  We study domain walls in 2d Ising spin glasses in terms of a minimum-weight
path problem. Using this approach, large systems can be treated exactly. Our
focus is on the fractal dimension $d_f$ of domain walls, which describes via
$<\ell >\simL^{d_f}$ the growth of the average domain-wall length with %%
systems size $L\times L$. %% 20.07.07 OM %% Exploring systems up to L=320 we
yield $d_f=1.274(2)$ for the case of Gaussian disorder, i.e. a much higher
accuracy compared to previous studies. For the case of bimodal disorder, where
many equivalent domain walls exist due to the degeneracy of this model, we
obtain a true lower bound $d_f=1.095(2)$ and a (lower) estimate $d_f=1.395(3)$
as upper bound. Furthermore, we study the distributions of the domain-wall
lengths. Their scaling with system size can be described also only by the
exponent $d_f$, i.e. the distributions are monofractal. Finally, we investigate
the growth of the domain-wall width with system size (``roughness'') and find a
linear behavior.
