Exploration of the T-Interval-Connected Dynamic Graphs: the Case of the Ring

David Ilcinkas (1) , Ahmed Mouhamadou Wade (2)

1 LaBRI - Laboratoire Bordelais de Recherche en Informatique
2 Ecole polytechnique de Thiès

In this paper, we study the $T$-interval-connected dynamic graphs from the point of view of the time necessary and sufficient for their exploration by a mobile entity (agent). A dynamic graph (more precisely, an evolving graph) is $T$-interval-connected ($T \geq 1$) if, for every window of $T$ consecutive time steps, there exists a connected spanning subgraph that is stable (always present) during this period. This property of connection stability over time was introduced by Kuhn, Lynch and Oshman (STOC 2010). We focus on the case when the underlying graph is a ring of size $n$, and we show that the worst-case time complexity for the exploration problem is $2n-T-\Theta(1)$ time units if the agent knows the dynamics of the graph, and $n+ \frac{n}{\max\{1, T-1\} } (\delta-1) \pm \Theta(\delta)$ time units otherwise, where $\delta$ is the maximum time between two successive appearances of an edge.

Mots clés: Exploration; Dynamic graphs; T-interval-connectivity; Mobile agent

Domaines: Calcul parallèle, distribué et partagé [cs.DC]

David Ilcinkas, Ahmed Mouhamadou Wade. Exploration of the T-Interval-Connected Dynamic Graphs: the Case of the Ring. Theory of Computing Systems, 2018, 62 (5), pp.1144 - 1160. ⟨10.1007/s00224-017-9796-3⟩. ⟨hal-01899735⟩