Near-optimal panel selection on typical random instances

Determine whether a polynomial-time algorithm can find a near-optimal reporter panel for a typical response matrix generated by the Boolean threshold network ensemble with independently uniform edge weights and uniformly random shock targets.

Background

The paper proves that the Reporter Panel decision problem is NP-complete when the measured binary response matrix is the input, establishing worst-case computational hardness for selecting a fixed-size panel that achieves a specified conditional-entropy threshold. However, the response matrices arising in the study are not adversarial: edge weights are sampled independently and uniformly from [-1,1], and shock targets are sampled uniformly at random.

The authors explicitly distinguish worst-case complexity from the behavior of typical instances drawn from this ensemble. Their experiments show that a genetic algorithm outperforms the polynomial-time heuristics tested, while the spring rule and greedy information-gain methods approach its performance. Whether polynomial-time methods can generally obtain near-optimal panels on typical random instances remains unresolved.

References

Whether a polynomial time algorithm finds a near optimal panel on such a draw is a question we do not resolve.

— Efficiently classifying shocks in complex systems requires dormant reporters  (2609.00725 - Brewster et al., 1 Sep 2026) in Supplementary Information, Part II, Section “How hard is choosing the panel?” (scope-of-theorem remarks)