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Black Hole Search in Dynamic Rings: The Scattered Case

Authors Giuseppe A. Di Luna, Paola Flocchini, Giuseppe Prencipe, Nicola Santoro

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Author Details

Giuseppe A. Di Luna
  • DIAG, Sapienza University of Rome, Italy
Paola Flocchini
  • School of Electrical Engineering and Computer Science, University of Ottawa, Canada
Giuseppe Prencipe
  • Department of Computer Science, University of Pisa, Italy
Nicola Santoro
  • School of Computer Science, Carleton University, Ottawa, Canada

Funding

The work was partially supported by the Natural Sciences and Engineering Research Council of Canada under Discovery Grants and by "PRA - Progetti di Ricerca di Ateneo" (Institutional Research Grants) - Project no. PRA_2022_81 of the Pisa University and PRA RM1221816C1760BF from Sapienza and by (PE00000014) under the MUR National Recovery and Resilience Plan funded by the European Union.

Cite AsGet BibTex

Giuseppe A. Di Luna, Paola Flocchini, Giuseppe Prencipe, and Nicola Santoro. Black Hole Search in Dynamic Rings: The Scattered Case. In 27th International Conference on Principles of Distributed Systems (OPODIS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 286, pp. 33:1-33:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.OPODIS.2023.33

Abstract

In this paper we investigate the problem of searching for a black hole in a dynamic graph by a set of scattered agents (i.e., the agents start from arbitrary locations of the graph). The black hole is a node that silently destroys any agent visiting it. This kind of malicious node nicely models network failures such as a crashed host or a virus that erases the visiting agents. The black hole search problem is solved when at least one agent survives, and it has the entire map of the graph with the location of the black hole. We consider the case in which the underlining graph is a dynamic 1-interval connected ring: a ring graph in which at each round at most one edge can be missing. We first show that the problem cannot be solved if the agents can only communicate by using a face-to-face mechanism: this holds for any set of agents of constant size, with respect to the size n of the ring. To circumvent this impossibility we consider agents equipped with movable pebbles that can be left on nodes as a form of communication with other agents. When pebbles are available, three agents can localize the black hole in O(n²) moves. We show that such a number of agents is optimal. We also show that the complexity is tight, that is Ω(n²) moves are required for any algorithm solving the problem with three agents, even with stronger communication mechanisms (e.g., a whiteboard on each node on which agents can write messages of unlimited size). To the best of our knowledge this is the first paper examining the problem of searching a black hole in a dynamic environment with scattered agents.

Subject Classification

ACM Subject Classification
  • Computing methodologies → Distributed algorithms
  • Theory of computation → Self-organization
Keywords
  • Black hole search
  • mobile agents
  • dynamic graph

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References

  1. S. Abshoff and F. Meyer auf der Heide. Continuous aggregation in dynamic ad-hoc networks. In 21st Int. Coll. on Structural Inf. and Comm. Compl., pages 194-209, 2014. URL: https://doi.org/10.1007/978-3-319-09620-9_16.
  2. B. Balamohan, P. Flocchini, A. Miri, and N. Santoro. Time optimal algorithms for black hole search in rings. In 10th International Conference on Combinatorial Optimization and Applications, pages 58-71, 2010. URL: https://doi.org/10.1007/978-3-642-17461-2_5.
  3. M. Bournat, A.K. Datta, and S. Dubois. Self-stabilizing robots in highly dynamic environments. In 18th International Symposium on Stabilization, Safety, and Security of Distributed Systems, pages 54-69, 2016. URL: https://doi.org/10.1007/978-3-319-49259-9_5.
  4. M. Bournat, S. Dubois, and F. Petit. Computability of perpetual exploration in highly dynamic rings. In 37th IEEE International Conference on Distributed Computing Systems, pages 794-804, 2017. URL: https://doi.org/10.1109/ICDCS.2017.80.
  5. A. Casteigts, P. Flocchini, W. Quattrociocchi, and N. Santoro. Time-varying graphs and dynamic networks. Int. J. Parallel Emergent Distributed Syst., 27(5):387-408, 2012. URL: https://doi.org/10.1080/17445760.2012.668546.
  6. J. Chalopin, S. Das, A. Labourel, and E. Markou. Tight bounds for black hole search with scattered agents in a synchronous ring. Theoretical Computer Science, 509:70-85, 2013. URL: https://doi.org/10.1016/J.TCS.2013.02.010.
  7. J. Czyzowicz, D. Kowalski, E. Markou, and A. Pelc. Complexity of searching for a black hole. Fundamenta Informaticae, 71:229-242, 2006. URL: http://content.iospress.com/articles/fundamenta-informaticae/fi71-2-3-05.
  8. J. Czyzowicz, D. Kowalski, E. Markou, and A. Pelc. Searching for a black hole in synchronous tree networks. Combinatorial Probabilistic Computing, 16(4):595-619, 2007. URL: https://doi.org/10.1017/S0963548306008133.
  9. G.A. Di Luna. Mobile Agents on Dynamic Graphs, Chapter 20 of [P. Flocchini et al., 2019]. Springer, 2019. Google Scholar
  10. G.A. Di Luna and R. Baldoni. Brief announcement: Investigating the cost of anonymity on dynamic networks. In 34th Symposium on Principles of Distributed Computing, pages 339-341, 2015. URL: https://doi.org/10.1145/2767386.2767442.
  11. G.A. Di Luna, S. Dobrev, P. Flocchini, and N. Santoro. Distributed exploration of dynamic rings. Distributed Computing, 33:41-67, 2020. URL: https://doi.org/10.1007/S00446-018-0339-1.
  12. G.A. Di Luna, P. Flocchini, L. Pagli, G. Prencipe, N. Santoro, and G. Viglietta. Gathering in dynamic rings. Theoretical Computer Science, 811:79-98, 2020. URL: https://doi.org/10.1016/J.TCS.2018.10.018.
  13. G.A. Di Luna, P. Flocchini, G. Prencipe, and N. Santoro. Black hole search in dynamic rings. In 41st IEEE International Conference on Distributed Computing Systems, ICDCS 2021, Washington DC, USA, July 7-10, 2021, pages 987-997, 2021. URL: https://doi.org/10.1109/ICDCS51616.2021.00098.
  14. S. Dobrev, P. Flocchini, R. Královič, and N. Santoro. Exploring an unknown dangerous graph using tokens. Theoretical Computer Science, 472:28-45, 2013. URL: https://doi.org/10.1016/J.TCS.2012.11.022.
  15. S. Dobrev, P. Flocchini, G. Prencipe, and N. Santoro. Searching for a black hole in arbitrary networks: optimal mobile agents protocols. Distributed Computing, 19(1):1-35, 2006. URL: https://doi.org/10.1007/S00446-006-0154-Y.
  16. S. Dobrev, P. Flocchini, G. Prencipe, and N. Santoro. Mobile search for a black hole in an anonymous ring. Algorithmica, 48(1):67-90, 2007. URL: https://doi.org/10.1007/S00453-006-1232-Z.
  17. S. Dobrev, N. Santoro, and W. Shi. Locating a black hole in an un-oriented ring using tokens: The case of scattered agents. In 13th International Euro-Par Conference European Conference on Parallel and Distributed Computing, pages 608-617. Springer, 2007. URL: https://doi.org/10.1007/978-3-540-74466-5_64.
  18. P. Flocchini, D. Ilcinkas, and N. Santoro. Ping pong in dangerous graphs: optimal black hole search with pebbles. Algorithmica, 62(3-4):1006-1033, 2012. URL: https://doi.org/10.1007/S00453-011-9496-3.
  19. P. Flocchini, M. Kellett, P. Mason, and N. Santoro. Searching for black holes in subways. Theory of Computing Systems, 50(1):158-184, 2012. URL: https://doi.org/10.1007/S00224-011-9341-8.
  20. P. Flocchini, G. Prencipe, and N. Santoro (Eds.). Distributed Computing by Mobile Entities. Springer, 2019. URL: https://doi.org/10.1007/978-3-030-11072-7.
  21. B. Haeupler and F. Kuhn. Lower bounds on information dissemination in dynamic networks. In 26th Int. Symp. on Distributed Computing, pages 166-180, 2012. URL: https://doi.org/10.1007/978-3-642-33651-5_12.
  22. F. Kuhn, T. Locher, and R. Oshman. Gradient clock synchronization in dynamic networks. Theory of Computing Systems, 49(4):781-816, 2011. URL: https://doi.org/10.1007/S00224-011-9348-1.
  23. F. Kuhn, N. Lynch, and R. Oshman. Distributed computation in dynamic networks. In 42nd ACM Symposium on Theory of Computing, pages 513-522, 2010. URL: https://doi.org/10.1145/1806689.1806760.
  24. E. Markou and M. Paquette. Black hole search and exploration in unoriented tori with synchronous scattered finite automata. In 14th International Conference on Principles of Distributed Systems, pages 239-253, 2012. URL: https://doi.org/10.1007/978-3-642-35476-2_17.
  25. E. Markou and W. Shi. Dangerous Graphs, Chapter 18 of [P. Flocchini et al., 2019]. Springer, 2019. Google Scholar
  26. R. O'Dell and R.Wattenhofer. Information dissemination in highly dynamic graphs. In Joint Workshop on Foundations of Mobile Computing, pages 104-110, 2005. URL: https://doi.org/10.1145/1080810.1080828.
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