A Computational Physics-Based Algorithm for Target Coverage Problems

The problem of optimally covering a set of point targets in a region with areas of a specific shape has several important applications in the fields of communications, remote sensing, and logistics. We consider the case where a target is covered when it falls within a coverage area (so-called “Boolean” coverage), and we specialize to the case of identical circular (or spherical) coverage areas. The problem has been shown to be NP-hard, and most practical algorithms use statistical methods to look for near-optimal solutions. Previous algorithms cannot guarantee 100% target coverage. In this chapter we demonstrate a physics-based algorithm (called the “nebular algorithm”) that guarantees full coverage while seeking to minimize the number of coverage areas employed. This approach can generate solutions with reduced numbers of sensors for systems with thousands of targets within a few hours. The algorithm, its implementation, and simulation results are presented, as well as its potential applicability to other coverage problems such as area and/or probabilistic coverage.