Abstract
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.
Access provided by Autonomous University of Puebla. Download to read the full chapter text
Chapter PDF
Similar content being viewed by others
Keywords
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.
References
Baldoni, R., Bonnet, F., Milani, A., Raynal, M.: Anonymous graph exploration without collision by mobile robots. Inf. Process. Lett. 109(2), 98–103 (2008)
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)
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)
Bienstock, D., Seymour, P.D.: Monotonicity in graph searching. J. Algorithms 12(2), 239–245 (1991)
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)
Blin, L., Burman, J., Nisse, N.: Exclusive graph searching. Technical report, INRIA (2013), http://hal.archives-ouvertes.fr/hal-00837543
Blin, L., Fraigniaud, P., Nisse, N., Vial, S.: Distributed chasing of network intruders. Theor. Comput. Sci. 399(1-2), 12–37 (2008)
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)
Breisch, R.L.: An intuitive approach to speleotopology. Southwestern Cavers 6, 72–78 (1967)
Breisch, R.L.: Lost in a Cave-applying graph theory to cave exploration (2012)
Coudert, D., Huc, F., Mazauric, D.: A distributed algorithm for computing the node search number in trees. Algorithmica 63(1-2), 158–190 (2012)
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)
Dereniowski, D.: From pathwidth to connected pathwidth. SIAM J. Discrete Math. 26(4), 1709–1732 (2012)
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)
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)
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)
Fomin, F.V., Heggernes, P., Mihai, R.: Mixed search number and linear-width of interval and split graphs. Networks 56(3), 207–214 (2010)
Fomin, F.V., Thilikos, D.M.: An annotated bibliography on guaranteed graph searching. Theor. Comput. Sci. 399(3), 236–245 (2008)
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)
Ilcinkas, D., Nisse, N., Soguet, D.: The cost of monotonicity in distributed graph searching. Distributed Comp. 22(2), 117–127 (2009)
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)
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)
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)
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)
Skodinis, K.: Computing optimal linear layouts of trees in linear time. J. Algorithms 47(1), 40–59 (2003)
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)
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)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Blin, L., Burman, J., Nisse, N. (2013). Exclusive Graph Searching. In: Bodlaender, H.L., Italiano, G.F. (eds) Algorithms – ESA 2013. ESA 2013. Lecture Notes in Computer Science, vol 8125. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40450-4_16
Download citation
DOI: https://doi.org/10.1007/978-3-642-40450-4_16
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-40449-8
Online ISBN: 978-3-642-40450-4
eBook Packages: Computer ScienceComputer Science (R0)