Finding Maximum Flows Research Articles

Maximum Flow in Planar Networks

Efficient algorithms for finding maximum flow in planar networks are presented. These algorithms take advantage of the planarity and are superior to the most efficient algorithms to date. If the source and the terminal are on the same face, an algorithm of Berge is improved and its time complexity is reduced to $O(n\log n)$. In the general case, for a given $D > 0$ a flow of value D is found if one exists; otherwise, it is indicated that no such flow exists. This algorithm requires $O(n^2 \log n)$ time. If the network is undirected a minimum cut may be found in $O(n^2 \log n)$ time. All algorithms require $O(n)$ space.

Two-Commodity Flow

An algorithm is given to fmd maxtmum two-commodity flow m an undirected graph The algorithm is an improvement on Hu's two-commodity flow algorithm using the methods of Dmlc's single-commodity flow algorithm Karzanov's Improvement of Dmlc's algorithm can be applied to yield an O(I V ) 3) algorithm. It is shown that finding maximum two-commodity flow m a dwected graph is much more dffficuh, in fact it Is as difficult as hnear programming FmaUy, the problem of finding feasible flow m an undirected graph with lower and upper bounds on the edges is shown to be NP-complete even for a single commodity

An O(| V| 3) algorithm for finding maximum flows in networks

An O(V cubed) algorithm is given for finding maximum flow in capacitated networks. THe algorithm is already well refenreces in literature and is being posted here to make it accessible to all in electronic form.

Multiprocessor Scheduling with the Aid of Network Flow Algorithms

In a distributed computing system a modular program must have its modules assigned among the processors so as to avoid excessive interprocessor communication while taking advantage of specific efficiencies of some processors in executing some program modules. In this paper we show that this program module assignment problem can be solved efficiently by making use of the well-known Ford–Fulkerson algorithm for finding maximum flows in commodity networks as modified by Edmonds and Karp, Dinic, and Karzanov. A solution to the two-processor problem is given, and extensions to three and n-processors are considered with partial results given without a complete efficient solution.