License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.SAND.2022.20
URN: urn:nbn:de:0030-drops-159626
URL: https://drops.dagstuhl.de/opus/volltexte/2022/15962/
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Yamada, Ryonosuke ; Yamauchi, Yukiko

Search by a Metamorphic Robotic System in a Finite 3D Cubic Grid

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LIPIcs-SAND-2022-20.pdf (10 MB)


Abstract

We consider search in a finite 3D cubic grid by a metamorphic robotic system (MRS), that consists of anonymous modules. A module can perform a sliding and rotation while the whole modules keep connectivity. As the number of modules increases, the variety of actions that the MRS can perform increases. The search problem requires the MRS to find a target in a given finite field. Doi et al. (SSS 2018) demonstrate a necessary and sufficient number of modules for search in a finite 2D square grid. We consider search in a finite 3D cubic grid and investigate the effect of common knowledge. We consider three different settings. First, we show that three modules are necessary and sufficient when all modules are equipped with a common compass, i.e., they agree on the direction and orientation of the x, y, and z axes. Second, we show that four modules are necessary and sufficient when all modules agree on the direction and orientation of the vertical axis. Finally, we show that five modules are necessary and sufficient when all modules are not equipped with a common compass. Our results show that the shapes of the MRS in the 3D cubic grid have richer structure than those in the 2D square grid.

BibTeX - Entry

@InProceedings{yamada_et_al:LIPIcs.SAND.2022.20,
  author =	{Yamada, Ryonosuke and Yamauchi, Yukiko},
  title =	{{Search by a Metamorphic Robotic System in a Finite 3D Cubic Grid}},
  booktitle =	{1st Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2022)},
  pages =	{20:1--20:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-224-2},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{221},
  editor =	{Aspnes, James and Michail, Othon},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2022/15962},
  URN =		{urn:nbn:de:0030-drops-159626},
  doi =		{10.4230/LIPIcs.SAND.2022.20},
  annote =	{Keywords: Distributed system, metamorphic robotic system, search, and 3D cubic grid}
}

Keywords: Distributed system, metamorphic robotic system, search, and 3D cubic grid
Collection: 1st Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2022)
Issue Date: 2022
Date of publication: 29.04.2022


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