Missions for autonomous systems often require agents to visit multiple targets in complex operating conditions. This work considers the problem of visiting a set minimum time by team non-communicating Markov decision process (MDP). The single-agent is at least NP-complete reducing it Hamiltonian path problem. We first discuss an optimal algorithm based on Bellman's optimality equation that expo...

We characterize all stationary time-reversible Markov processes whose finite-dimensional marginal distributions (of all orders) are infinitely divisible. Aside from two trivial cases (iid and constant), every such process with full support in both discrete and continuous time is a branching process with Poisson or Negative Binomial marginal distributions and a specific bivariate distribution at...

We develop analytic tools for the asymptotics of general trie statistics, which are particularly advantageous for clarifying the asymptotic variance. Many concrete examples are discussed for which new Fourier expansions are given. The tools are also useful for other splitting processes with an underlying binomial distribution. We specially highlight Philippe Flajolet’s contribution in the analy...