Abstract
We study the problem of exploration by a mobile entity (agent) of a class of dynamic networks, namely the periodically-varying graphs (the PV-graphs, modeling public transportation systems, among others). These are defined by a set of carriers following infinitely their prescribed route along the stations of the network. Flocchini, Mans, and Santoro [FMS09] (ISAAC 2009) studied this problem in the case when the agent must always travel on the carriers and thus cannot wait on a station. They described the necessary and sufficient conditions for the problem to be solvable and proved that the optimal number of steps (and thus of moves) to explore a n-node PV-graph of k carriers and maximal period p is in Θ(k·p 2) in the general case.
In this paper, we study the impact of the ability to wait at the stations. We exhibit the necessary and sufficient conditions for the problem to be solvable in this context, and we prove that waiting at the stations allows the agent to reduce the worst-case optimal number of moves by a multiplicative factor of at least Θ(p), while the time complexity is reduced to Θ(n·p). (In any connected PV-graph, we have n ≤ k·p.) We also show some complementary optimal results in specific cases (same period for all carriers, highly connected PV-graphs). Finally this new ability allows the agent to completely map the PV-graph, in addition to just explore it.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Avin, C., Koucký, M., Lotker, Z.: How to Explore a Fast-Changing World (Cover Time of a Simple Random Walk on Evolving Graphs). In: Aceto, L., Damgård, I., Goldberg, L.A., Halldórsson, M.M., Ingólfsdóttir, A., Walukiewicz, I. (eds.) ICALP 2008, Part I. LNCS, vol. 5125, pp. 121–132. Springer, Heidelberg (2008)
Casteigts, A., Flocchini, P., Quattrociocchi, W., Santoro, N.: Time-varying graphs and dynamic networks. CoRR, abs/1012.0009 (2010)
Cooper, C., Frieze, A.M.: Crawling on simple models of web graphs. Internet Mathematics 1(1) (2003)
Dessmark, A., Pelc, A.: Optimal graph exploration without good maps. Theor. Comput. Sci. 326(1-3), 343–362 (2004)
Flocchini, P., Kellett, M., Mason, P.C., Santoro, N.: Mapping an Unfriendly Subway System. In: Boldi, P. (ed.) FUN 2010. LNCS, vol. 6099, pp. 190–201. Springer, Heidelberg (2010)
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)
Kuhn, F., Lynch, N.A., Oshman, R.: Distributed computation in dynamic networks. In: 42nd ACM Symposium on Theory of Computing (STOC), pp. 513–522 (2010)
Panaite, P., Pelc, A.: Exploring Unknown Undirected Graphs. J. Algorithms 33(2), 281–295 (1999)
Reingold, O.: Undirected st-connectivity in log-space. In: 37th ACM Symposium on Theory of Computing (STOC), pp. 376–385 (2005)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Ilcinkas, D., Wade, A.M. (2011). On the Power of Waiting When Exploring Public Transportation Systems. In: Fernàndez Anta, A., Lipari, G., Roy, M. (eds) Principles of Distributed Systems. OPODIS 2011. Lecture Notes in Computer Science, vol 7109. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25873-2_31
Download citation
DOI: https://doi.org/10.1007/978-3-642-25873-2_31
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-25872-5
Online ISBN: 978-3-642-25873-2
eBook Packages: Computer ScienceComputer Science (R0)