  We investigate the problem of optimally assigning a large number of robots
(or other types of autonomous agents) to guard the perimeters of closed 2D
regions, where the perimeter of each region to be guarded may contain multiple
disjoint polygonal chains. Each robot is responsible for guarding a subset of a
perimeter and any point on a perimeter must be guarded by some robot. In
allocating the robots, the main objective is to minimize the maximum 1D
distance to be covered by any robot along the boundary of the regions. For this
optimization problem which we call optimal perimeter guarding (OPG), thorough
structural analysis is performed, which is then exploited to develop fast exact
algorithms that run in guaranteed low polynomial time. In addition to formal
analysis and proofs, experimental evaluations and simulations are performed
that further validate the correctness and effectiveness of our algorithmic
results.
