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

• ApplicationsMulti-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,

1 2 3 4

5 6 7 8

Partition-based strategies• 1) Compute a partition of the

graph in n regions:

• 2) Let each agent patrol in a region,

1 2 3 4

5 6etc…

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