Analysis of preflow push algorithms for maximum network flow
We study the class of preflow push algorithms recently introduced by Goldberg and Tarjan for solving the maximum network flow problem on a weighted digraph G(V,E). We improve Goldberg and Tarjanis O(n3) time bound for the maximum distance preflow push algorithm to O(n2√m) and show that this bound is tight by constructing a parametrized worst case network. We then develop the maximal excess preflow push algorithm and show that it achieves a bound of O(n2√m) pushes. Based on this we develop a maximum network flow algorithm for the synchronous distributed model of computation that uses at most O(n2√m) messages and O(n2) time, thereby improving upon the best previously known algorithms for this model.
Unable to display preview. Download preview PDF.
- [Aw]B. Awerbuch, "Reducing complexities of the distributed max-flow and breadth-first-search algorithms by means of network synchronization", Networks 15(1985), 425–437.Google Scholar
- [Ch]B. V. Cherkasky, "Algorithm of construction of maximal flow in networks with complexity of O(V2√E) operations", Mathematical Methods of Solution of Economical Problems 7(1977), 112.Google Scholar
- [D]E.A. Dinic, "Algorithm for solution of a problem of maximum flow in networks with power estimation", Soviet Math. Doklady 11(1980), 1277–1280.Google Scholar
- [Ga1]Z. Galil, "An O(V5/3E2/3) algorithm for the maximal flow problem", Acta Informatica 14(1980), 221–242.Google Scholar
- [Ga2]Z. Galil, "On the theoretical efficiency of various network flow algorithms", Theoretical Computer Science 14(1981) 103–111.Google Scholar
- [Go]A.V.Goldberg, "Efficient graph algorithms for sequential and parallel computers", Ph.D. Thesis, MIT/LCS/TR-374, Feb 1987.Google Scholar
- [GT]A.V.Goldberg and R.E.Tarjan, "A new approach to the maximum flow problem", Proc. 18th Annual ACM Symp. on Theory of Computing (1986).Google Scholar
- [MG]J.M.Marberg and E.Gafni, "An O(n2m1/2) distributed max-flow algorithm", Proc. International Conference on Parallel Processing, 1987.Google Scholar