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Decentralized Computation of Homology Groups in Networks by Gossip

In this paper, we present an approach towards the computation of certain topological invariants in real sensor networks. As shown by many researchers, these invariants are relevant for modeling certain properties of the network such as coverage and routing. What has been lacking so far is a concrete decentralized method to compute these invariants for proper implementation. In this paper, we give an approach towards such an implementation. The main tools being used here are the the so-called higher order Laplacian operators and distributed methods for their spectral analysis that resemble gossip algorithms.