Abstract
This paper addresses the graph searching problem in a distributed setting. We describe a distributed protocol that enables searchers with logarithmic size memory to clear any network, in a fully decentralized manner. The search strategy for the network in which the searchers are launched is computed online by the searchers themselves without knowing the topology of the network in advance. It performs in an asynchronous environment, i.e., it implements the necessary synchronization mechanism in a decentralized manner. In every network, our protocol performs a connected strategy using at most k + 1 searchers, where k is the minimum number of searchers required to clear the network in a monotone connected way, computed in the centralized and synchronous setting.
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Arnborg, S., Corneil, D., Proskurowski, A.: Complexity of finding embeddings in a k-tree. SIAM J. Alg. Disc. Meth. 8(2), 277–284 (1987)
Barrière, L., Flocchini, P., Fraigniaud, P., Santoro, N.: Capture of an intruder by mobile agents. In: 14th ACM Symp. on Parallel Algorithms and Architectures (SPAA), pp. 200–209 (2002)
Barrière, L., Fraigniaud, P., Santoro, N., Thilikos, D.M.: Searching is not jumping. In: Bodlaender, H.L. (ed.) WG 2003. LNCS, vol. 2880, pp. 34–45. Springer, Heidelberg (2003)
Bienstock, D.: Graph searching, path-width, tree-width and related problems (a survey). DIMACS Ser. in Discrete Mathematics and Theoretical Computer Science, vol. 5, pp. 33–49 (1991)
Bienstock, D., Seymour, P.: Monotonicity in graph searching. Journal of Algorithms 12, 239–245 (1991)
Breisch, R.: An intuitive approach to speleotopology. Southwestern Cavers VI(5), 72–78 (1967)
Feige, U., Hajiaghayi, M., Lee, J.: Improved approximation algorithms for minimum-weight vertex separators. In: 37th ACM Symposium on Theory of Computing (STOC) (2005)
Flocchini, P., Luccio, F.L., Song, L.: Decontamination of chordal rings and tori. In: Proc. of 8th Workshop on Advances in Parallel and Distributed Computational Models (APDCM) (2006)
Flocchini, P., Huang, M.J., Luccio, F.L.: Contiguous search in the hypercube for capturing an intruder. In: Proc. of 18th IEEE Int. Parallel and Distributed Processing Symposium (IPDPS) (2005)
Fomin, F., Fraigniaud, P., Nisse, N.: Nondeterministic Graph Searching: From Pathwidth to Treewidth. In: Jedrzejowicz, J., Szepietowski, A. (eds.) MFCS 2005. LNCS, vol. 3618, pp. 364–375. Springer, Heidelberg (2005)
Fomin, F.V., Kratsch, D., Todinca, I.: Exact (Exponential) algorithms for treewidth and minimum fill-in. In: Díaz, J., Karhumäki, J., Lepistö, A., Sannella, D. (eds.) ICALP 2004. LNCS, vol. 3142, pp. 568–580. Springer, Heidelberg (2004)
Fraigniaud, P., Ilcinkas, D.: Digraphs Exploration with Little Memory. In: Diekert, V., Habib, M. (eds.) STACS 2004. LNCS, vol. 2996, pp. 246–257. Springer, Heidelberg (2004)
Fraigniaud, P., Nisse, N.: Connected Treewidth and Connected Graph Searching. In: Correa, J.R., Hevia, A., Kiwi, M. (eds.) LATIN 2006. LNCS, vol. 3887, pp. 479–490. Springer, Heidelberg (2006)
Kirousis, L., Papadimitriou, C.: Interval graphs and searching. Discrete Math. 55, 181–184 (1985)
Kirousis, L., Papadimitriou, C.: Searching and Pebbling. Theoretical Computer Science 47, 205–218 (1986)
Lapaugh, A.: Recontamination does not help to search a graph. Journal of the ACM 40(2), 224–245 (1993)
Makedon, F.S., Sudborough, I.H.: On minimizing width in linear layouts. Discrete Appl. Math. 23, 243–265 (1989)
Megiddo, N., Hakimi, S., Garey, M., Johnson, D., Papadimitriou, C.: The complexity of searching a graph. Journal of the ACM 35(1), 18–44 (1988)
Parsons, T.: Pursuit-evasion in a graph. In: Theory and Applications of Graphs. Lecture Notes in Mathematics, pp. 426–441. Springer, Heidelberg (1976)
Skodinis, K.: Computing optimal linear layouts of trees in linear time. In: Paterson, M. (ed.) ESA 2000. LNCS, vol. 1879, pp. 403–414. Springer, Heidelberg (2000) (Also to appear in SIAM Journal on Computing)
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)
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Blin, L., Fraigniaud, P., Nisse, N., Vial, S. (2006). Distributed Chasing of Network Intruders. In: Flocchini, P., Gąsieniec, L. (eds) Structural Information and Communication Complexity. SIROCCO 2006. Lecture Notes in Computer Science, vol 4056. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11780823_7
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DOI: https://doi.org/10.1007/11780823_7
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