  Pen testing is the problem of selecting high-capacity resources when the only
way to measure the capacity of a resource expends its capacity. We have a set
of $n$ pens with unknown amounts of ink and our goal is to select a feasible
subset of pens maximizing the total ink in them. We are allowed to gather more
information by writing with them, but this uses up ink that was previously in
the pens. Algorithms are evaluated against the standard benchmark, i.e, the
optimal pen testing algorithm, and the omniscient benchmark, i.e, the optimal
selection if the quantity of ink in the pens are known.
  We identify optimal and near optimal pen testing algorithms by drawing
analogues to auction theoretic frameworks of deferred-acceptance auctions and
virtual values. Our framework allows the conversion of any near optimal
deferred-acceptance mechanism into a near optimal pen testing algorithm.
Moreover, these algorithms guarantee an additional overhead of at most
$(1+o(1)) \ln n$ in the approximation factor of the omniscient benchmark. We
use this framework to give pen testing algorithms for various combinatorial
constraints like matroid, knapsack, and general downward-closed constraints and
also for online environments.
