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The problem of determining the ground state of a $d$-dimensional interfaceembedded in a $(d+1)$-dimensional random medium is treated numerically. Using aminimum-cut algorithm, the exact ground states can be found for a number ofproblems for which other numerical methods are inexact and slow. In particular,results are presented for the roughness exponents and ground-state energyfluctuations in a random bond Ising model. It is found that the roughnessexponent $\zeta = 0.41 \pm 0.01, 0.22 \pm 0.01$, with the related energyexponent being $\theta = 0.84 \pm 0.03, 1.45 \pm 0.04$, in $d = 2, 3$,respectively. These results are compared with previous analytical and numericalestimates.Comment: 10 pages, REVTEX3.0; 3 ps files (separate:tar/gzip/uuencoded) for  figure

Numerical results for the ground-state interface in a random medium