Minimum Makespan Multi-vehicle Dial-a-Ride

TL;DR

This paper presents approximation algorithms for the multi-vehicle Dial-a-Ride problem aiming to minimize the maximum completion time, with improvements for special cases and specific graph structures.

Contribution

It introduces the first O(log^3 n)-approximation for the preemptive multi-vehicle Dial-a-Ride problem and improves ratios for special cases and certain graph classes.

Findings

O(log^3 n)-approximation algorithm for preemptive multi-vehicle Dial-a-Ride

O(log t)-approximation for the case without capacity constraints

Improved approximation ratios for fixed-minor-free graphs

Abstract

Dial a ride problems consist of a metric space (denoting travel time between vertices) and a set of m objects represented as source-destination pairs, where each object requires to be moved from its source to destination vertex. We consider the multi-vehicle Dial a ride problem, with each vehicle having capacity k and its own depot-vertex, where the objective is to minimize the maximum completion time (makespan) of the vehicles. We study the "preemptive" version of the problem, where an object may be left at intermediate vertices and transported by more than one vehicle, while being moved from source to destination. Our main results are an O(log^3 n)-approximation algorithm for preemptive multi-vehicle Dial a ride, and an improved O(log t)-approximation for its special case when there is no capacity constraint. We also show that the approximation ratios improve by a log-factor when the underlying metric is induced by a fixed-minor-free graph.