We consider the following Stochastic Boolean Function Evaluation problem, which is closely related to several problems from the literature. A matroid \(\mathcal{M}\) (in compact representation) on ground set \(E\) is given, and each element \(i \in E\) is active independently with known probability \(p_i \in (0,1)\). The elements can be queried, upon which it is revealed whether the respective element is active or not. The goal is to find an adaptive querying strategy for determining whether there is a basis of \(\mathcal{M}\) in which all elements are active, with the objective of minimizing the expected number of queries.

Abstract. We revisit the Stochastic Score Classification (SSC) problem introduced by Gkenosis et al. (ESA 2018): We are given [Formula: see text] tests. Each test [Formula: see text] can be conducted at cost [Formula: see text], and it succeeds independently with probability [Formula: see text]. Further, a partition of the (integer) interval [Formula: see text] into [Formula: see text] smaller intervals is known. The goal is to conduct tests so as to determine that interval from the partition in which the number of successful tests lies while minimizing the expected cost. Ghuge, Gupta, and Nagarajan (IPCO 2022) recently showed that a polynomial-time constant-factor approximation algorithm exists. We show that interweaving the two strategies that order tests increasingly by their [Formula: see text] and [Formula: see text] ratios, respectively—as already proposed by Gkensosis et al. for a special case—yields a small approximation ratio. We also show that the approximation ratio can be slightly decreased from 6 to [Formula: see text] by adding in a third strategy that simply orders tests increasingly by their costs. The similar analyses for both algorithms are nontrivial but arguably clean. Finally, we complement the implied upper bound of [Formula: see text] on the adaptivity gap with a lower bound of 3/2. Since the lower-bound instance is a so-called unit-cost [Formula: see text]-of-[Formula: see text] instance, we settle the adaptivity gap in this case.