Collision-Free Network Exploration

  • Jurek Czyzowicz
  • Dariusz Dereniowski
  • Leszek Gasieniec
  • Ralf Klasing
  • Adrian Kosowski
  • Dominik Pająk
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8392)


A set of mobile agents is placed at different nodes of a n-node network. The agents synchronously move along the network edges in a collision-free way, i.e., in no round may two agents occupy the same node. In each round, an agent may choose to stay at its currently occupied node or to move to one of its neighbors. An agent has no knowledge of the number and initial positions of other agents. We are looking for the shortest possible time required to complete the collision-free network exploration, i.e., to reach a configuration in which each agent is guaranteed to have visited all network nodes and has returned to its starting location.

We first consider the scenario when each mobile agent knows the map of the network, as well as its own initial position. We establish a connection between the number of rounds required for collision-free exploration and the degree of the minimum-degree spanning tree of the graph. We provide tight (up to a constant factor) lower and upper bounds on the collision-free exploration time in general graphs, and the exact value of this parameter for trees. For our second scenario, in which the network is unknown to the agents, we propose collision-free exploration strategies running in O(n 2) rounds for tree networks and in O(n 5logn) rounds for general networks.


Span Tree Mobile Agent Exploration Strategy Tree Network Port Number 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    Albers, S., Henzinger, M.R.: Exploring unknown environments. SIAM J. Comput. 29(4), 1164–1188 (2000)CrossRefzbMATHMathSciNetGoogle Scholar
  2. 2.
    Aleliunas, R., Karp, R.M., Lipton, R.J., Lovasz, L., Rackoff, C.: Random walks, universal traversal sequences, and the complexity of maze problems. In: Proceedings of the 20th Annual Symposium on Foundations of Computer Science, FOCS 1979, pp. 218–223. IEEE Computer Society, Washington, DC (1979)Google Scholar
  3. 3.
    Alon, N., Chung, F.R.K., Graham, R.L.: Routing permutations on graphs via matchings. In: STOC, pp. 583–591 (1993); Also SIAM J. Discrete Math. 7(3), 513–530 (1994)Google Scholar
  4. 4.
    Alpern, S., Gal, S.: Theory of Search Games and Rendezvous. Kluwer Acad. Publ. (2003)Google Scholar
  5. 5.
    Baldoni, R., Bonnet, F., Milani, A., Raynal, M.: Anonymous graph exploration without collision by mobile robots. Inf. Process. Lett. 109(2), 98–103 (2008)CrossRefMathSciNetGoogle Scholar
  6. 6.
    Blin, L., Milani, A., Potop-Butucaru, M., Tixeuil, S.: Exclusive perpetual ring exploration without chirality. In: Lynch, N.A., Shvartsman, A.A. (eds.) DISC 2010. LNCS, vol. 6343, pp. 312–327. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  7. 7.
    Edmonds, J.: Matroids and the greedy algorithm. Math. Programming 1, 127–136 (1971)CrossRefzbMATHMathSciNetGoogle Scholar
  8. 8.
    Fomin, F.V., Thilikos, D.M.: An annotated bibliography on guaranteed graph searching. Theor. Comput. Sci. 399(3), 236–245 (2008)CrossRefzbMATHMathSciNetGoogle Scholar
  9. 9.
    Fraigniaud, P., Ilcinkas, D., Peer, G., Pelc, A., Peleg, D.: Graph exploration by a finite automaton. Theoretical Computer Science 345(2-3), 331–344 (2005)CrossRefzbMATHMathSciNetGoogle Scholar
  10. 10.
    Fürer, M., Raghavachari, B.: Approximating the minimum-degree steiner tree to within one of optimal. J. Algorithms 17(3), 409–423 (1994)CrossRefMathSciNetGoogle Scholar
  11. 11.
    Goemans, M.X.: Minimum bounded degree spanning trees. In: FOCS, pp. 273–282 (2006)Google Scholar
  12. 12.
    Krizanc, D., Zhang, L.: Many-to-one packed routing via matchings. In: COCOON, pp. 11–17 (1997)Google Scholar
  13. 13.
    Panaite, P., Pelc, A.: Exploring unknown undirected graphs. J. Algorithms 33(2), 281–295 (1999)CrossRefzbMATHMathSciNetGoogle Scholar
  14. 14.
    Pantziou, G.E., Roberts, A., Symvonis, A.: Many-to-many routings on trees via matchings. Theor. Comput. Sci. 185(2), 347–377 (1997)CrossRefzbMATHMathSciNetGoogle Scholar
  15. 15.
    Zhang, L.: Optimal bounds for matching routing on trees. In: SODA, pp. 445–453 (1997)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Jurek Czyzowicz
    • 1
  • Dariusz Dereniowski
    • 2
  • Leszek Gasieniec
    • 3
  • Ralf Klasing
    • 4
  • Adrian Kosowski
    • 4
  • Dominik Pająk
    • 4
  1. 1.Université du Québec en OutaouaisCanada
  2. 2.Gdańsk University of TechnologyPoland
  3. 3.University of LiverpoolUK
  4. 4.LaBRI, CNRSUniversité de Bordeaux — InriaFrance

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