.
This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement number 754462.
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Guo, X., Luo, K. (2022). Algorithms for Online Car-Sharing Problem. In: Balachandran, N., Inkulu, R. (eds) Algorithms and Discrete Applied Mathematics. CALDAM 2022. Lecture Notes in Computer Science(), vol 13179. Springer, Cham. https://doi.org/10.1007/978-3-030-95018-7_18
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