License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.MFCS.2018.56
URN: urn:nbn:de:0030-drops-96381
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2018/9638/
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Bärtschi, Andreas ; Graf, Daniel ; Mihalák, Matús

Collective Fast Delivery by Energy-Efficient Agents

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LIPIcs-MFCS-2018-56.pdf (0.8 MB)

Abstract

We consider k mobile agents initially located at distinct nodes of an undirected graph (on n nodes, with edge lengths). The agents have to deliver a single item from a given source node s to a given target node t. The agents can move along the edges of the graph, starting at time 0, with respect to the following: Each agent i has a weight omega_i that defines the rate of energy consumption while travelling a distance in the graph, and a velocity upsilon_i with which it can move.
We are interested in schedules (operating the k agents) that result in a small delivery time T (time when the item arrives at t), and small total energy consumption E. Concretely, we ask for a schedule that: either (i) Minimizes T, (ii) Minimizes lexicographically (T,E) (prioritizing fast delivery), or (iii) Minimizes epsilon * T + (1-epsilon)* E, for a given epsilon in (0,1).
We show that (i) is solvable in polynomial time, and show that (ii) is polynomial-time solvable for uniform velocities and solvable in time O(n+k log k) for arbitrary velocities on paths, but in general is NP-hard even on planar graphs. As a corollary of our hardness result, (iii) is NP-hard, too. We show that there is a 2-approximation algorithm for (iii) using a single agent.

BibTeX - Entry

@InProceedings{brtschi_et_al:LIPIcs:2018:9638,
  author =	{Andreas B{\"a}rtschi and Daniel Graf and Mat{\'u}s Mihal{\'a}k},
  title =	{{Collective Fast Delivery by Energy-Efficient Agents}},
  booktitle =	{43rd International Symposium on Mathematical Foundations  of Computer Science (MFCS 2018)},
  pages =	{56:1--56:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-086-6},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{117},
  editor =	{Igor Potapov and Paul Spirakis and James Worrell},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/9638},
  URN =		{urn:nbn:de:0030-drops-96381},
  doi =		{10.4230/LIPIcs.MFCS.2018.56},
  annote =	{Keywords: delivery, mobile agents, time/energy optimization, complexity, algorithms}
}

Keywords: delivery, mobile agents, time/energy optimization, complexity, algorithms
Collection: 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)
Issue Date: 2018
Date of publication: 27.08.2018

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