Efficient Algorithms for Optimal Perimeter Guarding
This addresses efficient resource allocation for perimeter guarding in robotics, but it appears incremental as it builds on existing optimization frameworks.
The paper tackles the problem of optimally assigning robots to guard perimeters of 2D regions to minimize the maximum distance any robot must cover, developing fast exact algorithms with low polynomial time complexity and validating them through experiments.
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.