Optimal paths and domain walls in the strong disorder limit

An optimization problem that may be cast in the context of domain walls in ferromagnets and spin glasses, latice animals, and percolation is described. Numerical calculations in two and three dimensions show that a new universality class is obtained. In the strong disorder limit interfaces are not self-affine but fractal. Further, the nontrivial ground state of frustrated spin glasses is straightforwardly obtained in this limit.