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Optimal In-Place Compaction of Sliding Cubes

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

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Author Details

Irina Kostitsyna
  • TU Eindhoven, The Netherlands
Tim Ophelders
  • Utrecht University, The Netherlands
  • TU Eindhoven, The Netherlands
Irene Parada
  • Universitat Politècnica de Catalunya, Barcelona, Spain
Tom Peters
  • TU Eindhoven, The Netherlands
Willem Sonke
  • TU Eindhoven, The Netherlands
Bettina Speckmann
  • TU Eindhoven, The Netherlands

Funding

  • Ophelders, Tim: partially supported by the Dutch Research Council (NWO) under project no. VI.Veni.212.260.

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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)
https://doi.org/10.4230/LIPIcs.SWAT.2024.31

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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Computational geometry
Keywords
  • Sliding cubes
  • Reconfiguration algorithm
  • Modular robots

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References

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