Identifying faulty edges in resistive electrical networks
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866914330679705600 |
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| author | Fiedorowicz, Barbara Basu, Amitabh |
| author_facet | Fiedorowicz, Barbara Basu, Amitabh |
| contents | Given a resistive electrical network, we would like to determine whether all the resistances (edges) in the network are working, and if not, identify which edge (or edges) are faulty. To make this determination, we are allowed to measure the effective resistance between certain pairs of nodes (which can be done by measuring the amount of current when one unit of voltage difference is applied at the chosen pair of nodes). The goal is to determine which edge, if any, is not working in the network using the smallest number of measurements. We prove rigorous upper and lower bounds on this optimal number of measurements for different classes of graphs. These bounds are tight for several of these classes showing that our measurement strategies are optimal. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_23527 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Identifying faulty edges in resistive electrical networks Fiedorowicz, Barbara Basu, Amitabh Optimization and Control Discrete Mathematics Information Theory Combinatorics 94C12, 90C27, 05C50, 94C15, 94A15 Given a resistive electrical network, we would like to determine whether all the resistances (edges) in the network are working, and if not, identify which edge (or edges) are faulty. To make this determination, we are allowed to measure the effective resistance between certain pairs of nodes (which can be done by measuring the amount of current when one unit of voltage difference is applied at the chosen pair of nodes). The goal is to determine which edge, if any, is not working in the network using the smallest number of measurements. We prove rigorous upper and lower bounds on this optimal number of measurements for different classes of graphs. These bounds are tight for several of these classes showing that our measurement strategies are optimal. |
| title | Identifying faulty edges in resistive electrical networks |
| topic | Optimization and Control Discrete Mathematics Information Theory Combinatorics 94C12, 90C27, 05C50, 94C15, 94A15 |
| url | https://arxiv.org/abs/2512.23527 |