An Efficient Algorithm for the Fast Delivery Problem

  • Iago A. Carvalho
  • Thomas ErlebachEmail author
  • Kleitos Papadopoulos
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11651)


We study a problem where k autonomous mobile agents are initially located on distinct nodes of a weighted graph (with n nodes and m edges). Each autonomous mobile agent has a predefined velocity and is only allowed to move along the edges of the graph. We are interested in delivering a package, initially positioned in a source node s, to a destination node y. The delivery is achieved by the collective effort of the autonomous mobile agents, which can carry and exchange the package among them. The objective is to compute a delivery schedule that minimizes the delivery time of the package. In this paper, we propose an \(\mathcal {O}(kn\log (kn)+km)\) time algorithm for this problem. This improves the previous state-of-the-art \(\mathcal {O}(k^2 m + k n^2 + \mathrm {APSP})\) time algorithm for this problem, where \(\mathrm {APSP}\) stands for the running-time of an algorithm for the All-Pairs Shortest Paths problem.


Mobile agents Dijkstra’s algorithm Polynomial-time algorithm Time-dependent shortest paths 



Iago A. Carvalho was financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - Brasil (CAPES) - Finance Code 001.


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Authors and Affiliations

  1. 1.Department of Computer ScienceUniversidade Federal de Minas GeraisBelo HorizonteBrazil
  2. 2.Department of InformaticsUniversity of LeicesterLeicesterUK

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