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.FUN.2018.18
URN: urn:nbn:de:0030-drops-88098
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2018/8809/
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Demaine, Erik D. ; Grosof, Isaac ; Lynch, Jayson ; Rudoy, Mikhail

Computational Complexity of Motion Planning of a Robot through Simple Gadgets

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LIPIcs-FUN-2018-18.pdf (0.5 MB)

Abstract

We initiate a general theory for analyzing the complexity of motion planning of a single robot through a graph of "gadgets", each with their own state, set of locations, and allowed traversals between locations that can depend on and change the state. This type of setup is common to many robot motion planning hardness proofs. We characterize the complexity for a natural simple case: each gadget connects up to four locations in a perfect matching (but each direction can be traversable or not in the current state), has one or two states, every gadget traversal is immediately undoable, and that gadget locations are connected by an always-traversable forest, possibly restricted to avoid crossings in the plane. Specifically, we show that any single nontrivial four-location two-state gadget type is enough for motion planning to become PSPACE-complete, while any set of simpler gadgets (effectively two-location or one-state) has a polynomial-time motion planning algorithm. As a sample application, our results show that motion planning games with "spinners" are PSPACE-complete, establishing a new hard aspect of Zelda: Oracle of Seasons.

BibTeX - Entry

@InProceedings{demaine_et_al:LIPIcs:2018:8809,
  author =	{Erik D. Demaine and Isaac Grosof and Jayson Lynch and Mikhail Rudoy},
  title =	{{Computational Complexity of Motion Planning of a Robot through Simple Gadgets}},
  booktitle =	{9th International Conference on Fun with Algorithms (FUN 2018)},
  pages =	{18:1--18:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-067-5},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{100},
  editor =	{Hiro Ito and Stefano Leonardi and Linda Pagli and Giuseppe Prencipe},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/8809},
  URN =		{urn:nbn:de:0030-drops-88098},
  doi =		{10.4230/LIPIcs.FUN.2018.18},
  annote =	{Keywords: PSPACE, hardness, motion planning, puzzles}
}

Keywords: PSPACE, hardness, motion planning, puzzles
Collection: 9th International Conference on Fun with Algorithms (FUN 2018)
Issue Date: 2018
Date of publication: 04.06.2018

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