Continuous graph partitioning for camera network surveillance

In this note we discuss a novel graph partitioning problem, namely continuous graph partitioning, and we discuss its application to the design of surveillance trajectories for camera networks. In continuous graph partitioning, each edge is partitioned in a continuous fashion between its endpoint vertices, and the objective is to minimize the largest load among the vertices. We show that the continuous graph partitioning problem is convex and non-differentiable, and we characterize a solution amenable to distributed computation. The continuous graph partitioning problem naturally arises in the context of camera networks, where intruders appear at arbitrary locations and times, and the objective is to design camera trajectories for quickest detection of intruders. Finally, we propose a surveillance strategy for networks of PTZ cameras and we characterize its performance.