Optimal path in two and three dimensions

We apply the Dijkstra algorithm to generate optimal paths between two given sites on a lattice representing a disordered energy landscape. We study th e geometrical and energetic scaling properties of the optimal path where th e-energies are taken from a uniform distribution. Our numerical results for both two and three dimensions suggest that the optimal path for random uni formly distributed energies is in the same universality class as the direct ed polymers. We present physical realizations of polymers in a disordered e nergy landscape for which this result is relevant. [S1063-651X(98)08212-9].