We consider the problem of estimating the length of a shortest path in a DAG whose edge lengths are known only approximately but can be determined exactly at a cost. Initially, each edge e is known only to lie within an interval [l e ; he ]; the estimation algorithm can pay ce to find the exact length of e. In particular, we study the problem of finding the cheapest set of edges such that, if exactly these edges are queried, the length of the shortest path will be known, within an...