Optimal allocation of security sensors/guards-graph theoretic approach

The problem of optimal allocation of security sensors and/or guards is formulated as a graph/network problem, where the importance of the concept of degree of security or multiple minimal cut set is stressed. An algorithm for solving the formulated graph/network problem is developed and it is shown that the algorithm is very effective from the viewpoint of computational complexity. Examples are given to illustrate the concept of degree of security, optimal allocation of security sensors/guards, multiple minimal cut set, and computational efficiency. A typical example among them is: assume a terrorist or a thief is going to attack a target in a town. The problem is to find the minimum number of sensors/guards and where and how to allocate them in the town, detecting him at least twice (or more generally k times) on his way to the target, even if he may take any route among numerous possible routes.<>