3 Search Results for "Piranda, Benoît"

Document
DOI: 10.4230/LIPIcs.DISC.2025.7
On the Shape Containment Problem Within the Amoebot Model with Reconfigurable Circuits

Authors: Matthias Artmann, Andreas Padalkin, and Christian Scheideler

Published in: LIPIcs, Volume 356, 39th International Symposium on Distributed Computing (DISC 2025)

Abstract
In programmable matter, we consider a large number of tiny, primitive computational entities called particles that run distributed algorithms to control global properties of the particle structure. Shape formation problems, where the particles have to reorganize themselves into a desired shape using basic movement abilities, are particularly interesting. In the related shape containment problem, the particles are given the description of a shape S and have to find maximally scaled representations of S within the initial configuration, without movements. For example, if S is a triangle, they have to identify the largest subsets of particles that already form a triangle. While the shape formation problem is being studied extensively, no attention has been given to the shape containment problem, which may have additional uses besides shape formation, such as detecting structural flaws. In this paper, we consider the shape containment problem within the geometric amoebot model for programmable matter, using its reconfigurable circuit extension to enable the instantaneous transmission of primitive signals on connected subsets of particles. We first prove a lower runtime bound of Ω (√n) synchronous rounds for the general problem, where n is the number of particles. Then, we present simple and efficient primitives for identifying subsets that form the desired shape. Using these primitives, we construct a large class of shapes which we call snowflakes. This class contains, among others, all shapes composed of parallelograms and hexagons, and the class of star convex shapes. Let k be the maximum scale of the considered shape in a given amoebot structure. If the shape is star convex, we solve it within 𝒪 (log² k) rounds. If it is a snowflake but not star convex, we solve it within 𝒪 (√n log n) rounds.
Cite as

Matthias Artmann, Andreas Padalkin, and Christian Scheideler. On the Shape Containment Problem Within the Amoebot Model with Reconfigurable Circuits. In 39th International Symposium on Distributed Computing (DISC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 356, pp. 7:1-7:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{artmann_et_al:LIPIcs.DISC.2025.7,
  author =	{Artmann, Matthias and Padalkin, Andreas and Scheideler, Christian},
  title =	{{On the Shape Containment Problem Within the Amoebot Model with Reconfigurable Circuits}},
  booktitle =	{39th International Symposium on Distributed Computing (DISC 2025)},
  pages =	{7:1--7:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-402-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{356},
  editor =	{Kowalski, Dariusz R.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2025.7},
  URN =		{urn:nbn:de:0030-drops-248240},
  doi =		{10.4230/LIPIcs.DISC.2025.7},
  annote =	{Keywords: Programmable matter, amoebot model, reconfigurable circuits, shape containment}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.28
Sliding Squares in Parallel

Authors: Hugo A. Akitaya, Sándor P. Fekete, Peter Kramer, Saba Molaei, Christian Rieck, Frederick Stock, and Tobias Wallner

Published in: LIPIcs, Volume 351, 33rd Annual European Symposium on Algorithms (ESA 2025)

Abstract
We consider algorithmic problems motivated by modular robotic reconfiguration in the sliding square model, in which we are given n square-shaped modules in a (labeled or unlabeled) start configuration and need to find a schedule of sliding moves to transform it into a desired goal configuration, maintaining connectivity of the configuration at all times. Recent work has aimed at minimizing the total number of moves, resulting in fully sequential schedules that can perform reconfiguration in 𝒪(n²) moves, or 𝒪(nP) for arrangements of bounding box perimeter size P. We provide first results in the sliding square model that exploit parallel motion, performing reconfiguration in worst-case optimal makespan of 𝒪(P). We also provide tight bounds on the complexity of the problem by showing that even deciding the possibility of reconfiguration within makespan 1 is NP-complete in the unlabeled case. In the labeled variant, we note that deciding the same for makespan 2 is NP-complete, while makespan 1 is straightforward.
Cite as

Hugo A. Akitaya, Sándor P. Fekete, Peter Kramer, Saba Molaei, Christian Rieck, Frederick Stock, and Tobias Wallner. Sliding Squares in Parallel. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 28:1-28:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{a.akitaya_et_al:LIPIcs.ESA.2025.28,
  author =	{A. Akitaya, Hugo and Fekete, S\'{a}ndor P. and Kramer, Peter and Molaei, Saba and Rieck, Christian and Stock, Frederick and Wallner, Tobias},
  title =	{{Sliding Squares in Parallel}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{28:1--28:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-395-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{351},
  editor =	{Benoit, Anne and Kaplan, Haim and Wild, Sebastian and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2025.28},
  URN =		{urn:nbn:de:0030-drops-244961},
  doi =		{10.4230/LIPIcs.ESA.2025.28},
  annote =	{Keywords: Sliding squares, parallel motion, reconfigurability, motion planning, multi-agent path finding, makespan, swarm robotics, computational geometry}
}
Document
Media Exposition
DOI: 10.4230/LIPIcs.SoCG.2022.65
Space Ants: Episode II - Coordinating Connected Catoms (Media Exposition)

Authors: Julien Bourgeois, Sándor P. Fekete, Ramin Kosfeld, Peter Kramer, Benoît Piranda, Christian Rieck, and Christian Scheffer

Published in: LIPIcs, Volume 224, 38th International Symposium on Computational Geometry (SoCG 2022)

Abstract
How can a set of identical mobile agents coordinate their motions to transform their arrangement from a given starting to a desired goal configuration? We consider this question in the context of actual physical devices called Catoms, which can perform reconfiguration, but need to maintain connectivity at all times to ensure communication and energy supply. We demonstrate and animate algorithmic results, in particular a proof of hardness, as well as an algorithm that guarantees constant stretch for certain classes of arrangements: If mapping the start configuration to the target configuration requires a maximum Manhattan distance of d, then the total duration of our overall schedule is in 𝒪(d), which is optimal up to constant factors.
Cite as

Julien Bourgeois, Sándor P. Fekete, Ramin Kosfeld, Peter Kramer, Benoît Piranda, Christian Rieck, and Christian Scheffer. Space Ants: Episode II - Coordinating Connected Catoms (Media Exposition). In 38th International Symposium on Computational Geometry (SoCG 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 224, pp. 65:1-65:6, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{bourgeois_et_al:LIPIcs.SoCG.2022.65,
  author =	{Bourgeois, Julien and Fekete, S\'{a}ndor P. and Kosfeld, Ramin and Kramer, Peter and Piranda, Beno\^{i}t and Rieck, Christian and Scheffer, Christian},
  title =	{{Space Ants: Episode II - Coordinating Connected Catoms}},
  booktitle =	{38th International Symposium on Computational Geometry (SoCG 2022)},
  pages =	{65:1--65:6},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-227-3},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{224},
  editor =	{Goaoc, Xavier and Kerber, Michael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2022.65},
  URN =		{urn:nbn:de:0030-drops-160732},
  doi =		{10.4230/LIPIcs.SoCG.2022.65},
  annote =	{Keywords: Motion planning, parallel motion, bounded stretch, scaled shape, makespan, connectivity, swarm robotics}
}
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