Exclusive Graph Searching

  • Lélia Blin
  • Janna Burman
  • Nicolas Nisse
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8125)


This paper tackles the well known graph searching problem, where a team of searchers aims at capturing an intruder in a network, modeled as a graph. All variants of this problem assume that any node can be simultaneously occupied by several searchers. This assumption may be unrealistic, e.g., in the case of searchers modeling physical searchers, or may require each individual node to provide additional resources, e.g., in the case of searchers modeling software agents. We thus investigate exclusive graph searching, in which no two or more searchers can occupy the same node at the same time, and, as for the classical variants of graph searching, we study the minimum number of searchers required to capture the intruder. This number is called the exclusive search number of the considered graph. Exclusive graph searching appears to be considerably more complex than classical graph searching, for at least two reasons: (1) it does not satisfy the monotonicity property, and (2) it is not closed under minor. Nevertheless, we design a polynomial-time algorithm which, given any tree T, computes the exclusive search number of T. Moreover, for any integer k, we provide a characterization of the trees T with exclusive search number at most k. This characterization allows us to describe a special type of exclusive search strategies, that can be executed in a distributed environment, i.e., in a framework in which the searchers are limited to cooperate in a distributed manner.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Baldoni, R., Bonnet, F., Milani, A., Raynal, M.: Anonymous graph exploration without collision by mobile robots. Inf. Process. Lett. 109(2), 98–103 (2008)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Barrière, L., Flocchini, P., Fomin, F.V., Fraigniaud, P., Nisse, N., Santoro, N., Thilikos, D.M.: Connected graph searching. Inf. Comput. 219, 1–16 (2012)MATHCrossRefGoogle Scholar
  3. 3.
    Bienstock, D.: Graph searching, path-width, tree-width and related problems (a survey). DIMACS Ser. in Discr. Maths and Theoretical Comp. Sc. 5, 33–49 (1991)MathSciNetGoogle Scholar
  4. 4.
    Bienstock, D., Seymour, P.D.: Monotonicity in graph searching. J. Algorithms 12(2), 239–245 (1991)MathSciNetMATHCrossRefGoogle Scholar
  5. 5.
    Blin, L., Burman, J., Nisse, N.: Brief announcement: Distributed exclusive and perpetual tree searching. In: Aguilera, M.K. (ed.) DISC 2012. LNCS, vol. 7611, pp. 403–404. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  6. 6.
    Blin, L., Burman, J., Nisse, N.: Exclusive graph searching. Technical report, INRIA (2013), http://hal.archives-ouvertes.fr/hal-00837543
  7. 7.
    Blin, L., Fraigniaud, P., Nisse, N., Vial, S.: Distributed chasing of network intruders. Theor. Comput. Sci. 399(1-2), 12–37 (2008)MathSciNetMATHCrossRefGoogle Scholar
  8. 8.
    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
  9. 9.
    Breisch, R.L.: An intuitive approach to speleotopology. Southwestern Cavers 6, 72–78 (1967)Google Scholar
  10. 10.
    Breisch, R.L.: Lost in a Cave-applying graph theory to cave exploration (2012)Google Scholar
  11. 11.
    Coudert, D., Huc, F., Mazauric, D.: A distributed algorithm for computing the node search number in trees. Algorithmica 63(1-2), 158–190 (2012)MathSciNetMATHCrossRefGoogle Scholar
  12. 12.
    D’Angelo, G., Di Stefano, G., Navarra, A., Nisse, N., Suchan, K.: A unified approach for different tasks on rings in robot-based computing systems. In: 15th Workshop on Advances in Par. and Dist. Comp. Models (APDCM). IEEE (2013)Google Scholar
  13. 13.
    Dereniowski, D.: From pathwidth to connected pathwidth. SIAM J. Discrete Math. 26(4), 1709–1732 (2012)MathSciNetMATHCrossRefGoogle Scholar
  14. 14.
    Ellis, J.A., Sudborough, I.H., Turner, J.S.: The vertex separation and search number of a graph. Inf. Comput. 113(1), 50–79 (1994)MathSciNetMATHCrossRefGoogle Scholar
  15. 15.
    Flocchini, P., Huang, M.J., Luccio, F.L.: Contiguous search in the hypercube for capturing an intruder. In: 19th Int. Par. and Dist. Proc. Symp, IPDPS (2005)Google Scholar
  16. 16.
    Flocchini, P., Prencipe, G., Santoro, N., Widmayer, P.: Hard tasks for weak robots: The role of common knowledge in pattern formation by autonomous mobile robots. In: Aggarwal, A.K., Pandu Rangan, C. (eds.) ISAAC 1999. LNCS, vol. 1741, pp. 93–102. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  17. 17.
    Fomin, F.V., Heggernes, P., Mihai, R.: Mixed search number and linear-width of interval and split graphs. Networks 56(3), 207–214 (2010)MathSciNetMATHCrossRefGoogle Scholar
  18. 18.
    Fomin, F.V., Thilikos, D.M.: An annotated bibliography on guaranteed graph searching. Theor. Comput. Sci. 399(3), 236–245 (2008)MathSciNetMATHCrossRefGoogle Scholar
  19. 19.
    Heggernes, P., Mihai, R.: Edge search number of cographs in linear time. In: Deng, X., Hopcroft, J.E., Xue, J. (eds.) FAW 2009. LNCS, vol. 5598, pp. 16–26. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  20. 20.
    Ilcinkas, D., Nisse, N., Soguet, D.: The cost of monotonicity in distributed graph searching. Distributed Comp. 22(2), 117–127 (2009)MATHCrossRefGoogle Scholar
  21. 21.
    Megiddo, N., Hakimi, S.L., Garey, M.R., Johnson, D.S., Papadimitriou, C.H.: The complexity of searching a graph. J. Assoc. Comput. Mach. 35(1), 18–44 (1988)MathSciNetMATHCrossRefGoogle Scholar
  22. 22.
    Parsons, T.D.: The search number of a connected graph. In: 9th Southeastern Conf. on Combinatorics, Graph Theory, and Computing, Congress. Numer., XXI, Winnipeg, Man., Utilitas Math., pp. 549–554 (1978)Google Scholar
  23. 23.
    Peng, S.-L., Ho, C.-W., Hsu, T.-S., Ko, M.-T., Tang, C.Y.: Edge and node searching problems on trees. TCS 240(2), 429–446 (2000)MathSciNetMATHCrossRefGoogle Scholar
  24. 24.
    Prencipe, G.: Instantaneous actions vs. full asynchronicity: Controlling and coordinating a set of autonomous mobile robots. In: Restivo, A., Ronchi Della Rocca, S., Roversi, L. (eds.) ICTCS 2001. LNCS, vol. 2202, pp. 154–171. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  25. 25.
    Skodinis, K.: Computing optimal linear layouts of trees in linear time. J. Algorithms 47(1), 40–59 (2003)MathSciNetMATHCrossRefGoogle Scholar
  26. 26.
    Suchan, K., Todinca, I.: Pathwidth of circular-arc graphs. In: Brandstädt, A., Kratsch, D., Müller, H. (eds.) WG 2007. LNCS, vol. 4769, pp. 258–269. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  27. 27.
    Yang, B., Dyer, D., Alspach, B.: Sweeping graphs with large clique number (Extended abstract). In: Fleischer, R., Trippen, G. (eds.) ISAAC 2004. LNCS, vol. 3341, pp. 908–920. Springer, Heidelberg (2004)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Lélia Blin
    • 1
  • Janna Burman
    • 2
  • Nicolas Nisse
    • 3
  1. 1.Université d’Evry Val d’Essonne and LIP6-CNRSFrance
  2. 2.LRI (CNRS/UPSud)OrsayFrance
  3. 3.COATI, Inria, I3S (CNRS/UNS)Sophia AntipolisFrance

Personalised recommendations