Coordinate-free Coverage in Sensor Networks with Controlled Boundaries via Homology

We introduce tools from computational homology to verify coverage in a sensor network. Our methods are unique in that, while they are coordinate-free and assume no localization or orientation capabilities for the nodes, there are also no probabilistic assumptions. We demonstrate the robustness of the techniques by adapting them to a variety of settings, including static planar coverage, 3-d barrier coverage, and time-dependent sweeping coverage. We also give results on hole repair, error tolerance, and variable radii. draft; version 8.0; simulation-free