  We study the behavior of the optimal path between two sites separated by a
distance $r$ on a $d$-dimensional lattice of linear size $L$ with weight
assigned to each site. We focus on the strong disorder limit, i.e., when the
weight of a single site dominates the sum of the weights along each path. We
calculate the probability distribution $P(\ell_{\rm opt}|r,L)$ of the optimal
path length $\ell_{\rm opt}$, and find for $r\ll L$ a power law decay with
$\ell_{\rm opt}$, characterized by exponent $g_{\rm opt}$. We determine the
scaling form of $P(\ell_{\rm opt}|r,L)$ in two- and three-dimensional lattices.
To test the conjecture that the optimal paths in strong disorder and flow in
percolation clusters belong to the same universality class, we study the tracer
path length $\ell_{\rm tr}$ of tracers inside percolation through their
probability distribution $P(\ell_{\rm tr}|r,L)$. We find that, because the
optimal path is not constrained to belong to a percolation cluster, the two
problems are different. However, by constraining the optimal paths to remain
inside the percolation clusters in analogy to tracers in percolation, the two
problems exhibit similar scaling properties.
