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DOI: 10.4230/LIPIcs.OPODIS.2021.10

Pattern Formation by Robots with Inaccurate Movements

Authors: Kaustav Bose, Archak Das, and Buddhadeb Sau

Published in: LIPIcs, Volume 217, 25th International Conference on Principles of Distributed Systems (OPODIS 2021)

Abstract

Arbitrary Pattern Formation is a fundamental problem in autonomous mobile robot systems. The problem asks to design a distributed algorithm that moves a team of autonomous, anonymous and identical mobile robots to form any arbitrary pattern F given as input. In this paper, we study the problem for robots whose movements can be inaccurate. Our movement model assumes errors in both direction and extent of the intended movement. Forming the given pattern exactly is not possible in this setting. So we require that the robots must form a configuration which is close to the given pattern F. We call this the Approximate Arbitrary Pattern Formation problem. With no agreement in coordinate system, the problem is unsolvable, even by fully synchronous robots, if the initial configuration 1) has rotational symmetry and there is no robot at the center of rotation or 2) has reflectional symmetry and there is no robot on the reflection axis. From all other initial configurations, we solve the problem by 1) oblivious, silent and semi-synchronous robots and 2) oblivious, asynchronous robots that can communicate using externally visible lights.

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Kaustav Bose, Archak Das, and Buddhadeb Sau. Pattern Formation by Robots with Inaccurate Movements. In 25th International Conference on Principles of Distributed Systems (OPODIS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 217, pp. 10:1-10:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{bose_et_al:LIPIcs.OPODIS.2021.10,
  author =	{Bose, Kaustav and Das, Archak and Sau, Buddhadeb},
  title =	{{Pattern Formation by Robots with Inaccurate Movements}},
  booktitle =	{25th International Conference on Principles of Distributed Systems (OPODIS 2021)},
  pages =	{10:1--10:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-219-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{217},
  editor =	{Bramas, Quentin and Gramoli, Vincent and Milani, Alessia},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2021.10},
  URN =		{urn:nbn:de:0030-drops-157850},
  doi =		{10.4230/LIPIcs.OPODIS.2021.10},
  annote =	{Keywords: Distributed Algorithm, Mobile Robots, Movement Error, Approximate Arbitrary Pattern Formation, Look-Compute-Move, Minimum Enclosing Circle}
}

Document

DOI: 10.4230/LIPIcs.SoCG.2021.7

Complexity of Maximum Cut on Interval Graphs

Authors: Ranendu Adhikary, Kaustav Bose, Satwik Mukherjee, and Bodhayan Roy

Published in: LIPIcs, Volume 189, 37th International Symposium on Computational Geometry (SoCG 2021)

Abstract

We resolve the longstanding open problem concerning the computational complexity of Max Cut on interval graphs by showing that it is NP-complete.

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Ranendu Adhikary, Kaustav Bose, Satwik Mukherjee, and Bodhayan Roy. Complexity of Maximum Cut on Interval Graphs. In 37th International Symposium on Computational Geometry (SoCG 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 189, pp. 7:1-7:11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{adhikary_et_al:LIPIcs.SoCG.2021.7,
  author =	{Adhikary, Ranendu and Bose, Kaustav and Mukherjee, Satwik and Roy, Bodhayan},
  title =	{{Complexity of Maximum Cut on Interval Graphs}},
  booktitle =	{37th International Symposium on Computational Geometry (SoCG 2021)},
  pages =	{7:1--7:11},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-184-9},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{189},
  editor =	{Buchin, Kevin and Colin de Verdi\`{e}re, \'{E}ric},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2021.7},
  URN =		{urn:nbn:de:0030-drops-138067},
  doi =		{10.4230/LIPIcs.SoCG.2021.7},
  annote =	{Keywords: Maximum cut, Interval graph, NP-complete}
}

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Documents authored by Bose, Kaustav

Pattern Formation by Robots with Inaccurate Movements

Abstract

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Complexity of Maximum Cut on Interval Graphs

Abstract

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