Dear Sir:
I can get a solution, assuming the following previous conditions and concepts:
Planning that each point of the continental territory have to be covered by at least one tower signal, and overlapping must be minimized for get total cover with the less towers, the optimal distribution is a triangular mesh, with 173,2 miles between vertices. Each tower will had other six around it, looking like a honeycomb, with a tower in the center of each cell, minimizing overlay of their covers.
I have evaluate various approaches but I think than the best is to first select cities by relative distances with an R algorithm, and after confirm good land cover on maps, with QGIS.
I plan to write an R script to simulate various possible solutions, calculating distance from geographical coordinates of principal Cities, on a standard homogeneous WGS84 projection, looking for minimizing tower points needed for total cover.
Optimal apparent solutions will be plotted on a digital map, using QGIS. Total surface cover and overlapping of signal will be graphically probed with the buffer tool, detecting holes, and special situations, that will be resolute by simply adding or moving any strategical tower, or going back to the calculation process.
I have a data file with city limits considered for the us census, to process geocenters. Also I have the list of coordenates and names of all the US populated places. Any way I could use any list of city points that you wuold. Thanks