The Spatio-temporal Available Bandwidth estimator (STAB), a new edge-based probing tool, locates thin links --- those links with less available bandwidth than all links preceeding them --- on end-to-end network paths. By localizing thin links, STAB facilitates network operations and troubleshooting, provides insight into what causes network congestion, and aids network-aware applications. The tool uses special chirp probing trains, featuring an exponential flight pattern of packets, which have the advantage of employing few packets while giving an accurate estimate of available bandwidth.