A group of agents can be used to perform patrolling tasks in a variety of domains ranging from computer network administration to computer wargame simulations. The multi-agent patrolling problem has recently received growing attention from the multi-agent community, due to the wide range of potential applications. Many algorithms based on reactive and cognitive architectures have been developed, giving encouraging results. However, no theoretical analysis of this problem has been conducted. In this paper, various classes of patrolling strategies are proposed and compared. More precisely, these classes are compared to the optimal strategy by means of a standard complexity analysis.