On monday, at 2pm - UPEC CMC - Room P2-131
How efficiently can we find an unknown graph using shortest path queries between its vertices? This is a natural theoretical question from the standpoint of recovery of hidden information. This question is related to discovering the topology of Internet networks, which is a crucial step for building accurate network models and designing efficient algorithms for Internet applications.
In this talk, I will introduce the problems of graph reconstruction and verification via oracles. I will investigate randomized algorithms based on a Voronoi cell decomposition. I will also analyze greedy algorithms, and prove that they are near-optimal.
The talk is based on joint work with Claire Mathieu and Sampath Kannan.
Bertrand et al. (2017) introduced a model of parameterised
systems, where each agent is represented by a finite state system, and
studied the following control problem: for any number of agents, does
there exist a controller able to bring all agents to a target state? They
showed that the problem is decidable and EXPTIME-complete in the
adversarial setting, and posed as an open problem the stochastic setting,
where the agent is represented by a Markov decision process. In this
paper, we show that the stochastic control problem is decidable. Our
solution makes significant uses of well quasi orders, of the max-flow min-
cut theorem, and of the theory of regular cost functions.