We study the problem of link delay estimation in congested networks. Our
approach is based on compressive sensing. However the measurement design here
is
constrained by the network topology. For a variety of measurement models  we
show that O(k logk) measurements suffice to recover the value of delays over
uncongested links. Further, we show that the computational complexity required
for decoding the delay vector is O(k log k log |E|). We also consider a
localized tomography problem where the objective is to estimate the delay on a
few specific links based on an existing set of measurements. We show that by
querying just a few measurements, delay estimation for any single edge may be
performed in O(log|E|) time with a reasonably high probability.