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On the fast delivery problem with one or two packages

journal contribution
posted on 08.10.2020, 09:48 by Iago A Carvalho, Thomas Erlebach, Kleitos Papadopoulos
We study two problems where k autonomous mobile agents are initially located on distinct nodes of a weighted graph with n nodes and m edges. Each agent has a predefined velocity and can only move along the edges of the graph. The first problem is to deliver one package from a source node to a destination node. The second is to simultaneously deliver two packages, each from its source node to its destination node. These deliveries are achieved by the collective effort of the agents, which can carry and exchange a package among them. For one package, we propose an O(knlogn+km) time algorithm for computing a delivery schedule that minimizes the delivery time. For two packages, we show that the problem of minimizing the maximum or the sum of the delivery times is NP-hard for arbitrary agent velocities, but polynomial-time solvable for agents with equal velocity.

History

Citation

Journal of Computer and System Sciences, Volume 115, February 2021, Pages 246-263

Author affiliation

School of Informatics

Version

AM (Accepted Manuscript)

Published in

Journal of Computer and System Sciences

Volume

115

Pagination

246-263

Publisher

Elsevier

issn

0022-0000

Acceptance date

04/09/2020

Copyright date

2020

Available date

17/09/2022

Language

en