Polynomial representation or complexity classification for unrestricted period-dependent thresholds

Establish either a different polynomial-size representation for exact dynamic programming with unrestricted period-dependent all-units discount thresholds or a separate computational-complexity classification of that model.

Background

For period-dependent thresholds, the paper’s exact critical-state construction can generate exponentially many distinct subset sums, even when each period has only one positive threshold. The authors explicitly note that this exponential growth does not establish NP-hardness or otherwise classify the computational complexity of the model. The unresolved problem is therefore to find a polynomial-size exact representation or to determine the appropriate complexity classification.