  We derive exact reconstruction methods for cracks consisting of unions of
Lipschitz hypersurfaces in the context of Calder\'on's inverse conductivity
problem. Our first method obtains upper bounds for the unknown cracks, bounds
that can be shrunk to obtain the exact crack locations upon verifying certain
operator inequalities for differences of the local Neumann-to-Dirichlet maps.
This method can simultaneously handle perfectly insulating and perfectly
conducting cracks, and it appears to be the first rigorous reconstruction
method capable of this. Our second method assumes that only perfectly
insulating cracks or only perfectly conducting cracks are present. Once more
using operator inequalities, this method generates approximate cracks that are
guaranteed to be subsets of the unknown cracks that are being reconstructed.
