Adaptive and distributed homology computation with application to large scale sensor networks

The homology groups provide useful information about a space. In several applications, including sensor networks, a combinatorial space is built to reflect the data and their relations about a specific topic to be analyzed. Hence the computation of the homology groups is of prime interest. However, the combinatorial space may vary and the computation of its homology groups becomes more difficult. This paper proposes an adaptive algorithm which updates incrementally the homology groups, and because it uses mostly small local computations, it is inherently well adapted to large-scale network. In the second part of the paper, the algorithm is developed and applied to the sensing coverage problem in a sensor networks. Because of its structure, the algorithm is inherently distributed.