Abstract
We consider a class of highly dynamic networks modelled on an urban subway system. We examine the problem of creating a map of such a subway in less than ideal conditions, where the local residents are not enthusiastic about the process and there is a limited ability to communicate amongst the mappers. More precisely, we study the problem of a team of asynchronous computational entities (the mapping agents) determining the location of black holes in a highly dynamic graph, whose edges are defined by the asynchronous movements of mobile entities (the subway carriers). We present and analyze a solution protocol. The algorithm solves the problem with the minimum number of agents possible. We also establish lower bounds on the number of carrier moves in the worst case, showing that our protocol is also move-optimal.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Bui-Xuan, B., Ferreira, A., Jarry, A.: Computing shortest, fastest, and foremost journeys in dynamic networks. Int. J. Found. Comp. Sci. 14(2), 267–285 (2003)
Chalopin, J., Das, S., Santoro, N.: Rendezvous of mobile agents in unknown graphs with faulty links. In: Pelc, A. (ed.) DISC 2007. LNCS, vol. 4731, pp. 108–122. Springer, Heidelberg (2007)
Cooper, C., Klasing, R., Radzik, T.: Searching for black-hole faults in a network using multiple agents. In: Shvartsman, M.M.A.A. (ed.) OPODIS 2006. LNCS, vol. 4305, pp. 320–332. Springer, Heidelberg (2006)
Cooper, C., Klasing, R., Radzik, T.: Locating and repairing faults in a network with mobile agents. Theoretical Computer Science (to appear 2010)
Czyzowicz, J., Kowalski, D., Markou, E., Pelc, A.: Complexity of searching for a black hole. Fundamenta Informaticae 71(2,3), 229–242 (2006)
Czyzowicz, J., Kowalski, D., Markou, E., Pelc, A.: Searching for a black hole in synchronous tree networks. Combin. Probab. Comput. 16(4), 595–619 (2007)
Dobrev, S., Flocchini, P., Prencipe, G., Santoro, N.: Searching for a black hole in arbitrary networks. Distibuted Computing 19(1), 1–19 (2006)
Dobrev, S., Flocchini, P., Prencipe, G., Santoro, N.: Mobile search for a black hole in an anonymous ring. Algorithmica 48(1), 67–90 (2007)
Flocchini, P., Ilcinkas, D., Santoro, N.: Ping pong in dangerous graphs: Optimal black hole search with pure tokens. In: Taubenfeld, G. (ed.) DISC 2008. LNCS, vol. 5218, pp. 227–241. Springer, Heidelberg (2008)
Flocchini, P., Kellett, M., Mason, P., Santoro, N.: Map construction and exploration by mobile agents scattered in a dangerous network. In: IPDPS 2009, pp. 1–10 (2009)
Flocchini, P., Mans, B., Santoro, N.: Exploration of periodically varying graphs. In: Dong, Y., Du, D.-Z., Ibarra, O. (eds.) ISAAC 2009. LNCS, vol. 5878, pp. 534–543. Springer, Heidelberg (2009)
Glaus, P.: Locating a black hole without the knowledge of incoming links. In: Lerner, A. (ed.) ALGOSENSORS 2009. LNCS, vol. 5804, pp. 128–138. Springer, Heidelberg (2009)
Klasing, R., Markou, E., Radzik, T., Sarracco, F.: Hardness and approximation results for black hole search in arbitrary networks. Theoretical Computer Science 384(2-3), 201–221 (2007)
Klasing, R., Markou, E., Radzik, T., Sarracco, F.: Approximation bounds for black hole search problems. Networks 54(4), 216–226 (2008)
Kosowski, A., Navarra, A., Pinotti, M.C.: Synchronization helps robots to detect black holes in directed graphs. In: Abdelzaher, T., Raynal, M., Santoro, N. (eds.) OPODIS 2009. LNCS, vol. 5923, pp. 86–98. Springer, Heidelberg (2009)
Liu, C., Wu, J.: Scalable routing in cyclic mobile networks. IEEE Trans. Parallel Distrib. Syst. 20(9), 1325–1338 (2009)
O’Dell, R., Wattenhofer, R.: Information dissemination in highly dynamic graphs. In: 2005 Joint Work. on Foundations of Mobile Computing, pp. 104–110 (2005)
Zhang, X., Kurose, J., Levine, B., Towsley, D., Zhang, H.: Study of a bus-based disruption-tolerant network. In: 13th Int. Conf. on Mobile Computing and Networking, p. 206 (2007)
Zhang, Z.: Routing in intermittently connected mobile ad hoc networks and delay tolerant networks: Overview and challenges. IEEE Communications Surveys & Tutorials 8(1), 24–37 (2006)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Flocchini, P., Kellett, M., Mason, P.C., Santoro, N. (2010). Mapping an Unfriendly Subway System. In: Boldi, P., Gargano, L. (eds) Fun with Algorithms. FUN 2010. Lecture Notes in Computer Science, vol 6099. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13122-6_20
Download citation
DOI: https://doi.org/10.1007/978-3-642-13122-6_20
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-13121-9
Online ISBN: 978-3-642-13122-6
eBook Packages: Computer ScienceComputer Science (R0)