Exploration of Dynamic Cactuses with Sub-logarithmic Overhead
Résumé
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 [19]. 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 $O(n \log n / \log \log n)$ time units. We show that the lower bound of the algorithm is $\Omega(n \log n / (\log \log n)^2)$ time units (for infinitely many n).
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