The study and planning of cellular towers on an urban map is full of interesting computational geometry problems.
Part 1: topics in stochastic geometry: random point processes. We consider random points deployed on a plane, and examine statistical metrics to characterize their spatial regularity. We use this knowledge to design good point processes with tunable regularity, with various applications in planning point sets on a plane with maximal regularity (repulsiveness).
Part 2: an approximate art gallery problem with polygonal holes. Given the layout of a city’s buildings as polygonal footprints, we consider how to cover the maximum of the outdoor area with the minimum number of wall-mounted cellular access points.
Part 3: extensions to other applications. Automated partitioning of urban maps into meaningful components connected in a graph. Optimal planning with constraints of punctual and linear resources on an urban map.