Document Open Access Logo

Black Hole Search in Dynamic Tori

Authors Adri Bhattacharya , Giuseppe F. Italiano , Partha Sarathi Mandal

PDF
Thumbnail PDF

File

LIPIcs.SAND.2024.6.pdf
  • Filesize: 0.75 MB
  • 16 pages

Document Identifiers

Author Details

Adri Bhattacharya
  • Indian Institute of Technology Guwahati, Assam, India
Giuseppe F. Italiano
  • Luiss University, Rome, Italy
Partha Sarathi Mandal
  • Indian Institute of Technology Guwahati, Assam, India

Funding

  • Bhattacharya, Adri: Supported by CSIR, Govt. of India, Grant Number: 09/731(0178)/2020-EMR-I.

Acknowledgements

This work was done while Partha Sarathi Mandal was in the position of Visiting Professor at Luiss University, Rome, Italy.

Cite As Get BibTex

Adri Bhattacharya, Giuseppe F. Italiano, and Partha Sarathi Mandal. Black Hole Search in Dynamic Tori. In 3rd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 292, pp. 6:1-6:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.SAND.2024.6

Abstract

We investigate the black hole search problem using a set of mobile agents in a dynamic torus. A black hole is defined as a dangerous stationary node that has the capability to destroy any number of incoming agents without leaving any trace of its existence. A torus of size n× m (3 ≤ n ≤ m) is a collection of n row rings and m column rings, and the dynamicity is such that each ring is considered to be 1-interval connected, i.e., in other words at most one edge can be missing from each ring at any round. The parameters which define the efficiency of any black hole search algorithm are: the number of agents and the number of rounds (or time) for termination. We consider two initial configurations of mobile agents: first, the agents are co-located, second, the agents are scattered. In each case, we establish lower and upper bounds on the number of agents and on the amount of time required to solve the black hole search problem.

Subject Classification

ACM Subject Classification
  • Theory of computation → Distributed algorithms
Keywords
  • Black Hole Search
  • Time Varying Graphs
  • Dynamic Torus
  • Distributed Algorithms
  • Mobile Agents

Metrics

  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    0
    PDF Downloads
    0
    Metadata Views

Related Versions

References

  1. Balasingham Balamohan, Paola Flocchini, Ali Miri, and Nicola Santoro. Time optimal algorithms for black hole search in rings. Discrete Mathematics, Algorithms and Applications, 3(04):457-471, 2011. Google Scholar
  2. Adri Bhattacharya, Giuseppe F Italiano, and Partha Sarathi Mandal. Black hole search in dynamic cactus graph. In International Conference and Workshops on Algorithms and Computation, WALCOM 2024, pages 288-303. Springer, 2024. Google Scholar
  3. Adri Bhattacharya, Giuseppe F Italiano, and Partha Sarathi Mandal. Black hole search in dynamic tori. arXiv preprint arXiv:2402.04746, 2024. Google Scholar
  4. Sebastian Brandt, Jara Uitto, and Roger Wattenhofer. A tight lower bound for semi-synchronous collaborative grid exploration. Distributed Computing, 33:471-484, 2020. Google Scholar
  5. Jérémie Chalopin, Shantanu Das, Arnaud Labourel, and Euripides Markou. Black hole search with finite automata scattered in a synchronous torus. In Distributed Computing: 25th International Symposium, DISC 2011, Rome, Italy, September 20-22, 2011. Proceedings 25, pages 432-446. Springer, 2011. Google Scholar
  6. Jérémie Chalopin, Shantanu Das, Arnaud Labourel, and Euripides Markou. Tight bounds for black hole search with scattered agents in synchronous rings. Theoretical Computer Science, 509:70-85, 2013. Google Scholar
  7. Reuven Cohen, Pierre Fraigniaud, David Ilcinkas, Amos Korman, and David Peleg. Label-guided graph exploration by a finite automaton. ACM Transactions on Algorithms (TALG), 4(4):1-18, 2008. Google Scholar
  8. Jurek Czyzowicz, Stefan Dobrev, Rastislav Královič, Stanislav Miklík, and Dana Pardubská. Black hole search in directed graphs. In Structural Information and Communication Complexity: 16th International Colloquium, SIROCCO 2009, Piran, Slovenia, May 25-27, 2009, Revised Selected Papers 16, pages 182-194. Springer, 2010. Google Scholar
  9. Jurek Czyzowicz, Dariusz Kowalski, Euripides Markou, and Andrzej Pelc. Searching for a black hole in synchronous tree networks. Combinatorics, Probability and Computing, 16(4):595-619, 2007. Google Scholar
  10. Shantanu Das, Dariusz Dereniowski, and Christina Karousatou. Collaborative exploration of trees by energy-constrained mobile robots. Theory of Computing Systems, 62:1223-1240, 2018. Google Scholar
  11. Giuseppe Antonio Di Luna, Paola Flocchini, Giuseppe Prencipe, and Nicola Santoro. Tight bounds for black hole search in dynamic rings. arXiv preprint arXiv:2005.07453, 2020. Google Scholar
  12. Yann Disser, Jan Hackfeld, and Max Klimm. Tight bounds for undirected graph exploration with pebbles and multiple agents. Journal of the ACM (JACM), 66(6):1-41, 2019. Google Scholar
  13. S Dobrev, P Flocchini, R Kralovic, and N Santoro. Exploring a dangerous unknown graph using tokens. In Proceedings of 5th IFIP International Conference on Theoretical Computer Science, pages 131-150, 2006. Google Scholar
  14. Stefan Dobrev, Paola Flocchini, Rastislav Královič, P Ružička, Giuseppe Prencipe, and Nicola Santoro. Black hole search in common interconnection networks. Networks: An International Journal, 47(2):61-71, 2006. Google Scholar
  15. Stefan Dobrev, Paola Flocchini, Giuseppe Prencipe, and Nicola Santoro. Searching for a black hole in arbitrary networks: Optimal mobile agents protocols. Distributed Computing, 19:1-99999, 2006. Google Scholar
  16. Stefan Dobrev, Paola Flocchini, Giuseppe Prencipe, and Nicola Santoro. Mobile search for a black hole in an anonymous ring. Algorithmica, 48:67-90, 2007. Google Scholar
  17. Stefan Dobrev, Rastislav Královič, Nicola Santoro, and Wei Shi. Black hole search in asynchronous rings using tokens. In Algorithms and Complexity: 6th Italian Conference, CIAC 2006, Rome, Italy, May 29-31, 2006. Proceedings 6, pages 139-150. Springer, 2006. Google Scholar
  18. Stefan Dobrev, Nicola Santoro, and Wei Shi. Using scattered mobile agents to locate a black hole in an un-oriented ring with tokens. International Journal of Foundations of Computer Science, 19(06):1355-1372, 2008. Google Scholar
  19. Paola Flocchini, David Ilcinkas, Andrzej Pelc, and Nicola Santoro. Computing without communicating: Ring exploration by asynchronous oblivious robots. Algorithmica, 65:562-583, 2013. Google Scholar
  20. Paola Flocchini, David Ilcinkas, and Nicola Santoro. Ping pong in dangerous graphs: Optimal black hole search with pebbles. Algorithmica, 62:1006-1033, 2012. Google Scholar
  21. Tsuyoshi Gotoh, Paola Flocchini, Toshimitsu Masuzawa, and Nicola Santoro. Exploration of dynamic networks: tight bounds on the number of agents. Journal of Computer and System Sciences, 122:1-18, 2021. Google Scholar
  22. Tsuyoshi Gotoh, Yuichi Sudo, Fukuhito Ooshita, Hirotsugu Kakugawa, and Toshimitsu Masuzawa. Exploration of dynamic tori by multiple agents. Theoretical Computer Science, 850:202-220, 2021. Google Scholar
  23. Shota Nagahama, Fukuhito Ooshita, and Michiko Inoue. Ring exploration of myopic luminous robots with visibility more than one. Information and Computation, 292:105036, 2023. Google Scholar
  24. Claude E Shannon. Presentation of a maze-solving machine. Claude Elwood Shannon Collected Papers, pages 681-687, 1993. Google Scholar
  25. Wei Shi, Joaquin Garcia-Alfaro, and Jean-Pierre Corriveau. Searching for a black hole in interconnected networks using mobile agents and tokens. Journal of Parallel and Distributed Computing, 74(1):1945-1958, 2014. Google Scholar
  26. Yuichi Sudo, Daisuke Baba, Junya Nakamura, Fukuhito Ooshita, Hirotsugu Kakugawa, and Toshimitsu Masuzawa. A single agent exploration in unknown undirected graphs with whiteboards. IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, 98(10):2117-2128, 2015. Google Scholar
Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail
© 2023-2024 Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact