  In this paper we consider a robot patrolling problem in which events arrive
randomly over time at the vertices of a graph. When an event arrives it remains
active for a random amount of time. If that time active exceeds a certain
threshold, then we say that the event is a true event; otherwise it is a false
event. The robot(s) can traverse the graph to detect newly arrived events, and
can revisit these events in order to classify them as true or false. The goal
is to plan robot paths that maximize the number of events that are correctly
classified, with the constraint that there are no false positives. We show that
the offline version of this problem is NP-hard. We then consider a simple
patrolling policy based on the traveling salesman tour, and characterize the
probability of correctly classifying an event. We investigate the problem when
multiple robots follow the same path, and we derive the optimal (and not
necessarily uniform) spacing between robots on the path.
