Exploration of carrier-based time-varying networks: The power of waiting

Abstract

We study the problem of exploration by a mobile entity (agent) of a class of highly dynamic networks, namely the carrier graphs (the C-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 [9] 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 worst-case number of time units (and thus of moves) to explore a n-node C-graph of k carriers and maximal period p is in Θ(kp2) 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 optimal worst-case number of moves by a multiplicative factor of at least Θ(p), while the worst-case time complexity is reduced to Θ(np). (In any connected carrier graph, we have n≤kp.) We also show some complementary optimal results in specific cases (same period for all carriers, highly connected C-graphs). Finally this new ability allows the agent to completely map the C-graph, in addition to just exploring it.