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Unlabeled Multi-Robot Motion Planning with Improved Separation Trade-Offs

Authors Tsuri Farhana , Omrit Filtser , Shalev Goldshtein

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ACM Subject Classification
  • Theory of computation → Computational geometry
Keywords
  • multi-robot motion planning

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Abstract

We study unlabeled multi-robot motion planning for unit-disk robots in a polygonal environment. Although the problem is hard in general, polynomial-time solutions exist under appropriate separation assumptions on start and target positions. Solovey et al. (RSS'15) provide a near-optimal solution assuming that start/target positions must have pairwise distance at least 4, and at least √5≈2.236 from obstacles. This raises the question of whether polynomial-time algorithms can be obtained in even more densely packed environments.
In this paper we present a generalized algorithm that achieve different trade-offs on the robots-separation and obstacles-separation bounds, all significantly improving upon the state of the art. Specifically, we obtain polynomial-time constant-approximation algorithms to minimize the total path length when (i) the robots-separation is 2 2/3 and the obstacles-separation is 1 2/3, or (ii) the robots-separation is ≈3.291 and the obstacles-separation ≈1.354. Additionally, we introduce a different strategy yielding a polynomial-time solution when the robots-separation is only 2, and the obstacles-separation is 3. Finally, we show that without any robots-separation assumption, obstacles-separation of at least 1.5 may be necessary for a solution to exist.

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Tsuri Farhana, Omrit Filtser, and Shalev Goldshtein. Unlabeled Multi-Robot Motion Planning with Improved Separation Trade-Offs. In 42nd International Symposium on Computational Geometry (SoCG 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 367, pp. 43:1-43:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.SoCG.2026.43

Author Details

Tsuri Farhana
  • The Stein Faculty of Computer and Information Science, Ben-Gurion University of the Negev, Beer Sheva, Israel
Omrit Filtser
  • Department of Mathematics and Computer Science, The Open University of Israel, Ra'anana, Israel
Shalev Goldshtein
  • Department of Mathematics and Computer Science, The Open University of Israel, Ra'anana, Israel

Funding

  • Filtser, Omrit: This research was supported by the ISRAEL SCIENCE FOUNDATION (grant No. 2135/24).
  • Goldshtein, Shalev: This research was supported by the ISRAEL SCIENCE FOUNDATION (grant No. 2135/24).

Acknowledgements

We thank Dan Halperin for introducing us to the problem and for helpful discussions. We are also grateful to the anonymous reviewers for their insightful comments, which helped improve the structure and presentation of the paper.

References

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