  In this paper we study a multi-robot path planning problem for persistent
monitoring of an environment. We represent the areas to be monitored as the
vertices of a weighted graph. For each vertex, there is a constraint on the
maximum time spent by the robots between visits to that vertex, called the
latency, and the objective is to find the minimum number of robots that can
satisfy these latency constraints. The decision version of this problem is
known to be PSPACE-complete. We present a $O(\log \rho)$ approximation
algorithm for the problem where $\rho$ is the ratio of the maximum and the
minimum latency constraints. We also present an orienteering based heuristic to
solve the problem and show through simulations that in most of the cases the
heuristic algorithm gives better solutions than the approximation algorithm. We
evaluate our algorithms on large problem instances in a patrolling scenario and
in a persistent scene reconstruction application. We also compare the
algorithms with an existing solver on benchmark instances.
