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Documents authored by Shahrouzi, Gabriel

Document
DOI: 10.4230/LIPIcs.ESA.2026.26
Sliding Cubes in Parallel

Authors: Hugo A. Akitaya, Joseph Dorfer, Peter Kramer, Christian Rieck, Gabriel Shahrouzi, and Frederick Stock

Published in: LIPIcs, Volume 388, 34th Annual European Symposium on Algorithms (ESA 2026)

Abstract
In the classic sliding cube model for programmable matter in three dimensions, the task is to find a reconfiguration sequence between two connected configurations of n indistinguishable unit cube modules by sliding modules along their neighbors' faces. Depending on the objective, this sequence should minimize either the total energy expended (the number of moves) or the total elapsed time (the makespan). We give a number of results for the three-dimensional setting, including (i) the first algorithm that achieves worst-case optimal makespan under parallel motion in three dimensions, (ii) a proof of log-APX-hardness to decide either the optimal makespan or the optimal number of moves, which is the strongest known inapproximability bound in any related model, and (iii) a proof of NP-hardness to decide the optimal makespan under parallel motion, even if the two configurations differ only by one module and the optimal makespan is at most two. Our results strengthen the inapproximability claim from [Hugo A. Akitaya et al., 2022] and answer a question of [Akitaya et al., 2025] in the negative.
Cite as

Hugo A. Akitaya, Joseph Dorfer, Peter Kramer, Christian Rieck, Gabriel Shahrouzi, and Frederick Stock. Sliding Cubes in Parallel. In 34th Annual European Symposium on Algorithms (ESA 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 388, pp. 26:1-26:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{a.akitaya_et_al:LIPIcs.ESA.2026.26,
  author =	{A. Akitaya, Hugo and Dorfer, Joseph and Kramer, Peter and Rieck, Christian and Shahrouzi, Gabriel and Stock, Frederick},
  title =	{{Sliding Cubes in Parallel}},
  booktitle =	{34th Annual European Symposium on Algorithms (ESA 2026)},
  pages =	{26:1--26:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-445-1},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{388},
  editor =	{Bille, Philip and Pettie, Seth and Storandt, Sabine},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2026.26},
  URN =		{urn:nbn:de:0030-drops-271621},
  doi =		{10.4230/LIPIcs.ESA.2026.26},
  annote =	{Keywords: Sliding squares, parallel motion, reconfigurability, three dimensions, constant makespan, log-APX-hardness, NP-hardness, worst-case optimality}
}
Document
Media Exposition
DOI: 10.4230/LIPIcs.SoCG.2026.96
Sliding Cubes in Parallel (Media Exposition)

Authors: Hugo A. Akitaya, Joseph Dorfer, Peter Kramer, Christian Rieck, Soham Samanta, Gabriel Shahrouzi, and Frederick Stock

Published in: LIPIcs, Volume 367, 42nd International Symposium on Computational Geometry (SoCG 2026)

Abstract
The sliding cubes model serves as a well-established theoretical framework for formalizing and analyzing reconfiguration algorithms in modular robotic systems built from face-connected cubic modules. We extend the parallel sliding cubes model from two to three dimensions, presenting new algorithms, surprising complexity results, and a generalization of the best known bounds from two to three dimensions. A companion video visualizes and explains our results.
Cite as

Hugo A. Akitaya, Joseph Dorfer, Peter Kramer, Christian Rieck, Soham Samanta, Gabriel Shahrouzi, and Frederick Stock. Sliding Cubes in Parallel (Media Exposition). In 42nd International Symposium on Computational Geometry (SoCG 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 367, pp. 96:1-96:5, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{a.akitaya_et_al:LIPIcs.SoCG.2026.96,
  author =	{A. Akitaya, Hugo and Dorfer, Joseph and Kramer, Peter and Rieck, Christian and Samanta, Soham and Shahrouzi, Gabriel and Stock, Frederick},
  title =	{{Sliding Cubes in Parallel}},
  booktitle =	{42nd International Symposium on Computational Geometry (SoCG 2026)},
  pages =	{96:1--96:5},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-418-5},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{367},
  editor =	{Ahn, Hee-Kap and Hoffmann, Michael and Nayyeri, Amir},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2026.96},
  URN =		{urn:nbn:de:0030-drops-259020},
  doi =		{10.4230/LIPIcs.SoCG.2026.96},
  annote =	{Keywords: Sliding squares, parallel motion, reconfigurability, three dimensions, constant makespan, log-APX hardness, NP-hardness, worst-case optimality}
}
Document
Media Exposition
DOI: 10.4230/LIPIcs.SoCG.2025.85
Finding Shortest Reconfiguration Sequences for Modular Robots (Media Exposition)

Authors: UML Modular Robotics Group, Hugo A. Akitaya, Andrew Clements, Sam Downey, Jonathan Eisenbies, Soham Samanta, Gabriel Shahrouzi, and Frederick Stock

Published in: LIPIcs, Volume 332, 41st International Symposium on Computational Geometry (SoCG 2025)

Abstract
This paper introduces a set of tools built to help researchers design algorithms for modular robots. These tools can brute force solutions to specific reconfigurations, visualize movements of modular robots, and can be used to design specific configurations of robots. Multiple models of modular robots are supported, and can be added by users.
Cite as

UML Modular Robotics Group, Hugo A. Akitaya, Andrew Clements, Sam Downey, Jonathan Eisenbies, Soham Samanta, Gabriel Shahrouzi, and Frederick Stock. Finding Shortest Reconfiguration Sequences for Modular Robots (Media Exposition). In 41st International Symposium on Computational Geometry (SoCG 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 332, pp. 85:1-85:5, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{umlmodularroboticsgroup_et_al:LIPIcs.SoCG.2025.85,
  author =	{UML Modular Robotics Group and A. Akitaya, Hugo and Clements, Andrew and Downey, Sam and Eisenbies, Jonathan and Samanta, Soham and Shahrouzi, Gabriel and Stock, Frederick},
  title =	{{Finding Shortest Reconfiguration Sequences for Modular Robots}},
  booktitle =	{41st International Symposium on Computational Geometry (SoCG 2025)},
  pages =	{85:1--85:5},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-370-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{332},
  editor =	{Aichholzer, Oswin and Wang, Haitao},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2025.85},
  URN =		{urn:nbn:de:0030-drops-232371},
  doi =		{10.4230/LIPIcs.SoCG.2025.85},
  annote =	{Keywords: modular reconfigurable robots, sliding cube model, reconfiguration}
}

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