Document Open Access Logo

Natural Calamities Demand More Rescuers: Exploring Connectivity Time Dynamic Graphs

Authors Ashish Saxena , Kaushik Mondal

PDF

File

Thumbnail PDF
PDF
LIPIcs.DISC.2025.41.pdf
  • Filesize: 1.14 MB
  • 23 pages

Document Identifiers

Subject Classification

ACM Subject Classification
  • Theory of computation → Distributed algorithms
Keywords
  • Mobile agents
  • Anonymous graphs
  • Exploration
  • Dynamic graphs
  • Deterministic algorithm

Metrics

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

Abstract

We study the exploration problem by mobile agents in Connectivity Time dynamic graphs. The Connectivity Time model was introduced by Michail et al. [JPDC 2014] and is arguably one of the weakest dynamic graph connectivity models. We prove that exploration is impossible in such graphs using ((n-1)(n-2))/2 mobile agents starting from an arbitrary initial configuration, even when agents have full knowledge of system parameters, global communication, full visibility, and infinite memory. We then present an exploration algorithm that uses ((n-1)(n-2))/2 + 1 agents equipped with global communication, 1-hop visibility and O(log n) memory.

Cite As Get BibTex

Ashish Saxena and Kaushik Mondal. Natural Calamities Demand More Rescuers: Exploring Connectivity Time Dynamic Graphs. In 39th International Symposium on Distributed Computing (DISC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 356, pp. 41:1-41:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.DISC.2025.41

Author Details

Ashish Saxena
  • Indian Institute of Technology Ropar, Rupnagar, Punjab, India
Kaushik Mondal
  • Indian Institute of Technology Ropar, Rupnagar, Punjab, India

Funding

  • Saxena, Ashish: Acknowledge the financial support from IIT Ropar.
  • Mondal, Kaushik: Acknowledge the ISIRD grant provided by IIT Ropar.

References

  1. A. Agarwalla, J. Augustine, W. K. Moses, S. K. Madhav, and A. K. Sridhar. Deterministic dispersion of mobile robots in dynamic rings. In ICDCN, pages 1-4, 2018. Google Scholar
  2. S. Albers and M. Henzinger. Exploring unknown environments. SIAM Journal on Computing, 29(4):1164-1188, 2000. URL: https://doi.org/10.1137/S009753979732428X.
  3. Chen Avin, Michal Kouckỳ, and Zvi Lotker. How to explore a fast-changing world (cover time of a simple random walk on evolving graphs). In ICALP 2008, pages 121-132, 2008. Google Scholar
  4. Marjorie Bournat, Ajoy K Datta, and Swan Dubois. Self-stabilizing robots in highly dynamic environments. In SSS 2016, pages 54-69, 2016. URL: https://doi.org/10.1007/978-3-319-49259-9_5.
  5. Marjorie Bournat, Swan Dubois, and Franck Petit. Computability of perpetual exploration in highly dynamic rings. In ICDCS 2017, pages 794-804, 2017. URL: https://doi.org/10.1109/ICDCS.2017.80.
  6. J. Chalopin, P. Flocchini, B. Mans, and N. Santoro. Network exploration by silent and oblivious robots. In WG, pages 208-219, 2010. Google Scholar
  7. R. Cohen, P. Fraigniaud, D. Ilcinkas, A. Korman, and D. Peleg. Label-guided graph exploration by a finite automaton. ACM Transactions on Algorithms, 4(4):1-18, 2008. URL: https://doi.org/10.1145/1383369.1383373.
  8. S. Das, D. Dereniowski, and C. Karousatou. Collaborative exploration of trees by energy-constrained mobile robots. Theor. Comp. Sys., 62(5):1223-1240, July 2018. URL: https://doi.org/10.1007/S00224-017-9816-3.
  9. Shantanu Das. Graph Explorations with Mobile Agents, pages 403-422. Springer International Publishing, 2019. URL: https://doi.org/10.1007/978-3-030-11072-7_16.
  10. Shantanu Das, Nikos Giachoudis, Flaminia L. Luccio, and Euripides Markou. Broadcasting with Mobile Agents in Dynamic Networks. In OPODIS 2020, pages 24:1-24:16, 2021. Google Scholar
  11. X. Deng and C.H. Papadimitriou. Exploring an unknown graph. Journal of Graph Theory, 32(3):265-297, 1999. URL: https://doi.org/10.1002/(SICI)1097-0118(199911)32:3%3C265::AID-JGT6%3E3.0.CO;2-8.
  12. G Di Luna, Stefan Dobrev, Paola Flocchini, and Nicola Santoro. Distributed exploration of dynamic rings. Distributed Computing, 33:41-67, 2020. URL: https://doi.org/10.1007/S00446-018-0339-1.
  13. Y. Dieudonné and A. Pelc. Deterministic network exploration by anonymous silent agents with local traffic reports. ACM Transactions on Algorithms, 11(2):1-29, 2014. URL: https://doi.org/10.1145/2594581.
  14. S. Dobrev, L. Narayanan, J. Opatrny, and D. Pankratov. Exploration of high-dimensional grids by finite automata. In ICALP, pages 1-16, 2019. Google Scholar
  15. Thomas Erlebach, Michael Hoffmann, and Frank Kammer. On temporal graph exploration. Journal of Computer and System Sciences, 119:1-18, 2021. URL: https://doi.org/10.1016/J.JCSS.2021.01.005.
  16. Thomas Erlebach, Frank Kammer, Kelin Luo, Andrej Sajenko, and Jakob T Spooner. Two moves per time step make a difference. In ICALP 2019, page 141, 2019. Google Scholar
  17. Thomas Erlebach and Jakob T Spooner. Faster exploration of degree-bounded temporal graphs. In MFCS 2018), pages 36:1-36:13, 2018. URL: https://doi.org/10.4230/LIPICS.MFCS.2018.36.
  18. Paola Flocchini, Matthew Kellett, Peter C Mason, and Nicola Santoro. Searching for black holes in subways. Theory of Computing Systems, 50:158-184, 2012. URL: https://doi.org/10.1007/S00224-011-9341-8.
  19. Paola Flocchini, Bernard Mans, and Nicola Santoro. On the exploration of time-varying networks. Theoretical Computer Science, 469:53-68, 2013. URL: https://doi.org/10.1016/J.TCS.2012.10.029.
  20. P. Fraigniaud, L. Gasieniec, D. R. Kowalski, and A. Pelc. Collective tree exploration. Networks, 48(3):166-177, 2006. URL: https://doi.org/10.1002/NET.20127.
  21. P. Fraigniaud, D. Ilcinkas, G. Peer, A. Pelc, and D. Peleg. Graph exploration by a finite automaton. Theoretical Computer Science, 345(2-3):331-344, 2005. URL: https://doi.org/10.1016/J.TCS.2005.07.014.
  22. P. Fraigniaud, D. Ilcinkas, and A. Pelc. Impact of memory size on graph exploration capability. Discrete Applied Mathematics, 156(12):2310-2319, 2008. URL: https://doi.org/10.1016/J.DAM.2007.11.001.
  23. 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. URL: https://doi.org/10.1016/J.JCSS.2021.04.003.
  24. Tsuyoshi Gotoh, Yuichi Sudo, Fukuhito Ooshita, Hirotsugu Kakugawa, and Toshimitsu Masuzawa. Group exploration of dynamic tori. In ICDCS 2018, pages 775-785, 2018. URL: https://doi.org/10.1109/ICDCS.2018.00080.
  25. Tsuyoshi Gotoh, Yuichi Sudo, Fukuhito Ooshita, and Toshimitsu Masuzawa. Exploration of dynamic ring networks by a single agent with the h-hops and s-time steps view. In SSS 2019, pages 165-177, 2019. URL: https://doi.org/10.1007/978-3-030-34992-9_14.
  26. David Ilcinkas, Ralf Klasing, and Ahmed Mouhamadou Wade. Exploration of constantly connected dynamic graphs based on cactuses. In SIROCCO, pages 250-262, 2014. URL: https://doi.org/10.1007/978-3-319-09620-9_20.
  27. David Ilcinkas and Ahmed M Wade. Exploration of the t-interval-connected dynamic graphs: the case of the ring. Theory of Computing Systems, 62:1144-1160, 2018. URL: https://doi.org/10.1007/S00224-017-9796-3.
  28. David Ilcinkas and Ahmed Mouhamadou Wade. On the power of waiting when exploring public transportation systems. In OPODIS 2011, pages 451-464, 2011. URL: https://doi.org/10.1007/978-3-642-25873-2_31.
  29. Ajay D. Kshemkalyani and Faizan Ali. Efficient dispersion of mobile robots on graphs. In Proceedings of the 20th International Conference on Distributed Computing and Networking, ICDCN '19, page 218–227, New York, NY, USA, 2019. Association for Computing Machinery. URL: https://doi.org/10.1145/3288599.3288610.
  30. Ajay D. Kshemkalyani, Anisur Rahaman Molla, and Gokarna Sharma. Dispersion of mobile robots in the global communication model. In Proceedings of the 21st International Conference on Distributed Computing and Networking, ICDCN '20, New York, NY, USA, 2020. Association for Computing Machinery. URL: https://doi.org/10.1145/3369740.3369775.
  31. Ajay D. Kshemkalyani, Anisur Rahaman Molla, and Gokarna Sharma. Dispersion of mobile robots on grids. In WALCOM: Algorithms and Computation: 14th International Conference, WALCOM 2020, Singapore, Singapore, March 31 – April 2, 2020, Proceedings, page 183–197, Berlin, Heidelberg, 2020. Springer-Verlag. URL: https://doi.org/10.1007/978-3-030-39881-1_16.
  32. F. Kuhn, N. Lynch, and R. Oshman. Distributed computation in dynamic networks. In STOC, pages 513-522, New York, NY, USA, 2010. Google Scholar
  33. O. Michail, I. Chatzigiannakis, and P. G. Spirakis. Causality, influence, and computation in possibly disconnected synchronous dynamic networks. Journal of Parallel and Distributed Computing, 74(1):2016-2026, 2014. URL: https://doi.org/10.1016/J.JPDC.2013.07.007.
  34. A. Miller and U. Saha. Fast byzantine gathering with visibility in graphs. In Algorithms for Sensor Systems, pages 140-153, 2020. Google Scholar
  35. William K. Moses Jr., Amanda Redlich, and Frederick Stock. Brief Announcement: Broadcast via Mobile Agents in a Dynamic Network: Interplay of Graph Properties & Agents. In SAND 2025, pages 17:1-17:5, 2025. URL: https://doi.org/10.4230/LIPICS.SAND.2025.17.
  36. C. Ortolf and C. Schindelhauer. Online multi-robot exploration of grid graphs with rectangular obstacles. In SPAA 2012, pages 27-36, New York, NY, USA, 2012. Google Scholar
  37. P. Panaite and A. Pelc. Exploring unknown undirected graphs. Journal of Algorithms, 33:281-295, 1999. URL: https://doi.org/10.1006/JAGM.1999.1043.
  38. Ashish Saxena and Kaushik Mondal. Path connected dynamic graphs with a study of dispersion and exploration. Theoretical Computer Science, 1050:115390, 2025. URL: https://doi.org/10.1016/J.TCS.2025.115390.
  39. Claude E Shannon. Presentation of a maze-solving machine. Claude Elwood Shannon Collected Papers, pages 681-687, 1993. Google Scholar
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
© 2023-2025 Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact