Polynomial-time solvability of faulty edge detection

Determine for which classes of graphs the faulty edge detection problem in resistive electrical networks can be solved in polynomial time.

Background

The paper formulates faulty edge detection as the problem of selecting the smallest set of effective-resistance measurements that distinguishes every possible faulty edge in a given electrical network. The authors establish exact or tight measurement bounds for complete graphs and complete k-partite graphs, but do not develop an efficient algorithm for solving the optimization problem on general graph classes.

The authors note that the problem can be modeled as a set-cover or integer-programming problem, motivating a complexity-theoretic investigation of graph families for which an exact polynomial-time solution method exists. The question is explicitly presented as open and is left unresolved by the paper.

References

For what class of graphs can the faulty edge detection problem be solved in polynomial time?

— Identifying faulty edges in resistive electrical networks  (2512.23527 - Fiedorowicz et al., 29 Dec 2025) in Section 5, Conclusion and future directions, subsection “Algorithmic aspects”