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arXiv · 2312.04825

Weighted Combinatorial Laplacian and its Application to Coverage Repair in Sensor Networks

Shunsaku Yadokoro·Subhrajit Bhattacharya
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Abstract

We define the weighted combinatorial Laplacian operators on a simplicial complex and investigate their spectral properties. Eigenvalues close to zero and the corresponding eigenvectors of them are especially of our interest, and we show that they can detect almost $n$-dimensional holes in the given complex. Real-valued weights on simplices allow gradient descent based optimization, which in turn gives an efficient dynamic coverage repair algorithm for the sensor network of a mobile robot team. Using the theory of relative homology, we also extend the problem of dynamic coverage repair to environments with obstacles.

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Shunsaku Yadokoro, Subhrajit Bhattacharya. 2023-12-08. Weighted Combinatorial Laplacian and its Application to Coverage Repair in Sensor Networks. https://arxiv.org/abs/2312.04825

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