A Theoretical Analysis of Multi-Agent Patrolling Strategies Patrolling = moving through a territory « visiting » areas The patrolling problem = given a graph representing a territory, how to move n agents around the graph, such that nodes are visited as often as possible Applications Multi-robot patrolling, computer games, military applications Approaches –Reactive agent based architecture (agents move towards least visited nodes) –Partition based approach (1 agent per region) –Combinatorial optimization approach

Cyclic strategies 1) Compute a cycle covering the entire graph: 2) Let agents turn around this cycle,

Partition-based strategies 1) Compute a partition of the graph in n regions: 2) Let each agent patrol in a region, etc…

Results Cyclic strategies single agent case: if the cycle is obtained is the optimal TSP cycle (traveling salesman problem), then strategy is optimal Multi-agent case: If cycle is obtained with a TSP approximation algorithm, then Max visiting time < 3xoptimal + c (near optimal!) Partition-based strategies Max visiting time > optimal(cyclic) - c Thus, cyclic-based is probably nearly always better !! Conclusion: Cyclic-based approach is excellent except when c (length of longest edge) is big, in which case partitioning is a good idea! Experimentally : cyclic strategy is at least as good as other state-of-the-art strategies