Document Open Access Logo

Sliding Cubes in Parallel (Media Exposition)

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

PDF

File

Thumbnail PDF
PDF
LIPIcs.SoCG.2026.96.pdf
  • Filesize: 6.6 MB
  • 5 pages

Document Identifiers

Related Versions

Subject Classification

ACM Subject Classification
  • Theory of computation → Computational geometry
Keywords
  • Sliding squares
  • parallel motion
  • reconfigurability
  • three dimensions
  • constant makespan
  • log-APX hardness
  • NP-hardness
  • worst-case optimality

Metrics

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 Get BibTex

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) https://doi.org/10.4230/LIPIcs.SoCG.2026.96

Author Details

Hugo A. Akitaya
  • Miner School of Computer and Information Sciences, University of Massachusetts Lowell, MA, USA
Joseph Dorfer
  • Institute of Algorithms and Theory, Graz University of Technology, Austria
Peter Kramer
  • Department of Computer Science, TU Braunschweig, Germany
Christian Rieck
  • Institute of Mathematics, University of Kassel, Germany
Soham Samanta
  • Greater Commonwealth Virtual School, Medford, MA, USA
Gabriel Shahrouzi
  • Miner School of Computer and Information Sciences, University of Massachusetts Lowell, MA, USA
Frederick Stock
  • Miner School of Computer and Information Sciences, University of Massachusetts Lowell, MA, USA

Funding

Hugo A. Akitaya, Gabriel Shahrouzi, and Frederick Stock: Supported by the National Science Foundation (NSF), grant CCF-2348067.
  • Dorfer, Joseph: Austrian Science Fund (FWF) 10.55776/DOC183.
  • Kramer, Peter: Partially funded by a fellowship of the German Academic Exchange Service (DAAD) and the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation), grant 530918134.
  • Rieck, Christian: Funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation), grant 522790373.

References

  1. Hugo A. Akitaya, Joseph Dorfer, Peter Kramer, Christian Rieck, Gabriel Shahrouzi, and Frederick Stock. Sliding cubes in parallel, 2026. URL: https://doi.org/10.48550/arXiv.2603.08537.
  2. Hugo A. Akitaya, Sándor P. Fekete, Peter Kramer, Saba Molaei, Christian Rieck, Frederick Stock, and Tobias Wallner. Sliding squares in parallel. In European Symposium on Algorithms (ESA), pages 28:1-28:17, 2025. URL: https://doi.org/10.4230/LIPIcs.ESA.2025.28.
  3. Mark de Berg and Amirali Khosravi. Optimal binary space partitions for segments in the plane. International Journal on Computational Geometry and Applications, 22(3):187-206, 2012. URL: https://doi.org/10.1142/S0218195912500045.
  4. Irit Dinur and David Steurer. Analytical approach to parallel repetition. In Symposium on Theory of Computing (STOC), pages 624-633, 2014. URL: https://doi.org/10.1145/2591796.2591884.
  5. Robert Fitch, Zack J. Butler, and Daniela L. Rus. Reconfiguration planning for heterogeneous self-reconfiguring robots. In International Conference on Intelligent Robots and Systems (IROS), pages 2460-2467, 2003. URL: https://doi.org/10.1109/IROS.2003.1249239.
  6. 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. In Symposium on Computational Geometry (SoCG), pages 85:1-85:5, 2025. URL: https://doi.org/10.4230/LIPIcs.SoCG.2025.85.
  7. Irina Kostitsyna, Tim Ophelders, Irene Parada, Tom Peters, Willem Sonke, and Bettina Speckmann. Optimal in-place compaction of sliding cubes. In Symposium on Computational Geometry (SoCG), pages 89:1-89:4, 2024. URL: https://doi.org/10.4230/LIPIcs.SoCG.2024.89.
Any Issues?
X

Feedback on the Current Page

CAPTCHA

Thanks for your feedback!

Feedback submitted to Dagstuhl Publishing

Could not send message

Please try again later or send an E-mail
© 2023-2026 Schloss Dagstuhl – LZI GmbH Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact