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Patrolling on Dynamic Ring Networks

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SOFSEM 2019: Theory and Practice of Computer Science (SOFSEM 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11376))

Abstract

We study the problem of patrolling the nodes of a network collaboratively by a team of mobile agents, such that each node of the network is visited by at least one agent once in every I(n) time units, with the objective of minimizing the idle time I(n). While patrolling has been studied previously for static networks, we investigate the problem on dynamic networks with a fixed set of nodes, but dynamic edges. In particular, we consider 1-interval-connected ring networks and provide various patrolling algorithms for such networks, for \(k=2\) or \(k>2\) agents. We also show almost matching lower bounds that hold even for the best starting configurations. Thus, our algorithms achieve close to optimal idle time. Further, we show a clear separation in terms of idle time, for agents that have prior knowledge of the dynamic networks compared to agents that do not have such knowledge. This paper provides the first known results for collaborative patrolling on dynamic graphs.

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Notes

  1. 1.

    A pair of nodes is antipodal if the distance between them in the ring is \(\lfloor \frac{n}{2} \rfloor \).

References

  1. Aaron, E., Krizanc, D., Meyerson, E.: DMVP: foremost waypoint coverage of time-varying graphs. In: Kratsch, D., Todinca, I. (eds.) WG 2014. LNCS, vol. 8747, pp. 29–41. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-12340-0_3

    Chapter  Google Scholar 

  2. Aaron, E., Krizanc, D., Meyerson, E.: Multi-robot foremost coverage of time-varying graphs. In: Gao, J., Efrat, A., Fekete, S.P., Zhang, Y. (eds.) ALGOSENSORS 2014. LNCS, vol. 8847, pp. 22–38. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-46018-4_2

    Chapter  Google Scholar 

  3. Augustine, J., Pandurangan, G., Robinson, P.: Fast byzantine agreement in dynamic networks. In: Proceedings of the 32nd Symposium on Principles of Distributed Computing, PODC, pp. 74–83 (2013)

    Google Scholar 

  4. Awerbuch, B., Even, S.: Efficient and reliable broadcast is achievable in an eventually connected network. In: Proceedings of the 3rd Symposium on Principles of Distributed Computing, PODC, pp. 278–281 (1984)

    Google Scholar 

  5. Biely, M., Robinson, P., Schmid, U.: Agreement in directed dynamic networks. In: Even, G., Halldórsson, M.M. (eds.) SIROCCO 2012. LNCS, vol. 7355, pp. 73–84. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-31104-8_7

    Chapter  Google Scholar 

  6. Bournat, M., Datta, A.K., Dubois, S.: Self-stabilizing robots in highly dynamic environments. In: Bonakdarpour, B., Petit, F. (eds.) SSS 2016. LNCS, vol. 10083, pp. 54–69. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-49259-9_5

    Chapter  Google Scholar 

  7. Carlsson, S., Jonsson, H., Nilsson, B.J.: Finding the shortest watchman route in a simple polygon. Discrete Comput. Geom. 22(3), 377–402 (1999)

    Article  MathSciNet  Google Scholar 

  8. Casteigts, A., Flocchini, P., Quattrociocchi, W., Santoro, N.: Time-varying graphs and dynamic networks. Int. J. Parallel Emergent Distrib. Syst. 27(5), 387–408 (2012)

    Article  Google Scholar 

  9. Chan, M.Y., Chin, F.Y.L.: Schedulers for larger classes of pinwheel instances. Algorithmica 9(5), 425–462 (1993)

    Article  MathSciNet  Google Scholar 

  10. Chin, W., Ntafos, S.C.: Optimum watchman routes. Inf. Process. Lett. 28(1), 39–44 (1988)

    Article  MathSciNet  Google Scholar 

  11. Clementi, A., Monti, A., Pasquale, F., Silvestri, R.: Information spreading in stationary markovian evolving graphs. IEEE Trans. Parallel Distrib. Syst. 22(9), 1425–1432 (2011)

    Article  Google Scholar 

  12. Collins, A., et al.: Optimal patrolling of fragmented boundaries. In: 25th ACM Symposium on Parallelism in Algorithms and Architectures, SPAA 2013, Montreal, pp. 241–250 (2013)

    Google Scholar 

  13. Czyzowicz, J., Gąsieniec, L., Kosowski, A., Kranakis, E.: Boundary patrolling by mobile agents with distinct maximal speeds. In: Demetrescu, C., Halldórsson, M.M. (eds.) ESA 2011. LNCS, vol. 6942, pp. 701–712. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-23719-5_59

    Chapter  Google Scholar 

  14. Czyzowicz, J., Gasieniec, L., Kosowski, A., Kranakis, E., Krizanc, D., Taleb, N.: When patrolmen become corrupted: monitoring a graph using faulty mobile robots. Algorithmica 79(3), 925–940 (2017)

    Article  MathSciNet  Google Scholar 

  15. Di Luna, G.A., Baldoni, R.: Brief announcement: investigating the cost of anonymity on dynamic networks. In: Proceedings of the 34th Symposium on Principles of Distributed Computing, PODC, pp. 339–341 (2015)

    Google Scholar 

  16. Di Luna, G.A., Dobrev, S., Flocchini, P., Santoro, N.: Live exploration of dynamic rings. In: Proceedings of the 36th IEEE International Conference on Distributed Computing Systems, ICDCS, pp. 570–579 (2016)

    Google Scholar 

  17. Di Luna, G.A., Flocchini, P., Pagli, L., Prencipe, G., Santoro, N., Viglietta, G.: Gathering in dynamic rings. In: Das, S., Tixeuil, S. (eds.) SIROCCO 2017. LNCS, vol. 10641, pp. 339–355. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-72050-0_20

    Chapter  Google Scholar 

  18. Erlebach, T., Hoffmann, M., Kammer, F.: On temporal graph exploration. In: Halldórsson, M.M., Iwama, K., Kobayashi, N., Speckmann, B. (eds.) ICALP 2015. LNCS, vol. 9134, pp. 444–455. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-47672-7_36

    Chapter  Google Scholar 

  19. Flocchini, P., Mans, B., Santoro, N.: On the exploration of time-varying networks. Theoret. Comput. Sci. 469, 53–68 (2013)

    Article  MathSciNet  Google Scholar 

  20. Gąsieniec, L., Klasing, R., Levcopoulos, C., Lingas, A., Min, J., Radzik, T.: Bamboo garden trimming problem (perpetual maintenance of machines with different attendance urgency factors). In: Steffen, B., Baier, C., van den Brand, M., Eder, J., Hinchey, M., Margaria, T. (eds.) SOFSEM 2017. LNCS, vol. 10139, pp. 229–240. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-51963-0_18

    Chapter  MATH  Google Scholar 

  21. Harary, F., Gupta, G.: Dynamic graph models. Math. Comput. Model. 25(7), 79–88 (1997)

    Article  MathSciNet  Google Scholar 

  22. Ilcinkas, D., Klasing, R., Wade, A.M.: Exploration of constantly connected dynamic graphs based on cactuses. In: Halldórsson, M.M. (ed.) SIROCCO 2014. LNCS, vol. 8576, pp. 250–262. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09620-9_20

    Chapter  Google Scholar 

  23. Ilcinkas, D., Wade, A.M.: On the power of waiting when exploring public transportation systems. In: Fernàndez Anta, A., Lipari, G., Roy, M. (eds.) OPODIS 2011. LNCS, vol. 7109, pp. 451–464. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-25873-2_31

    Chapter  Google Scholar 

  24. Ilcinkas, D., Wade, A.M.: Exploration of the T-interval-connected dynamic graphs: the case of the ring. Theory Comput. Syst. 62(5), 1144–1160 (2018)

    Article  MathSciNet  Google Scholar 

  25. Kawamura, A., Kobayashi, Y.: Fence patrolling by mobile agents with distinct speeds. Distrib. Comput. 28(2), 147–154 (2015)

    Article  MathSciNet  Google Scholar 

  26. Kowalski, D., Miguel, A.M.: Polynomial counting in anonymous dynamic networks with applications to anonymous dynamic algebraic computations. In: Proceedings of the 45th International Colloquium on Automata, Languages, and Programming, ICALP (2018, to appear)

    Google Scholar 

  27. Kuhn, F., Lynch, N., Oshman, R.: Distributed computation in dynamic networks. In: Proceedings of the 42nd Symposium on Theory of Computing, STOC, pp. 513–522 (2010)

    Google Scholar 

  28. Kuhn, F., Moses, Y., Oshman, R.: Coordinated consensus in dynamic networks. In: Proceedings of the 30th Symposium on Principles of Distributed Computing, PODC, pp. 1–10 (2011)

    Google Scholar 

  29. Kuhn, F., Oshman, R.: Dynamic networks: models and algorithms. SIGACT News 42(1), 82–96 (2011)

    Article  Google Scholar 

  30. Michail, O.: An introduction to temporal graphs: an algorithmic perspective. Internet Math. 12(4), 239–280 (2016)

    Article  MathSciNet  Google Scholar 

  31. Michail, O., Spirakis, P.G.: Traveling salesman problems in temporal graphs. Theoret. Comput. Sci. 634, 1–23 (2016)

    Article  MathSciNet  Google Scholar 

  32. Ntafos, S.C.: On gallery watchmen in grids. Inf. Process. Lett. 23(2), 99–102 (1986)

    Article  MathSciNet  Google Scholar 

  33. O’Dell, R., Wattenhofer, R.: Information dissemination in highly dynamic graphs. In: Proceedings of the Joint Workshop on Foundations of Mobile Computing, DIALM-POMC, pp. 104–110 (2005)

    Google Scholar 

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Authors and Affiliations

  1. Aix-Marseille University, CNRS, LIS, Marseille, France

    Shantanu Das & Giuseppe A. Di Luna

  2. University of Liverpool, Liverpool, UK

    Leszek A. Gasieniec

Authors
  1. Shantanu Das
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  2. Giuseppe A. Di Luna
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  3. Leszek A. Gasieniec
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Correspondence to Shantanu Das .

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Editors and Affiliations

  1. University of Genoa, Genoa, Italy

    Barbara Catania

  2. Comenius University, Bratislava, Slovakia

    Rastislav Královič

  3. Poznań University of Technology, Poznań, Poland

    Jerzy Nawrocki

  4. Università degli Studi di Milano, Milan, Italy

    Giovanni Pighizzini

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Das, S., Di Luna, G.A., Gasieniec, L.A. (2019). Patrolling on Dynamic Ring Networks. In: Catania, B., Královič, R., Nawrocki, J., Pighizzini, G. (eds) SOFSEM 2019: Theory and Practice of Computer Science. SOFSEM 2019. Lecture Notes in Computer Science(), vol 11376. Springer, Cham. https://doi.org/10.1007/978-3-030-10801-4_13

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  • DOI: https://doi.org/10.1007/978-3-030-10801-4_13

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-10800-7

  • Online ISBN: 978-3-030-10801-4

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