  Using mappings to computer-science problems and by applying sophisticated
algorithms, one can study numerically many problems much better compared to
applying standard approaches like Monte Carlo simulations. Here, using
calculations of ground states of suitable perturbed systems, droplets are
obtained in two-dimensional +-J spin glasses, which are in the focus of a
currently very lifely debate. Since a sophisticated matching algorithm is
applied here, exact ground states of large systems up to L^2=256^2 spins can be
generated. Furthermore, no equilibration or extrapolation to T=0 is necessary.
Three different +-J models are studied here: a) with open boundary conditions,
b) with fixed boundary conditions and c) a diluted system where a fraction
p=0.125 of all bonds is zero. For large systems, the droplet energy shows for
all three models a power-law behavior E_D L^\theta'_D with \theta'_D<0. This is
different from previous studies of domain walls, where a convergence to a
constant non-zero value (\theta_dw=0) has been found for such models. After
correcting for the non-compactness of the droplets, the results are likely to
be compatible with \theta_D= -0.29 for all three models.
  This is in accordance with the Gaussian system where \theta_D=-0.287(4)
(\nu=3.5 via \nu=-1/\theta_D). Nevertheless, the disorder-averaged spin-spin
correlation exponent \eta is determined here via the probability to have a
non-zero-energy droplet, and \eta~0.22$ is found for all three models, this
being in contrast to the behavior of the model with Gaussian interactions,
where exactly \eta=0.
