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

13 years 4 months ago

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ABSTRACT. We introduce tools from computational homology to verify coverage in an idealized 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. The key ingredient is the theory of homology from algebraic topology. We demonstrate the robustness of these tools by adapting them to a variety of settings, including static planar coverage, 3d barrier coverage, and time-dependent sweeping coverage. We also give results on hole repair, error tolerance, optimal coverage, and variable radii. An overview of implementation is given.

V. de Silva, R. Ghrist

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