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Media Exposition
DOI: 10.4230/LIPIcs.SoCG.2024.89
Optimal In-Place Compaction of Sliding Cubes (Media Exposition)

Authors: Irina Kostitsyna, Tim Ophelders, Irene Parada, Tom Peters, Willem Sonke, and Bettina Speckmann

Published in: LIPIcs, Volume 293, 40th International Symposium on Computational Geometry (SoCG 2024)

Abstract
The sliding cubes model is a well-established theoretical framework that supports the analysis of reconfiguration algorithms for modular robots consisting of face-connected cubes. This note accompanies a video that explains our in-place algorithm for reconfiguration in the sliding cubes model. Specifically, our algorithm [Irina Kostitsyna et al., 2023] reconfigures any n-cube configuration into a compact canonical shape using a number of moves proportional to the sum of coordinates of the input cubes. As is common in the literature, we can then reconfigure between two arbitrary shapes via their canonical configurations. The number of moves performed by our algorithm is asymptotically worst-case optimal and strictly improves upon the current state-of-the-art.
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Irina Kostitsyna, Tim Ophelders, Irene Parada, Tom Peters, Willem Sonke, and Bettina Speckmann. Optimal In-Place Compaction of Sliding Cubes (Media Exposition). In 40th International Symposium on Computational Geometry (SoCG 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 293, pp. 89:1-89:4, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{kostitsyna_et_al:LIPIcs.SoCG.2024.89,
  author =	{Kostitsyna, Irina and Ophelders, Tim and Parada, Irene and Peters, Tom and Sonke, Willem and Speckmann, Bettina},
  title =	{{Optimal In-Place Compaction of Sliding Cubes}},
  booktitle =	{40th International Symposium on Computational Geometry (SoCG 2024)},
  pages =	{89:1--89:4},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-316-4},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{293},
  editor =	{Mulzer, Wolfgang and Phillips, Jeff M.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2024.89},
  URN =		{urn:nbn:de:0030-drops-200347},
  doi =		{10.4230/LIPIcs.SoCG.2024.89},
  annote =	{Keywords: Sliding cubes, Reconfiguration algorithm, Modular robots}
}
Document
DOI: 10.4230/LIPIcs.SWAT.2024.31
Optimal In-Place Compaction of Sliding Cubes

Authors: Irina Kostitsyna, Tim Ophelders, Irene Parada, Tom Peters, Willem Sonke, and Bettina Speckmann

Published in: LIPIcs, Volume 294, 19th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2024)

Abstract
The sliding cubes model is a well-established theoretical framework that supports the analysis of reconfiguration algorithms for modular robots consisting of face-connected cubes. As is common in the literature, we focus on reconfiguration via an intermediate canonical shape. Specifically, we present an in-place algorithm that reconfigures any n-cube configuration into a compact canonical shape using a number of moves proportional to the sum of coordinates of the input cubes. This result is asymptotically optimal and strictly improves on all prior work. Furthermore, our algorithm directly extends to dimensions higher than three.
Cite as

Irina Kostitsyna, Tim Ophelders, Irene Parada, Tom Peters, Willem Sonke, and Bettina Speckmann. Optimal In-Place Compaction of Sliding Cubes. In 19th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 294, pp. 31:1-31:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{kostitsyna_et_al:LIPIcs.SWAT.2024.31,
  author =	{Kostitsyna, Irina and Ophelders, Tim and Parada, Irene and Peters, Tom and Sonke, Willem and Speckmann, Bettina},
  title =	{{Optimal In-Place Compaction of Sliding Cubes}},
  booktitle =	{19th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2024)},
  pages =	{31:1--31:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-318-8},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{294},
  editor =	{Bodlaender, Hans L.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2024.31},
  URN =		{urn:nbn:de:0030-drops-200713},
  doi =		{10.4230/LIPIcs.SWAT.2024.31},
  annote =	{Keywords: Sliding cubes, Reconfiguration algorithm, Modular robots}
}
Document
DOI: 10.4230/LIPIcs.DISC.2023.27
Fast Reconfiguration for Programmable Matter

Authors: Irina Kostitsyna, Tom Peters, and Bettina Speckmann

Published in: LIPIcs, Volume 281, 37th International Symposium on Distributed Computing (DISC 2023)

Abstract
The concept of programmable matter envisions a very large number of tiny and simple robot particles forming a smart material. Even though the particles are restricted to local communication, local movement, and simple computation, their actions can nevertheless result in the global change of the material’s physical properties and geometry. A fundamental algorithmic task for programmable matter is to achieve global shape reconfiguration by specifying local behavior of the particles. In this paper we describe a new approach for shape reconfiguration in the amoebot model. The amoebot model is a distributed model which significantly restricts memory, computing, and communication capacity of the individual particles. Thus the challenge lies in coordinating the actions of particles to produce the desired behavior of the global system. Our reconfiguration algorithm is the first algorithm that does not use a canonical intermediate configuration when transforming between arbitrary shapes. We introduce new geometric primitives for amoebots and show how to reconfigure particle systems, using these primitives, in a linear number of activation rounds in the worst case. In practice, our method exploits the geometry of the symmetric difference between input and output shape: it minimizes unnecessary disassembly and reassembly of the particle system when the symmetric difference between the initial and the target shapes is small. Furthermore, our reconfiguration algorithm moves the particles over as many parallel shortest paths as the problem instance allows.
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Irina Kostitsyna, Tom Peters, and Bettina Speckmann. Fast Reconfiguration for Programmable Matter. In 37th International Symposium on Distributed Computing (DISC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 281, pp. 27:1-27:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{kostitsyna_et_al:LIPIcs.DISC.2023.27,
  author =	{Kostitsyna, Irina and Peters, Tom and Speckmann, Bettina},
  title =	{{Fast Reconfiguration for Programmable Matter}},
  booktitle =	{37th International Symposium on Distributed Computing (DISC 2023)},
  pages =	{27:1--27:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-301-0},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{281},
  editor =	{Oshman, Rotem},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2023.27},
  URN =		{urn:nbn:de:0030-drops-191533},
  doi =		{10.4230/LIPIcs.DISC.2023.27},
  annote =	{Keywords: Programmable matter, amoebot model, shape reconfiguration}
}
Document
Brief Announcement
DOI: 10.4230/LIPIcs.DISC.2022.47
Brief Announcement: An Effective Geometric Communication Structure for Programmable Matter

Authors: Irina Kostitsyna, Tom Peters, and Bettina Speckmann

Published in: LIPIcs, Volume 246, 36th International Symposium on Distributed Computing (DISC 2022)

Abstract
The concept of programmable matter envisions a very large number of tiny and simple robot particles forming a smart material that can change its physical properties and shape based on the outcome of computation and movement performed by the individual particles in a concurrent manner. We use geometric insights to develop a new type of shortest path tree for programmable matter systems. Our feather trees utilize geometry to allow particles and information to traverse the programmable matter structure via shortest paths even in the presence of multiple overlapping trees.
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Irina Kostitsyna, Tom Peters, and Bettina Speckmann. Brief Announcement: An Effective Geometric Communication Structure for Programmable Matter. In 36th International Symposium on Distributed Computing (DISC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 246, pp. 47:1-47:3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{kostitsyna_et_al:LIPIcs.DISC.2022.47,
  author =	{Kostitsyna, Irina and Peters, Tom and Speckmann, Bettina},
  title =	{{Brief Announcement: An Effective Geometric Communication Structure for Programmable Matter}},
  booktitle =	{36th International Symposium on Distributed Computing (DISC 2022)},
  pages =	{47:1--47:3},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-255-6},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{246},
  editor =	{Scheideler, Christian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2022.47},
  URN =		{urn:nbn:de:0030-drops-172386},
  doi =		{10.4230/LIPIcs.DISC.2022.47},
  annote =	{Keywords: Programmable matter, amoebot model, shape reconfiguration}
}
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