  We prove that a quantum walk can detect the presence of a marked element in a
graph in $O(\sqrt{WR})$ steps for any initial probability distribution on
vertices. Here, $W$ is the total weight of the graph, and $R$ is the effective
resistance. This generalizes the result by Szegedy that is only applicable if
the initial distribution is stationary. We describe a time-efficient quantum
algorithm for 3-distinctness based on these ideas.
