Advertisement

Minimizing the Cost of Team Exploration

  • Dorota OsulaEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11376)

Abstract

A group of mobile agents is given a task to explore an edge-weighted graph G, i.e., every vertex of G has to be visited by at least one agent. There is no centralized unit to coordinate their actions, but they can freely communicate with each other. The goal is to construct a deterministic strategy which allows agents to complete their task optimally. In this paper we are interested in a cost-optimal strategy, where the cost is understood as the total distance traversed by agents coupled with the cost of invoking them. Two graph classes are analyzed, rings and trees, in the off-line and on-line setting, i.e., when a structure of a graph is known and not known to agents in advance. We present algorithms that compute the optimal solutions for a given ring and tree of order n, in O(n) time units. For rings in the on-line setting, we give the 2-competitive algorithm and prove the lower bound of 3/2 for the competitive ratio for any on-line strategy. For every strategy for trees in the on-line setting, we prove the competitive ratio to be no less than 2, which can be achieved by the DFS algorithm.

Keywords

Graph exploration Distributed searching Cost minimization Mobile agents On-line searching 

References

  1. 1.
    Bellmore, M., Nemhauser, G.L.: The traveling salesman problem: a survey. Oper. Res. 16(3), 538–558 (1968)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Berbeglia, G., Cordeau, J.F., Gribkovskaia, I., Laporte, G.: Static pickup and delivery problems: a classification scheme and survey. Top 15(1), 1–31 (2007)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Brass, P., Vigan, I., Xu, N.: Improved analysis of a multirobot graph exploration strategy. In: 2014 13th International Conference on Control Automation Robotics & Vision (ICARCV), pp. 1906–1910. IEEE (2014)Google Scholar
  4. 4.
    Czyzowicz, J., Diks, K., Moussi, J., Rytter, W.: Energy-optimal broadcast in a tree with mobile agents. In: Fernández Anta, A., Jurdzinski, T., Mosteiro, M.A., Zhang, Y. (eds.) ALGOSENSORS 2017. LNCS, vol. 10718, pp. 98–113. Springer, Cham (2017).  https://doi.org/10.1007/978-3-319-72751-6_8CrossRefGoogle Scholar
  5. 5.
    Das, S., Dereniowski, D., Karousatou, C.: Collaborative exploration by energy-constrained mobile robots. In: Scheideler, C. (ed.) Structural Information and Communication Complexity. LNCS, vol. 9439, pp. 357–369. Springer, Cham (2015).  https://doi.org/10.1007/978-3-319-25258-2_25CrossRefGoogle Scholar
  6. 6.
    Dereniowski, D., Disser, Y., Kosowski, A., Pajak, D., Uznanski, P.: Fast collaborative graph exploration. Inf. Comput. 243, 37–49 (2015)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Disser, Y., Mousset, F., Noever, A., Škorić, N., Steger, A.: A general lower bound for collaborative tree exploration. In: Das, S., Tixeuil, S. (eds.) SIROCCO 2017. LNCS, vol. 10641, pp. 125–139. Springer, Cham (2017).  https://doi.org/10.1007/978-3-319-72050-0_8CrossRefGoogle Scholar
  8. 8.
    Dynia, M., Korzeniowski, M., Schindelhauer, C.: Power-aware collective tree exploration. In: Grass, W., Sick, B., Waldschmidt, K. (eds.) ARCS 2006. LNCS, vol. 3894, pp. 341–351. Springer, Heidelberg (2006).  https://doi.org/10.1007/11682127_24CrossRefGoogle Scholar
  9. 9.
    Dynia, M., Łopuszański, J., Schindelhauer, C.: Why robots need maps. In: Prencipe, G., Zaks, S. (eds.) SIROCCO 2007. LNCS, vol. 4474, pp. 41–50. Springer, Heidelberg (2007).  https://doi.org/10.1007/978-3-540-72951-8_5CrossRefGoogle Scholar
  10. 10.
    Fomin, F., Thilikos, D.: An annotated bibliography on guaranteed graph searching. Theor. Comput. Sci. 399(3), 236–245 (2008)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Fraigniaud, P., Gasieniec, L., Kowalski, D.R., Pelc, A.: Collective tree exploration. Networks 48(3), 166–177 (2006)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Golden, B.L., Raghavan, S., Wasil, E.A.: The Vehicle Routing Problem: Latest Advances and New Challenges, vol. 43. Springer, Heidelberg (2008).  https://doi.org/10.1007/978-0-387-77778-8CrossRefzbMATHGoogle Scholar
  13. 13.
    Higashikawa, Y., Katoh, N., Langerman, S., Tanigawa, S.: Online graph exploration algorithms for cycles and trees by multiple searchers. J. Comb. Optim. 28(2), 480–495 (2014)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Kumar, S.N., Panneerselvam, R.: A survey on the vehicle routing problem and its variants. Intell. Inf. Manag. 4(03), 66 (2012)Google Scholar
  15. 15.
    Ortolf, C., Schindelhauer, C.: Online multi-robot exploration of grid graphs with rectangular obstacles. In: Proceedings of the Twenty-Fourth Annual ACM Symposium on Parallelism in Algorithms and Architectures, pp. 27–36. ACM (2012)Google Scholar
  16. 16.
    Vaishnav, P., Choudhary, N., Jain, K.: Traveling salesman problem using genetic algorithm: a survey. Int. J. Sci. Res. Comput. Sci. Eng. Inf. Technol. 2(3), 105–108 (2017)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Faculty of Electronics, Telecommunications and InformaticsGdańsk University of TechnologyGdańskPoland

Personalised recommendations