Best-case teaching dimension for finite-VC concept classes

Characterize whether every concept class C of finite VC dimension d contains a concept with a teaching set of size O(d), equivalently whether the best-case teaching dimension TS is universally bounded by O(d), thereby addressing the corresponding conjectured O(d) bound for Recursive Teaching Dimension.

Background

The paper identifies the universal characterization of the best-case teaching dimension TS as a fundamental unresolved question in learning theory. Given a concept class C over a finite domain with VC dimension d, the problem is to determine whether at least one concept in C can be uniquely identified by labeling only O(d) domain points.

A positive resolution would imply the conjectured O(d) upper bound for Recursive Teaching Dimension. The paper studies lower bounds for a particular greedy teaching-set construction and shows that the construction can require substantially larger teaching sets for small greediness parameters, but it does not resolve the general TS = O(d) question.