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Documents authored by Warner, Daniel

Document
DOI: 10.4230/LIPIcs.DNA.28.8
The Structural Power of Reconfigurable Circuits in the Amoebot Model

Authors: Andreas Padalkin, Christian Scheideler, and Daniel Warner

Published in: LIPIcs, Volume 238, 28th International Conference on DNA Computing and Molecular Programming (DNA 28) (2022)

Abstract
The amoebot model [Derakhshandeh et al., SPAA 2014] has been proposed as a model for programmable matter consisting of tiny, robotic elements called amoebots. We consider the reconfigurable circuit extension [Feldmann et al., JCB 2022] of the geometric (variant of the) amoebot model that allows the amoebot structure to interconnect amoebots by so-called circuits. A circuit permits the instantaneous transmission of signals between the connected amoebots. In this paper, we examine the structural power of the reconfigurable circuits. We start with some fundamental problems like the stripe computation problem where, given any connected amoebot structure S, an amoebot u in S, and some axis X, all amoebots belonging to axis X through u have to be identified. Second, we consider the global maximum problem, which identifies an amoebot at the highest possible position with respect to some direction in some given amoebot (sub)structure. A solution to this problem can then be used to solve the skeleton problem, where a (not necessarily simple) cycle of amoebots has to be found in the given amoebot structure which contains all boundary amoebots. A canonical solution to that problem can then be used to come up with a canonical path, which provides a unique characterization of the shape of the given amoebot structure. Constructing canonical paths for different directions will then allow the amoebots to set up a spanning tree and to check symmetry properties of the given amoebot structure. The problems are important for a number of applications like rapid shape transformation, energy dissemination, and structural monitoring. Interestingly, the reconfigurable circuit extension allows polylogarithmic-time solutions to all of these problems.
Cite as

Andreas Padalkin, Christian Scheideler, and Daniel Warner. The Structural Power of Reconfigurable Circuits in the Amoebot Model. In 28th International Conference on DNA Computing and Molecular Programming (DNA 28). Leibniz International Proceedings in Informatics (LIPIcs), Volume 238, pp. 8:1-8:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{padalkin_et_al:LIPIcs.DNA.28.8,
  author =	{Padalkin, Andreas and Scheideler, Christian and Warner, Daniel},
  title =	{{The Structural Power of Reconfigurable Circuits in the Amoebot Model}},
  booktitle =	{28th International Conference on DNA Computing and Molecular Programming (DNA 28)},
  pages =	{8:1--8:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-253-2},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{238},
  editor =	{Ouldridge, Thomas E. and Wickham, Shelley F. J.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DNA.28.8},
  URN =		{urn:nbn:de:0030-drops-167935},
  doi =		{10.4230/LIPIcs.DNA.28.8},
  annote =	{Keywords: progammable matter, amoebot model, reconfigurable circuits, spanning tree, symmetry detection}
}
Document
DOI: 10.4230/LIPIcs.DNA.28.9
Fault-Tolerant Shape Formation in the Amoebot Model

Authors: Irina Kostitsyna, Christian Scheideler, and Daniel Warner

Published in: LIPIcs, Volume 238, 28th International Conference on DNA Computing and Molecular Programming (DNA 28) (2022)

Abstract
The amoebot model is a distributed computing model of programmable matter. It envisions programmable matter as a collection of computational units called amoebots or particles that utilize local interactions to achieve tasks of coordination, movement and conformation. In the geometric amoebot model the particles operate on a hexagonal tessellation of the plane. Within this model, numerous problems such as leader election, shape formation or object coating have been studied. One area that has not received much attention so far, but is highly relevant for a practical implementation of programmable matter, is fault tolerance. The existing literature on that aspect allows particles to crash but assumes that crashed particles do not recover. We proposed a new model [Kostitsyna et al., 2022] in which a crash causes the memory of a particle to be reset and a crashed particle can detect that it has crashed and try to recover using its local information and communication capabilities. We present an algorithm that solves the hexagon shape formation problem in our model if a finite number of crashes occur and a designated leader particle does not fail. At the heart of our solution lies a fault-tolerant implementation of the spanning forest primitive, which, since other algorithms in the amoebot model also make use of it, is also of general interest.
Cite as

Irina Kostitsyna, Christian Scheideler, and Daniel Warner. Fault-Tolerant Shape Formation in the Amoebot Model. In 28th International Conference on DNA Computing and Molecular Programming (DNA 28). Leibniz International Proceedings in Informatics (LIPIcs), Volume 238, pp. 9:1-9:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{kostitsyna_et_al:LIPIcs.DNA.28.9,
  author =	{Kostitsyna, Irina and Scheideler, Christian and Warner, Daniel},
  title =	{{Fault-Tolerant Shape Formation in the Amoebot Model}},
  booktitle =	{28th International Conference on DNA Computing and Molecular Programming (DNA 28)},
  pages =	{9:1--9:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-253-2},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{238},
  editor =	{Ouldridge, Thomas E. and Wickham, Shelley F. J.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DNA.28.9},
  URN =		{urn:nbn:de:0030-drops-167949},
  doi =		{10.4230/LIPIcs.DNA.28.9},
  annote =	{Keywords: programmable matter, amoebot model, fault tolerance, shape formation}
}
Document
Brief Announcement
DOI: 10.4230/LIPIcs.SAND.2022.23
Brief Announcement: Fault-Tolerant Shape Formation in the Amoebot Model

Authors: Irina Kostitsyna, Christian Scheideler, and Daniel Warner

Published in: LIPIcs, Volume 221, 1st Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2022)

Abstract
The amoebot model is a distributed computing model of programmable matter. It envisions programmable matter as a collection of computational units called amoebots or particles that utilize local interactions to achieve tasks of coordination, movement and conformation. In the geometric amoebot model the particles operate on a hexagonal tessellation of the plane. Within this model, numerous problems such as leader election, shape formation or object coating have been studied. One area that has not received much attention so far, but is highly relevant for a practical implementation of programmable matter, is fault tolerance. The existing literature on that aspect allows particles to crash but assumes that crashed particles do not recover. We propose a new model in which a crash causes the memory of a particle to be reset and a crashed particle can detect that it has crashed and try to recover using its local information and communication capabilities. We propose an algorithm that solves the hexagon shape formation problem in our model if a finite number of crashes occur and a designated leader particle does not fail. At the heart of our solution lies a fault-tolerant implementation of the spanning forest primitive, which, since other algorithms in the amoebot model also make use of it, is also of general interest.
Cite as

Irina Kostitsyna, Christian Scheideler, and Daniel Warner. Brief Announcement: Fault-Tolerant Shape Formation in the Amoebot Model. In 1st Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 221, pp. 23:1-23:3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{kostitsyna_et_al:LIPIcs.SAND.2022.23,
  author =	{Kostitsyna, Irina and Scheideler, Christian and Warner, Daniel},
  title =	{{Brief Announcement: Fault-Tolerant Shape Formation in the Amoebot Model}},
  booktitle =	{1st Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2022)},
  pages =	{23:1--23:3},
  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/entities/document/10.4230/LIPIcs.SAND.2022.23},
  URN =		{urn:nbn:de:0030-drops-159656},
  doi =		{10.4230/LIPIcs.SAND.2022.23},
  annote =	{Keywords: Programmable matter, Geometric amoebot model, Fault tolerance, Shape formation}
}
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