Collaborative Delivery with Energy-Constrained Mobile Robots

TL;DR

This paper studies energy-constrained mobile robots collaboratively delivering messages in graphs, introducing new algorithms for returning delivery, and establishing resource bounds, thus advancing understanding of energy-efficient multi-agent routing.

Contribution

It provides the first polynomial-time algorithm for returning delivery on trees and resource-augmented algorithms with tight bounds for general graphs.

Findings

Polynomial-time algorithm for returning delivery on trees.

Resource-augmented algorithms for general graphs.

Tight lower bounds on resource augmentation needed.

Abstract

We consider the problem of collectively delivering some message from a specified source to a designated target location in a graph, using multiple mobile agents. Each agent has a limited energy which constrains the distance it can move. Hence multiple agents need to collaborate to move the message, each agent handing over the message to the next agent to carry it forward. Given the positions of the agents in the graph and their respective budgets, the problem of finding a feasible movement schedule for the agents can be challenging. We consider two variants of the problem: in non-returning delivery, the agents can stop anywhere; whereas in returning delivery, each agent needs to return to its starting location, a variant which has not been studied before. We first provide a polynomial-time algorithm for returning delivery on trees, which is in contrast to the known (weak) NP-hardness of the non-returning version. In addition, we give resource-augmented algorithms for returning delivery in general graphs. Finally, we give tight lower bounds on the required resource augmentation for both variants of the problem. In this sense, our results close the gap left by previous research.