Exploring unknown undirected graphs
Journal of Algorithms
Optimal graph exploration without good maps
Theoretical Computer Science
Undirected ST-connectivity in log-space
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
How to Explore a Fast-Changing World (Cover Time of a Simple Random Walk on Evolving Graphs)
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part I
Exploration of Periodically Varying Graphs
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Distributed computation in dynamic networks
Proceedings of the forty-second ACM symposium on Theory of computing
Mapping an unfriendly subway system
FUN'10 Proceedings of the 5th international conference on Fun with algorithms
FUN'12 Proceedings of the 6th international conference on Fun with Algorithms
On the exploration of time-varying networks
Theoretical Computer Science
Expressivity of time-varying graphs
FCT'13 Proceedings of the 19th international conference on Fundamentals of Computation Theory
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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·p2) 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.