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Invited Paper: One Bit Agent Memory is Enough for Snap-Stabilizing Perpetual Exploration of Cactus Graphs with Distinguishable Cycles

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Stabilization, Safety, and Security of Distributed Systems (SSS 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13751))

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Abstract

This paper considers perpetual exploration of anonymous cactus graphs with distinguishable cycles by a single mobile agent under the restriction that nodes have no storage (e.g., whiteboards or token places). A cactus with distinguishable cycles allows the agent to distinguish at each node the two incident edges contained in each cycle from other incident edges. This paper introduces the concept of snap-stabilization into the perpetual exploration and shows that snap-stabilizing perpetual exploration is possible when the agent has one-bit persistent memory. The exploration time of the presented algorithm exactly matches a trivial lower bound. This paper also shows the necessity of one-bit agent memory by showing that any oblivious (or memory-less) agent cannot explore a cactus graph even when it has only a single distinguishable cycle. Finally, this paper shows that snap-stabilizing perpetual exploration by an oblivious agent is possible when a cactus graph with distinguishable cycles has a sense of direction.

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References

  1. Altisen, K., Devismes, S., Dubois, S., Petit, F.: Introduction to Distributed Self-Stabilizing Algorithms. Synthesis Lectures on Distributed Computing Theory. Morgan & Claypool Publishers, San Rafael (2019)

    Google Scholar 

  2. Ambühl, C., Gasieniec, L., Pelc, A., Radzik, T., Zhang, X.: Tree exploration with logarithmic memory. ACM Trans. Algorithms 7(2), 17:1–17:21 (2011)

    Google Scholar 

  3. Becha, H., Flocchini, P.: Optimal construction of sense of direction in a torus by a mobile agent. Int. J. Found. Comput. Sci. 18(3), 529–546 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  4. Bui, A., Datta, A.K., Petit, F., Villain, V.: State-optimal snap-stabilizing PIF in tree networks. In: Proceedings of ICDCS Workshop on Self-stabilizing Systems, pp. 78–85 (1999)

    Google Scholar 

  5. Cohen, R., Fraigniaud, P., Ilcinkas, D., Korman, A., Peleg, D.: Label-guided graph exploration by a finite automaton. ACM Trans. Algorithms 4(4), 42:1–42:18 (2008)

    Google Scholar 

  6. Czyzowicz, J., et al.: More efficient periodic traversal in anonymous undirected graphs. Theor. Comput. Sci. 444, 60–76 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  7. Das, S.: Graph explorations with mobile agents. In: Flocchini, P., Prencipe, G., Santoro, N. (eds.) Distributed Computing by Mobile Entities, Current Research in Moving and Computing. LNCS, vol. 11340, pp. 403–422. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-11072-7_16

  8. Dijkstra, E.W.: Self-stabilizing systems in spite of distributed control. Commun. ACM 17(11), 643–644 (1974)

    Article  MATH  Google Scholar 

  9. Diks, K., Fraigniaud, P., Kranakis, E., Pelc, A.: Tree exploration with little memory. J. Algorithms 51(1), 38–63 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  10. Disser, Y., Hackfeld, J., Klimm, M.: Tight bounds for undirected graph exploration with pebbles and multiple agents. J. ACM 66(6), 40:1–40:41 (2019)

    Google Scholar 

  11. Dobrev, S., Jansson, J., Sadakane, K., Sung, W.-K.: Finding short right-hand-on-the-wall walks in graphs. In: Pelc, A., Raynal, M. (eds.) SIROCCO 2005. LNCS, vol. 3499, pp. 127–139. Springer, Heidelberg (2005). https://doi.org/10.1007/11429647_12

    Chapter  Google Scholar 

  12. Dolev, S.: Self-Stabilization. MIT Press, Cambridge (2000)

    Book  MATH  Google Scholar 

  13. Flocchini, P., Huang, M.J., Luccio, F.L.: Decontamination of hypercubes by mobile agents. Networks 52(3), 167–178 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  14. Flocchini, P., Prencipe, G., Santoro, N. (eds.): Distributed Computing by Mobile Entities, Current Research in Moving and Computing. LNCS, vol. 11340. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-11072-7

  15. Fraigniaud, P., Ilcinkas, D., Peer, G., Pelc, A., Peleg, D.: Graph exploration by a finite automaton. Theor. Comput. Sci. 345(2–3), 331–344 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  16. Fraigniaud, P., Ilcinkas, D., Rajsbaum, S., Tixeuil, S.: Space lower bounds for graph exploration via reduced automata. In: Pelc, A., Raynal, M. (eds.) SIROCCO 2005. LNCS, vol. 3499, pp. 140–154. Springer, Heidelberg (2005). https://doi.org/10.1007/11429647_13

    Chapter  Google Scholar 

  17. Gasieniec, L., Klasing, R., Martin, R.A., Navarra, A., Zhang, X.: Fast periodic graph exploration with constant memory. J. Comput. Syst. Sci. 74(5), 808–822 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  18. Ilcinkas, D.: Setting port numbers for fast graph exploration. Theor. Comput. Sci. 401(1–3), 236–242 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  19. Ilcinkas, D.: Oblivious robots on graphs: exploration. In: Flocchini, P., Prencipe, G., Santoro, N. (eds.) Distributed Computing by Mobile Entities, Current Research in Moving and Computing. LNCS, vol. 11340, pp. 218–233. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-11072-7_9

  20. Kosowski, A., Navarra, A.: Graph decomposition for memoryless periodic exploration. Algorithmica 63(1–2), 26–38 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  21. Masuzawa, T., Tixeuil, S.: Quiescence of self-stabilizing gossiping among mobile agents in graphs. Theor. Comput. Sci. 411(14–15), 1567–1582 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  22. Menc, A., Pajak, D., Uznanski, P.: Time and space optimality of rotor-router graph exploration. Inf. Process. Lett. 127, 17–20 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  23. Panaite, P., Pelc, A.: Exploring unknown undirected graphs. J. Algorithms 33(2), 281–295 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  24. Priezzhev, V.B., Dhar, D., Dhar, A., Krishnamurthy, S.: Eulerian walkers as a model of self-organized criticality. Phys. Rev. Lett. 77, 5079–5082 (1996)

    Article  Google Scholar 

  25. Reingold, O.: Undirected connectivity in log-space. J. ACM 55(4), 17:1–17:24 (2008)

    Google Scholar 

  26. Yanovski, V., Wagner, I.A., Bruckstein, A.M.: A distributed ant algorithm for efficiently patrolling a network. Algorithmica 37(3), 165–186 (2003)

    Article  MathSciNet  MATH  Google Scholar 

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Acknowledgements

This work was partially supported by JSPS KAKENHI Grant Numbers 19H04085, 19K11826, 20H04140, and 20KK0232.

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Authors and Affiliations

  1. Osaka University, Osaka, Japan

    Kohei Shimoyama & Toshimitsu Masuzawa

  2. Hosei University, Tokyo, Japan

    Yuichi Sudo

  3. Ryukoku University, Kyoto, Shiga, Japan

    Hirotsugu Kakugawa

Authors
  1. Kohei Shimoyama
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  2. Yuichi Sudo
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  3. Hirotsugu Kakugawa
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  4. Toshimitsu Masuzawa
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Corresponding author

Correspondence to Toshimitsu Masuzawa .

Editor information

Editors and Affiliations

  1. University of Picardie Jules Verne, Amiens, France

    Stéphane Devismes

  2. Sorbonne University, Paris, France

    Franck Petit

  3. Grenoble Alpes University, Saint-Martin-d'Hères, France

    Karine Altisen

  4. Sapienza University of Rome, Rome, Italy

    Giuseppe Antonio Di Luna

  5. IMDEA Networks Institute, Madrid, Spain

    Antonio Fernandez Anta

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Shimoyama, K., Sudo, Y., Kakugawa, H., Masuzawa, T. (2022). Invited Paper: One Bit Agent Memory is Enough for Snap-Stabilizing Perpetual Exploration of Cactus Graphs with Distinguishable Cycles. In: Devismes, S., Petit, F., Altisen, K., Di Luna, G.A., Fernandez Anta, A. (eds) Stabilization, Safety, and Security of Distributed Systems. SSS 2022. Lecture Notes in Computer Science, vol 13751. Springer, Cham. https://doi.org/10.1007/978-3-031-21017-4_2

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  • DOI: https://doi.org/10.1007/978-3-031-21017-4_2

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-21016-7

  • Online ISBN: 978-3-031-21017-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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