Résumé | 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 (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 $Theta(kcdot p^2)$ in the general case.
In this talk, 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 $Theta(p)$, while the time complexity is reduced to $Theta(ncdot p)$. (In any connected PV-graph, we have $n leq kcdot p$.) 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 joint work with David Ilcinkas.
Orateur: Ahmed Wade |