Weighted Combinatorial Laplacian and its Application to Coverage Repair in Sensor Networks
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866910409066283008 |
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| author | Yadokoro, Shunsaku Bhattacharya, Subhrajit |
| author_facet | Yadokoro, Shunsaku Bhattacharya, Subhrajit |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_04825 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Weighted Combinatorial Laplacian and its Application to Coverage Repair in Sensor Networks Yadokoro, Shunsaku Bhattacharya, Subhrajit Robotics Algebraic Topology 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. |
| title | Weighted Combinatorial Laplacian and its Application to Coverage Repair in Sensor Networks |
| topic | Robotics Algebraic Topology |
| url | https://arxiv.org/abs/2312.04825 |