A new algorithm for global flow analysis on reducible graphs is presented. The algorithm is shown to treat a very general class of function spaces. For a graph of e edges, the algorithm has a worst case time bound of 0(e log2e) function operations. In programming terms, the number of operations is shown to be proportional to e + the number of exit nodes from program loops. Consequently a restriction to one-entry one-exit control structures guarantees linearity. It is shown that by relaxing these time bounds, a yet wider class of function spaces can be handled.