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| Main Authors: | , |
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| Format: | Preprint |
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2026
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| Online Access: | https://arxiv.org/abs/2601.21652 |
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| _version_ | 1866914291046678528 |
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| author | Zhao, Jingyang Xiao, Mingyu |
| author_facet | Zhao, Jingyang Xiao, Mingyu |
| contents | The multi-vehicle dial-a-ride problem (mDaRP) is a fundamental vehicle routing problem with pickups and deliveries, widely applicable in ride-sharing, economics, and transportation. Given a set of $n$ locations, $h$ vehicles of identical capacity $λ$ located at various depots, and $m$ ride requests each defined by a source and a destination, the goal is to plan non-preemptive routes that serve all requests while minimizing the total travel distance, ensuring that no vehicle carries more than $λ$ passengers at any time. The best-known approximation ratio for the mDaRP remains $\mathcal{O}(\sqrtλ\log m)$.
We propose two simple algorithms: the first achieves the same approximation ratio of $\mathcal{O}(\sqrtλ\log m)$ with improved running time, and the second attains an approximation ratio of $\mathcal{O}(\sqrt{\frac{m}λ})$. A combination of them yields an approximation ratio of $\mathcal{O}(\sqrt[4]{n}\log^{\frac{1}{2}}n)$ under $m=Θ(n)$. Moreover, for the case $m\gg n$, by extending our algorithms, we derive an $\mathcal{O}(\sqrt{n\log n})$-approximation algorithm, which also improves the current best-known approximation ratio of $\mathcal{O}(\sqrt{n}\log^2n)$ for the classic (single-vehicle) DaRP, obtained by Gupta et al. (ACM Trans. Algorithms, 2010). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_21652 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Improved Approximations for Dial-a-Ride Problems Zhao, Jingyang Xiao, Mingyu Data Structures and Algorithms The multi-vehicle dial-a-ride problem (mDaRP) is a fundamental vehicle routing problem with pickups and deliveries, widely applicable in ride-sharing, economics, and transportation. Given a set of $n$ locations, $h$ vehicles of identical capacity $λ$ located at various depots, and $m$ ride requests each defined by a source and a destination, the goal is to plan non-preemptive routes that serve all requests while minimizing the total travel distance, ensuring that no vehicle carries more than $λ$ passengers at any time. The best-known approximation ratio for the mDaRP remains $\mathcal{O}(\sqrtλ\log m)$. We propose two simple algorithms: the first achieves the same approximation ratio of $\mathcal{O}(\sqrtλ\log m)$ with improved running time, and the second attains an approximation ratio of $\mathcal{O}(\sqrt{\frac{m}λ})$. A combination of them yields an approximation ratio of $\mathcal{O}(\sqrt[4]{n}\log^{\frac{1}{2}}n)$ under $m=Θ(n)$. Moreover, for the case $m\gg n$, by extending our algorithms, we derive an $\mathcal{O}(\sqrt{n\log n})$-approximation algorithm, which also improves the current best-known approximation ratio of $\mathcal{O}(\sqrt{n}\log^2n)$ for the classic (single-vehicle) DaRP, obtained by Gupta et al. (ACM Trans. Algorithms, 2010). |
| title | Improved Approximations for Dial-a-Ride Problems |
| topic | Data Structures and Algorithms |
| url | https://arxiv.org/abs/2601.21652 |