  In this paper we study the BPS state counting in the geometry of local
obstructed curve with normal bundle O+O(-2). We find that the BPS states have a
framed quiver description. Using this quiver description along with the Seiberg
duality and the localization techniques, we can compute the BPS state indices
in different chambers dictated by stability parameter assignments. This
provides a well-defined method to compute the generalized Donaldson-Thomas
invariants. This method can be generalized to other affine ADE quiver theories.
