  We apply the localization technique to topologically twisted N=(2,2)
supersymmetric gauge theory on a discretized Riemann surface (the generalized
Sugino model). We exactly evaluate the partition function and the vacuum
expectation value (vev) of a specific Q-closed operator. We show that both the
partition function and the vev of the operator depend only on the Euler
characteristic and the area of the discretized Riemann surface and are
independent of the detail of the discretization. This localization technique
may not only simplify numerical analysis of the supersymmetric lattice models
but also connect the well-defined equivariant localization to the empirical
supersymmetric localization.
