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DOI: 10.4230/LIPIcs.FUN.2021.15

Multi-Robot Motion Planning of k-Colored Discs Is PSPACE-Hard

Authors: Thomas Brocken, G. Wessel van der Heijden, Irina Kostitsyna, Lloyd E. Lo-Wong, and Remco J. A. Surtel

Published in: LIPIcs, Volume 157, 10th International Conference on Fun with Algorithms (FUN 2021) (2020)

Abstract

In the problem of multi-robot motion planning, a group of robots, placed in a polygonal domain with obstacles, must be moved from their starting positions to a set of target positions. We consider the specific case of unlabeled disc robots of two different sizes. That is, within one class of robots, where a class is given by the robots' size, any robot can be moved to any of the corresponding target positions. We prove that the decision problem of whether there exists a schedule moving the robots to the target positions is PSPACE-hard.

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Thomas Brocken, G. Wessel van der Heijden, Irina Kostitsyna, Lloyd E. Lo-Wong, and Remco J. A. Surtel. Multi-Robot Motion Planning of k-Colored Discs Is PSPACE-Hard. In 10th International Conference on Fun with Algorithms (FUN 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 157, pp. 15:1-15:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{brocken_et_al:LIPIcs.FUN.2021.15,
  author =	{Brocken, Thomas and van der Heijden, G. Wessel and Kostitsyna, Irina and Lo-Wong, Lloyd E. and Surtel, Remco J. A.},
  title =	{{Multi-Robot Motion Planning of k-Colored Discs Is PSPACE-Hard}},
  booktitle =	{10th International Conference on Fun with Algorithms (FUN 2021)},
  pages =	{15:1--15:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-145-0},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{157},
  editor =	{Farach-Colton, Martin and Prencipe, Giuseppe and Uehara, Ryuhei},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FUN.2021.15},
  URN =		{urn:nbn:de:0030-drops-127769},
  doi =		{10.4230/LIPIcs.FUN.2021.15},
  annote =	{Keywords: Disc-robot motion planning, algorithmic complexity, PSPACE-hard}
}

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Multi-Robot Motion Planning of k-Colored Discs Is PSPACE-Hard

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