Improved Approximations for Dial-a-Ride Problems

2026-01-29

AI Summary

This work addresses the multi-vehicle Dial-a-Ride Problem (mDaRP), aiming to minimize total travel distance while respecting vehicle capacity and non-preemptive service constraints. The authors propose two novel approximation algorithms that integrate route decomposition, load balancing strategies, and combinatorial optimization techniques to ensure complete request coverage while significantly improving computational efficiency. Theoretical analysis establishes approximation ratios of $O(\sqrt{m/\lambda})$ and $O(\sqrt[4]{n} \cdot \sqrt{\log n})$, respectively. Notably, when the number of vehicles $m$ greatly exceeds the number of requests $n$, the bound improves to $O(\sqrt{n \log n})$, surpassing the previous best-known result of $O(\sqrt{n} \cdot \log^2 n)$ and also refining the performance guarantee for the classical single-vehicle setting.

Technology Category

• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Search and Optimization: Combinatorial Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

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 $\lambda$ 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 $\lambda$ passengers at any time. The best-known approximation ratio for the mDaRP remains $\mathcal{O}(\sqrt{\lambda}\log m)$. We propose two simple algorithms: the first achieves the same approximation ratio of $\mathcal{O}(\sqrt{\lambda}\log m)$ with improved running time, and the second attains an approximation ratio of $\mathcal{O}(\sqrt{\frac{m}{\lambda}})$. A combination of them yields an approximation ratio of $\mathcal{O}(\sqrt[4]{n}\log^{\frac{1}{2}}n)$ under $m=\Theta(n)$. 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).

Problem

• dial-a-ride
• vehicle routing
• pickup and delivery
• approximation algorithm
• capacity constraint

Innovation

• dial-a-ride problem
• approximation algorithm
• vehicle routing
• multi-vehicle
• pickup and delivery