Node listings for reducible flow graphs

K. Kennedy recently conjectured that for every n node reducible flow graph, there is a sequence of nodes (with repetitions) of length O(n log n) such that all acyclic paths are subsequences thereof. Such a sequence would, if it could be found easily, enable one to do various kinds of global data flow analyses quickly. We show that for all reducible flow graphs such a sequence does exist, even if the number of edges is much larger than n. If the number of edges is O(n), the node listing can be found in O(n log n) time