We investigate the problem of computing the strictly-second shortest p
ath connecting a given pair of vertices in a directed graph. We show t
hat this problem is intractable when the path is restricted to be simp
le. When cycles are allowed, we give an algorithm that solves it in as
ymptotically the same number of steps as it takes to compute the short
est path between the given vertex pair. (C) 1997 Elsevier Science B.V.