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Brief Announcement: Efficient Distributed Algorithms for Shape Reduction via Reconfigurable Circuits

Authors Nada Almalki , Siddharth Gupta , Othon Michail , Andreas Padalkin

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ACM Subject Classification
  • Theory of computation → Computational geometry
  • Theory of computation → Distributed computing models
Keywords
  • growth process
  • shrinking process
  • collision avoidance
  • programmable matter

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Abstract

In this paper, we study the problem of efficiently reducing geometric shapes into other such shapes in a distributed setting through size-changing operations. We develop distributed algorithms using the reconfigurable circuit model to enable fast node-to-node communication. Let n denote the number of nodes and k the number of turning points in the initial shape. We show that the system of nodes can reduce itself from any tree to a single node using only shrinking operations in O(k log n) rounds w.h.p. and any tree to its incompressible form in O(log n) rounds given prior knowledge of the incompressible nodes, or O(k log n) without it, w.h.p. We also give an algorithm to transform any tree to a topologically equivalent tree in O(k log n+log² n) rounds w.h.p. using both shrinking and growth operations. On the negative side, we show that one cannot hope for o(log² n)-round transformations for all shapes of Θ(log n) turning points.

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Nada Almalki, Siddharth Gupta, Othon Michail, and Andreas Padalkin. Brief Announcement: Efficient Distributed Algorithms for Shape Reduction via Reconfigurable Circuits. In 4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 330, pp. 20:1-20:6, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.SAND.2025.20

Author Details

Nada Almalki
  • Department of Computer Science, University of Liverpool, UK
Siddharth Gupta
  • Department of Computer Science & Information Systems, BITS Pilani Goa Campus, India
Othon Michail
  • Department of Computer Science, University of Liverpool, UK
Andreas Padalkin
  • Paderborn University, Germany

Funding

  • Padalkin, Andreas: This author was supported by the DFG Project SCHE 1592/10-1.

References

  1. Nada Almalki, Siddharth Gupta, and Othon Michail. On the exponential growth of geometric shapes. In ALGOWIN, volume 15026 of LNCS, pages 16-30. Springer, 2024. URL: https://doi.org/10.1007/978-3-031-74580-5_2.
  2. Nada Almalki and Othon Michail. On geometric shape construction via growth operations. Theor. Comput. Sci., 984:114324, 2024. URL: https://doi.org/10.1016/J.TCS.2023.114324.
  3. Chen Avin and Stefan Schmid. Toward demand-aware networking: a theory for self-adjusting networks. Comput. Commun. Rev., 48(5):31-40, 2018. URL: https://doi.org/10.1145/3310165.3310170.
  4. Michael Feldmann, Andreas Padalkin, Christian Scheideler, and Shlomi Dolev. Coordinating amoebots via reconfigurable circuits. J. Comput. Biol., 29(4):317-343, 2022. URL: https://doi.org/10.1089/CMB.2021.0363.
  5. Thorsten Götte, Kristian Hinnenthal, Christian Scheideler, and Julian Werthmann. Time-optimal construction of overlay networks. Distributed Comput., 36(3):313-347, 2023. URL: https://doi.org/10.1007/S00446-023-00442-4.
  6. Siddharth Gupta, Marc J. van Kreveld, Othon Michail, and Andreas Padalkin. Collision detection for modular robots - it is easy to cause collisions and hard to avoid them. In ALGOWIN, volume 15026 of LNCS, pages 76-90. Springer, 2024. URL: https://doi.org/10.1007/978-3-031-74580-5_6.
  7. George B. Mertzios, Othon Michail, George Skretas, Paul G. Spirakis, and Michail Theofilatos. The complexity of growing a graph. J. Comput. Syst. Sci., 147:103587, 2025. URL: https://doi.org/10.1016/J.JCSS.2024.103587.
  8. Othon Michail, George Skretas, and Paul G. Spirakis. Distributed computation and reconfiguration in actively dynamic networks. Distributed Comput., 35(2):185-206, 2022. URL: https://doi.org/10.1007/S00446-021-00415-5.
  9. Andreas Padalkin, Christian Scheideler, and Daniel Warner. The structural power of reconfigurable circuits in the amoebot model. Nat. Comput., 23(4):603-625, 2024. URL: https://doi.org/10.1007/S11047-024-09981-6.
  10. Damien Woods, Ho-Lin Chen, Scott Goodfriend, Nadine Dabby, Erik Winfree, and Peng Yin. Active self-assembly of algorithmic shapes and patterns in polylogarithmic time. In Innovations in Theoretical Computer Science, ITCS '13, pages 353-354. ACM, 2013. URL: https://doi.org/10.1145/2422436.2422476.
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