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We consider the following problem: Given a finite set of straight linesegments in the plane, determine the positions of a minimal number of points onthe segments, from which guards can see all segments. This problem can beinterpreted as looking for a minimal number of locations of policemen, guards,cameras or other sensors, that can observe a network of streets, corridors,tunnels, tubes, etc. We show that the problem is strongly NP-complete even fora set of segments with a cubic graph structure, but in P for tree structures.

Patrolling a Street Network is Strongly NP-Complete but in P for Tree Structures