  Standard algorithms for finding the shortest path in a graph require that the
cost of a path be additive in edge costs, and typically assume that costs are
deterministic. We consider the problem of uncertain edge costs, with potential
probabilistic dependencies among the costs. Although these dependencies violate
the standard dynamic-programming decomposition, we identify a weaker stochastic
consistency condition that justifies a generalized dynamic-programming approach
based on stochastic dominance. We present a revised path-planning algorithm and
prove that it produces optimal paths under time-dependent uncertain costs. We
test the algorithm by applying it to a model of stochastic bus networks, and
present empirical performance results comparing it to some alternatives.
Finally, we consider extensions of these concepts to a more general class of
problems of heuristic search under uncertainty.
