Exploration of Constantly Connected Dynamic Graphs Based on Cactuses

Abstract : We study the problem of exploration by a mobile entity (agent) of a class of dynamic networks, namely constantly connected dynamic graphs. This problem has already been studied in the case where the agent knows the dynamics of the graph and the underlying graph is a ring of $n$ vertices \cite{IW13}. In this paper, we consider the same problem and we suppose that the underlying graph is a cactus graph (a connected graph in which any two simple cycles have at most one vertex in common). We propose an algorithm that allows the agent to explore these dynamic graphs in at most $2^{O(\sqrt{\log n})} n$ time units. We show that the lower bound of the algorithm is $2^{\Omega(\sqrt{\log n})} n$ time units.
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David Ilcinkas, Ralf Klasing, Ahmed Mouhamadou Wade. Exploration of Constantly Connected Dynamic Graphs Based on Cactuses. 21th International Colloquium on Structural Information and Communication Complexity (SIROCCO 2014), Jul 2014, Hida Takayama, Japan. pp.250--262, ⟨10.1007/978-3-319-09620-9_20⟩. ⟨hal-01068904⟩

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