Document Open Access Logo

Tilt Automata: Gathering Particles with Uniform External Control

Authors Sándor P. Fekete , Jonas Friemel , Peter Kramer , Jan-Marc Reinhardt , Christian Rieck , Christian Scheffer

PDF

File

Thumbnail PDF
PDF
LIPIcs.SoCG.2026.44.pdf
  • Filesize: 1.24 MB
  • 19 pages

Document Identifiers

Related Versions

Subject Classification

ACM Subject Classification
  • Theory of computation → Computational geometry
Keywords
  • Uniform control
  • gathering
  • full tilt
  • polyominoes
  • synchronizing automata

Metrics

Abstract

Motivated by targeted drug delivery, we investigate the gathering of particles in the full tilt model of externally controlled motion planning: A set of particles is located at the tiles of a polyomino with all particles reacting uniformly to an external force by moving as far as possible in one of the four axis-parallel directions until they hit the boundary. The goal is to choose a sequence of directions that moves all particles to a common position. Our results include a polynomial-time algorithm for gathering in a completely filled polyomino as well as hardness reductions for approximating shortest gathering sequences and for determining whether the particles in a partially filled polyomino can be gathered. We pay special attention to the impact of restricted geometry, particularly polyominoes without holes. As a corollary, we make progress on an open question from [Balanza-Martinez et al., SODA 2020] by showing that deciding whether a given position can be occupied remains NP-hard in polyominoes without holes. Our results build on a connection we establish between tilt models and the theory of synchronizing automata.

Cite As Get BibTex

Sándor P. Fekete, Jonas Friemel, Peter Kramer, Jan-Marc Reinhardt, Christian Rieck, and Christian Scheffer. Tilt Automata: Gathering Particles with Uniform External Control. In 42nd International Symposium on Computational Geometry (SoCG 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 367, pp. 44:1-44:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.SoCG.2026.44

Author Details

Sándor P. Fekete
  • Department of Computer Science, TU Braunschweig, Germany
  • L3S Research Center, Hannover, Germany
Jonas Friemel
  • Department of Electrical Engineering and Computer Science, Bochum University of Applied Sciences, Germany
Peter Kramer
  • Department of Computer Science, TU Braunschweig, Germany
Jan-Marc Reinhardt
  • Department of Electrical Engineering and Computer Science, Bochum University of Applied Sciences, Germany
Christian Rieck
  • Institute of Mathematics, University of Kassel, Germany
Christian Scheffer
  • Department of Electrical Engineering and Computer Science, Bochum University of Applied Sciences, Germany

Funding

Sándor P. Fekete, Jonas Friemel, Peter Kramer, Christian Scheffer: Supported by the German Research Foundation (Deutsche Forschungsgemeinschaft, DFG) - project SpaceAnts, 530918134. Christian Rieck: Supported by the German Research Foundation (Deutsche Forschungsgemeinschaft, DFG) - 522790373.

References

  1. Ahmed Abdelkader, Aditya Acharya, and Philip Dasler. 2048 without new tiles is still hard. In Fun with Algorithms (FUN), pages 1:1-1:14, 2016. URL: https://doi.org/10.4230/LIPIcs.FUN.2016.1.
  2. Hugo A. Akitaya, Greg Aloupis, Maarten Löffler, and Anika Rounds. Trash compaction. In European Workshop on Computational Geometry (EuroCG), pages 107-110, 2016. URL: https://www.eurocg2016.usi.ch/sites/default/files/paper_77.pdf.
  3. Hugo A. Akitaya, Erik D. Demaine, Jason S. Ku, Jayson Lynch, and Csaba D. Tóth. 2048 without merging. In Canadian Conference on Computational Geometry (CCCG), pages 285-291, 2020. URL: http://vga.usask.ca/cccg2020/papers/2048%20Without%20Merging.pdf.
  4. Hugo A. Akitaya, Maarten Löffler, and Giovanni Viglietta. Pushing blocks by sweeping lines. In Fun with Algorithms (FUN), pages 1:1-1:21, 2022. URL: https://doi.org/10.4230/LIPIcs.FUN.2022.1.
  5. Hugo A. Akitaya, Maarten Löffler, and Giovanni Viglietta. Pushing blocks by sweeping lines. Computation in Geometry and Topology, 2(1):6:1-6:28, 2023. A conference version of this paper appeared at FUN 2022 [Hugo A. Akitaya et al., 2022]. URL: https://doi.org/10.57717/cgt.v2i1.31.
  6. Alberto Avila-Jimenez, David Barreda, Sarah-Laurie Evans, Austin Luchsinger, Aiden Massie, Robert Schweller, Evan Tomai, and Tim Wylie. General computation using slidable tiles with deterministic global forces. In Innovations in Theoretical Computer Science (ITCS), pages 14:1-14:25, 2026. URL: https://doi.org/10.4230/LIPIcs.ITCS.2026.14.
  7. Jose Balanza-Martinez, Timothy Gomez, David Caballero, Austin Luchsinger, Angel A. Cantu, Rene Reyes, Mauricio Flores, Robert T. Schweller, and Tim Wylie. Hierarchical shape construction and complexity for slidable polyominoes under uniform external forces. In Symposium on Discrete Algorithms (SODA), pages 2625-2641, 2020. URL: https://doi.org/10.1137/1.9781611975994.160.
  8. Jose Balanza-Martinez, Austin Luchsinger, David Caballero, Rene Reyes, Angel A. Cantu, Robert T. Schweller, Luis Angel Garcia, and Tim Wylie. Full tilt: Universal constructors for general shapes with uniform external forces. In Symposium on Discrete Algorithms (SODA), pages 2689-2708, 2019. URL: https://doi.org/10.1137/1.9781611975482.167.
  9. Aaron T. Becker, Erik D. Demaine, Sándor P. Fekete, Golnaz Habibi, and James McLurkin. Reconfiguring massive particle swarms with limited, global control. In Symposium on Algorithms and Experiments for Sensor Systems, Wireless Networks and Distributed Robotics (ALGOSENSORS), pages 51-66, 2013. URL: https://doi.org/10.1007/978-3-642-45346-5_5.
  10. Aaron T. Becker, Erik D. Demaine, Sándor P. Fekete, Jarrett Lonsford, and Rose Morris-Wright. Particle computation: complexity, algorithms, and logic. Natural Computing, 18(1):181-201, 2019. Conference versions related to this paper appeared at ALGOSENSORS 2013 [Aaron T. Becker et al., 2013], ICRA 2014 [Aaron T. Becker et al., 2014], and ICRA 2015 [Hamed Mohtasham Shad et al., 2015]. URL: https://doi.org/10.1007/S11047-017-9666-6.
  11. Aaron T. Becker, Erik D. Demaine, Sándor P. Fekete, and James McLurkin. Particle computation: Designing worlds to control robot swarms with only global signals. In International Conference on Robotics and Automation (ICRA), pages 6751-6756, 2014. URL: https://doi.org/10.1109/ICRA.2014.6907856.
  12. Aaron T. Becker, Erik D. Demaine, Sándor P. Fekete, Hamed Mohtasham Shad, and Rose Morris-Wright. Tilt: The video - designing worlds to control robot swarms with only global signals. In International Symposium on Computational Geometry (SoCG), pages 16-18, 2015. URL: https://doi.org/10.4230/LIPIcs.SOCG.2015.16.
  13. Aaron T. Becker, Sándor P. Fekete, Li Huang, Phillip Keldenich, Linda Kleist, Dominik Krupke, Christian Rieck, and Arne Schmidt. Targeted drug delivery: Algorithmic methods for collecting a swarm of particles with uniform, external forces. In International Conference on Robotics and Automation (ICRA), pages 2508-2514, 2020. URL: https://doi.org/10.1109/ICRA40945.2020.9196551.
  14. Aaron T. Becker, Sándor P. Fekete, Phillip Keldenich, Dominik Krupke, Christian Rieck, Christian Scheffer, and Arne Schmidt. Tilt assembly: Algorithms for micro-factories that build objects with uniform external forces. In International Symposium on Algorithms and Computation (ISAAC), pages 11:1-11:13, 2017. URL: https://doi.org/10.4230/LIPIcs.ISAAC.2017.11.
  15. Aaron T. Becker, Sándor P. Fekete, Phillip Keldenich, Dominik Krupke, Christian Rieck, Christian Scheffer, and Arne Schmidt. Tilt assembly: Algorithms for micro-factories that build objects with uniform external forces. Algorithmica, 82(2):165-187, 2020. A conference version related to this paper appeared at ISAAC 2017 [Aaron T. Becker et al., 2017]. URL: https://doi.org/10.1007/S00453-018-0483-9.
  16. Aaron T. Becker, Golnaz Habibi, Justin Werfel, Michael Rubenstein, and James McLurkin. Massive uniform manipulation: Controlling large populations of simple robots with a common input signal. In International Conference on Intelligent Robots and Systems (IROS), pages 520-527, 2013. URL: https://doi.org/10.1109/IROS.2013.6696401.
  17. Mikhail V. Berlinkov. Approximating the minimum length of synchronizing words is hard. In International Computer Science Symposium in Russia (CSR), pages 37-47, 2010. URL: https://doi.org/10.1007/978-3-642-13182-0_4.
  18. Mikhail V. Berlinkov. Approximating the minimum length of synchronizing words is hard. Theory of Computing Systems, 54(2):211-223, 2014. A conference version of this paper appeared at CSR 2010 [Mikhail V. Berlinkov, 2010]. URL: https://doi.org/10.1007/S00224-013-9511-Y.
  19. Mikhail V. Berlinkov. On two algorithmic problems about synchronizing automata (short paper). In Developments in Language Theory (DLT), pages 61-67, 2014. URL: https://doi.org/10.1007/978-3-319-09698-8_6.
  20. Patrick Blumenberg, Arne Schmidt, and Aaron T. Becker. Computing motion plans for assembling particles with global control. In International Conference on Intelligent Robots and Systems (IROS), pages 7296-7302, 2023. URL: https://doi.org/10.1109/IROS55552.2023.10341556.
  21. Prosenjit Bose and Thomas C. Shermer. Gathering by repulsion. In Scandinavian Symposium and Workshops on Algorithm Theory (SWAT), pages 13:1-13:12, 2018. URL: https://doi.org/10.4230/LIPIcs.SWAT.2018.13.
  22. Prosenjit Bose and Thomas C. Shermer. Gathering by repulsion. Computational Geometry, 90:101627, 2020. A conference version of this paper appeared at SWAT 2018 [Prosenjit Bose and Thomas C. Shermer, 2018]. URL: https://doi.org/10.1016/J.COMGEO.2020.101627.
  23. David Caballero, Angel A. Cantu, Timothy Gomez, Austin Luchsinger, Robert T. Schweller, and Tim Wylie. Hardness of reconfiguring robot swarms with uniform external control in limited directions. Journal of Information Processing, 28:782-790, 2020. URL: https://doi.org/10.2197/IPSJJIP.28.782.
  24. David Caballero, Angel A. Cantu, Timothy Gomez, Austin Luchsinger, Robert T. Schweller, and Tim Wylie. Relocating units in robot swarms with uniform control signals is PSPACE-complete. In Canadian Conference on Computational Geometry (CCCG), pages 49-55, 2020. URL: https://vga.usask.ca/cccg2020/papers/Relocating%20Units%20in%20Robot%20Swarms%20with%20Uniform%20Control%20Signals.pdf.
  25. David Caballero, Angel A. Cantu, Timothy Gomez, Austin Luchsinger, Robert T. Schweller, and Tim Wylie. Fast reconfiguration of robot swarms with uniform control signals. Natural Computing, 20(4):659-669, 2021. URL: https://doi.org/10.1007/S11047-021-09864-0.
  26. David Caballero, Angel A. Cantu, Timothy Gomez, Austin Luchsinger, Robert T. Schweller, and Tim Wylie. Uniform robot relocation is hard in only two directions even without obstacles. In Unconventional Computation and Natural Computation (UCNC), pages 17-31, 2023. URL: https://doi.org/10.1007/978-3-031-34034-5_2.
  27. David Caballero, Angel A. Cantu, Timothy Gomez, Austin Luchsinger, Robert T. Schweller, and Tim Wylie. Uniform robot relocation is hard in only two directions even without obstacles. Natural Computing, 24(1):3-16, 2025. A conference version of this paper appeared at UCNC 2023 [David Caballero et al., 2023]. URL: https://doi.org/10.1007/S11047-024-10007-4.
  28. Ján Černý. Poznámka k homogénnym experimentom s konečnỳmi automatmi. Matematicko-fyzikálny časopis, 14(3):208-216, 1964. URL: https://dml.cz/dmlcz/126647.
  29. Ján Černý. A note on homogeneous experiments with finite automata. Journal of Automata, Languages and Combinatorics, 24(2-4):123-132, 2019. The original article was published in 1964 in Slovak [Ján Černý, 1964]. English translation by Markus Holzer and Bianca Truthe. URL: https://doi.org/10.25596/jalc-2019-123.
  30. Birgit Engels and Tom Kamphans. Randolphs robot game is NP-hard! Electronic Notes in Discrete Mathematics, 25:49-53, 2006. URL: https://doi.org/10.1016/J.ENDM.2006.06.062.
  31. David Eppstein. Reset sequences for monotonic automata. SIAM Journal on Computing, 19(3):500-510, 1990. URL: https://doi.org/10.1137/0219033.
  32. Sándor P. Fekete, Jonas Friemel, Peter Kramer, Jan-Marc Reinhardt, Christian Rieck, and Christian Scheffer. Tilt automata: Gathering particles with uniform external control. CoRR, 2026. URL: https://arxiv.org/abs/2603.02796.
  33. Sándor P. Fekete, Peter Kramer, Jan-Marc Reinhardt, Christian Rieck, and Christian Scheffer. Drainability and fillability of polyominoes in diverse models of global control. In International Colloquium on Automata, Languages, and Programming (ICALP), pages 74:1-74:19, 2025. URL: https://doi.org/10.4230/LIPIcs.ICALP.2025.74.
  34. Paweł Gawrychowski and Damian Straszak. Strong inapproximability of the shortest reset word. In Mathematical Foundations of Computer Science (MFCS), pages 243-255, 2015. URL: https://doi.org/10.1007/978-3-662-48057-1_19.
  35. Michael Gerbush and Brent Heeringa. Approximating minimum reset sequences. In Conference on Implementation and Application of Automata (CIAA), pages 154-162, 2010. URL: https://doi.org/10.1007/978-3-642-18098-9_17.
  36. Adam Hesterberg and Justin Kopinsky. The parameterized complexity of ricochet robots. Journal of Information Processing, 25:716-723, 2017. URL: https://doi.org/10.2197/IPSJJIP.25.716.
  37. Markus Holzer and Martin Kutrib. Descriptional and computational complexity of finite automata. In Language and Automata Theory and Applications (LATA), pages 23-42, 2009. URL: https://doi.org/10.1007/978-3-642-00982-2_3.
  38. Markus Holzer and Martin Kutrib. Descriptional and computational complexity of finite automata - A survey. Information and Computation, 209(3):456-470, 2011. A conference version of this paper appeared at LATA 2009 [Markus Holzer and Martin Kutrib, 2009]. URL: https://doi.org/10.1016/J.IC.2010.11.013.
  39. Markus Holzer and Stefan Schwoon. Assembling molecules in ATOMIX is hard. Theoretical Computer Science, 313(3):447-462, 2004. URL: https://doi.org/10.1016/J.TCS.2002.11.002.
  40. Tao Jiang and Ming Li. On the approximation of shortest common supersequences and longest common subsequences. In International Colloquium on Automata, Languages, and Programming (ICALP), pages 191-202, 1994. URL: https://doi.org/10.1007/3-540-58201-0_68.
  41. Tao Jiang and Ming Li. On the approximation of shortest common supersequences and longest common subsequences. SIAM Journal on Computing, 24(5):1122-1139, 1995. A conference version of this paper appeared at ICALP 1994 [Tao Jiang and Ming Li, 1994]. URL: https://doi.org/10.1137/S009753979223842X.
  42. Jarkko Kari. Synchronizing finite automata on Eulerian digraphs. In Mathematical Foundations of Computer Science (MFCS), pages 432-438, 2001. URL: https://doi.org/10.1007/3-540-44683-4_38.
  43. Jarkko Kari. Synchronizing finite automata on Eulerian digraphs. Theoretical Computer Science, 295:223-232, 2003. A conference version of this paper appeared at MFCS 2001 [Jarkko Kari, 2001]. URL: https://doi.org/10.1016/S0304-3975(02)00405-X.
  44. Phillip Keldenich, Sheryl Manzoor, Li Huang, Dominik Krupke, Arne Schmidt, Sándor P. Fekete, and Aaron T. Becker. On designing 2D discrete workspaces to sort or classify polyominoes. In International Conference on Intelligent Robots and Systems (IROS), pages 1-9, 2018. URL: https://doi.org/10.1109/IROS.2018.8594150.
  45. Jakob Keller, Christian Rieck, Christian Scheffer, and Arne Schmidt. Particle-based assembly using precise global control. In Algorithms and Data Structures Symposium (WADS), pages 513-527, 2021. URL: https://doi.org/10.1007/978-3-030-83508-8_37.
  46. Jakob Keller, Christian Rieck, Christian Scheffer, and Arne Schmidt. Particle-based assembly using precise global control. Algorithmica, 84(10):2871-2897, 2022. A conference version of this paper appeared at WADS 2021 [Jakob Keller et al., 2021]. URL: https://doi.org/10.1007/S00453-022-00992-2.
  47. Stefan Kiefer and Andrew Ryzhikov. Efficiently computing the minimum rank of a matrix in a monoid of zero-one matrices. In Symposium on Theoretical Aspects of Computer Science (STACS), pages 61:1-61:22, 2025. URL: https://doi.org/10.4230/LIPIcs.STACS.2025.61.
  48. Matthias Konitzny, Yitong Lu, Julien Leclerc, Sándor P. Fekete, and Aaron T. Becker. Gathering physical particles with a global magnetic field using reinforcement learning. In International Conference on Intelligent Robots and Systems (IROS), pages 10126-10132, 2022. URL: https://doi.org/10.1109/IROS47612.2022.9982256.
  49. Dexter Kozen. Lower bounds for natural proof systems. In Symposium on Foundations of Computer Science, pages 254-266, 1977. URL: https://doi.org/10.1109/SFCS.1977.16.
  50. Fabian C. Landers, Lukas Hertle, Vitaly Pustovalov, Derick Sivakumaran, Cagatay M. Oral, Oliver Brinkmann, Kirstin Meiners, Pascal Theiler, Valentin Gantenbein, Andrea Veciana, Michael Mattmann, Silas Riss, Simone Gervasoni, Christophe Chautems, Hao Ye, Semih Sevim, Andreas D. Flouris, Josep Puigmartí-Luis, Tiago Sotto Mayor, Pedro Alves, Tessa Lühmann, Xiangzhong Chen, Nicole Ochsenbein, Ueli Moehrlen, Tilman Schubert, Zsolt Kulcsar, Philipp Gruber, Miriam Weisskopf, Quentin Boehler, Salvador Pané, and Bradley J. Nelson. Clinically ready magnetic microrobots for targeted therapies. Science, 390(6774):710-715, 2025. URL: https://doi.org/10.1126/science.adx1708.
  51. Arun Mahadev, Dominik Krupke, Sándor P. Fekete, and Aaron T. Becker. Mapping and coverage with a particle swarm controlled by uniform inputs. In International Conference on Intelligent Robots and Systems (IROS), pages 1097-1104, 2017. URL: https://doi.org/10.1109/IROS.2017.8202280.
  52. Arun V. Mahadev, Dominik Krupke, Jan-Marc Reinhardt, Sándor P. Fekete, and Aaron T. Becker. Collecting a swarm in a grid environment using shared, global inputs. In International Conference on Automation Science and Engineering (CASE), pages 1231-1236, 2016. URL: https://doi.org/10.1109/COASE.2016.7743547.
  53. Sheryl Manzoor, Samuel Sheckman, Jarrett Lonsford, Hoyeon Kim, Min Jun Kim, and Aaron T. Becker. Parallel self-assembly of polyominoes under uniform control inputs. Robotics and Automation Letters, 2(4):2040-2047, 2017. URL: https://doi.org/10.1109/LRA.2017.2715402.
  54. Rachel A. Moan, Victor M. Baez, Aaron T. Becker, and Jason M. O'Kane. Aggregation and localization of simple robots in curved environments. In International Conference on Robotics and Automation (ICRA), pages 165-171, 2020. URL: https://doi.org/10.1109/ICRA40945.2020.9197198.
  55. Nils Morawietz, Carolin Rehs, and Mathias Weller. A timecop’s work is harder than you think. In Mathematical Foundations of Computer Science (MFCS), pages 71:1-71:14, 2020. URL: https://doi.org/10.4230/LIPIcs.MFCS.2020.71.
  56. Balas K. Natarajan. An algorithmic approach to the automated design of parts orienters. In Symposium on Foundations of Computer Science, pages 132-142, 1986. URL: https://doi.org/10.1109/SFCS.1986.5.
  57. Jason M. O'Kane and Steven M. LaValle. Localization with limited sensing. Transactions on Robotics, 23(4):704-716, 2007. URL: https://doi.org/10.1109/TRO.2007.900636.
  58. Kari-Jouko Räihä and Esko Ukkonen. The shortest common supersequence problem over binary alphabet is NP-complete. Theoretical Computer Science, 16:187-198, 1981. URL: https://doi.org/10.1016/0304-3975(81)90075-X.
  59. Igor K. Rystsov. Polynomial complete problems in automata theory. Information Processing Letters, 16(3):147-151, 1983. URL: https://doi.org/10.1016/0020-0190(83)90067-4.
  60. Sven Sandberg. Homing and synchronizing sequences. In Model-Based Testing of Reactive Systems, pages 5-33, 2004. URL: https://doi.org/10.1007/11498490_2.
  61. Walter J. Savitch. Deterministic simulation of non-deterministic turing machines (detailed abstract). In Symposium on Theory of Computing (STOC), pages 247-248, 1969. URL: https://doi.org/10.1145/800169.805439.
  62. Walter J. Savitch. Relationships between nondeterministic and deterministic tape complexities. Journal of Computer and System Sciences, 4(2):177-192, 1970. A conference version of this paper appeared at STOC 1969 [Walter J. Savitch, 1969]. URL: https://doi.org/10.1016/S0022-0000(70)80006-X.
  63. Arne Schmidt, Sheryl Manzoor, Li Huang, Aaron T. Becker, and Sándor P. Fekete. Efficient parallel self-assembly under uniform control inputs. Robotics and Automation Letters, 3(4):3521-3528, 2018. URL: https://doi.org/10.1109/LRA.2018.2853758.
  64. Hamed Mohtasham Shad, Rose Morris-Wright, Erik D. Demaine, Sándor P. Fekete, and Aaron T. Becker. Particle computation: Device fan-out and binary memory. In International Conference on Robotics and Automation (ICRA), pages 5384-5389, 2015. URL: https://doi.org/10.1109/ICRA.2015.7139951.
  65. Yaroslav Shitov. An improvement to a recent upper bound for synchronizing words of finite automata. Journal of Automata, Languages and Combinatorics, 24(2-4):367-373, 2019. URL: https://doi.org/10.25596/JALC-2019-367.
  66. Larry J. Stockmeyer and Albert R. Meyer. Word problems requiring exponential time: Preliminary report. In Symposium on Theory of Computing (STOC), pages 1-9, 1973. URL: https://doi.org/10.1145/800125.804029.
  67. Marek Szykuła. Improving the upper bound on the length of the shortest reset word. In Symposium on Theoretical Aspects of Computer Science (STACS), pages 56:1-56:13, 2018. URL: https://doi.org/10.4230/LIPIcs.STACS.2018.56.
  68. Marek Szykuła and Adam Zyzik. An improved algorithm for finding the shortest synchronizing words. In European Symposium on Algorithms (ESA), pages 85:1-85:15, 2022. URL: https://doi.org/10.4230/LIPIcs.ESA.2022.85.
  69. Mikhail V. Volkov. Synchronizing automata and the Černý conjecture. In Language and Automata Theory and Applications (LATA), pages 11-27, 2008. URL: https://doi.org/10.1007/978-3-540-88282-4_4.
  70. Mikhail V. Volkov. Synchronization of finite automata. Russian Mathematical Surveys, 77(5):819-891, 2022. URL: https://doi.org/10.4213/rm10005e.
  71. Vojtěch Vorel. Subset synchronization of transitive automata. In Automata and Formal Languages (AFL), pages 370-381, 2014. URL: https://doi.org/10.4204/EPTCS.151.26.
  72. Vojtěch Vorel. Subset synchronization and careful synchronization of binary finite automata. International Journal of Foundations of Computer Science, 27(5):557-578, 2016. A conference version of this paper appeared at AFL 2014 [Vojtěch Vorel, 2014]. URL: https://doi.org/10.1142/S0129054116500167.
  73. Yinan Zhang, Xiaolei Chen, Hang Qi, and Devin J. Balkcom. Rearranging agents in a small space using global controls. In International Conference on Intelligent Robots and Systems (IROS), pages 3576-3582, 2017. URL: https://doi.org/10.1109/IROS.2017.8206202.
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