End-to-end data paths: quickest or most reliable?

Let N=(V,E,c,l,p) be a network where V is the set of n vertices, E is the set of m edges, c(u,v)/spl ges/0 is the capacity of edge {u,v}, l(u,v)/spl ges/0 is the delay of edge {u,v}, p(u,v)/spl isin/[0,1] is the operational probability of edge {u,v}. In this letter, we present O(rm+rnlog n) time algorithms for the most reliable quickest path problem and the quickest most reliable path problem, where r is the number of different capacity values in the network.