Results 1 
4 of
4
A new approach to the maximum flow problem
 JOURNAL OF THE ACM
, 1988
"... All previously known efficient maximumflow algorithms work by finding augmenting paths, either one path at a time (as in the original Ford and Fulkerson algorithm) or all shortestlength augmenting paths at once (using the layered network approach of Dinic). An alternative method based on the pre ..."
Abstract

Cited by 676 (34 self)
 Add to MetaCart
(Show Context)
All previously known efficient maximumflow algorithms work by finding augmenting paths, either one path at a time (as in the original Ford and Fulkerson algorithm) or all shortestlength augmenting paths at once (using the layered network approach of Dinic). An alternative method based on the preflow concept of Karzanov is introduced. A preflow is like a flow, except that the total amount flowing into a vertex is allowed to exceed the total amount flowing out. The method maintains a preflow in the original network and pushes local flow excess toward the sink along what are estimated to be shortest paths. The algorithm and its analysis are simple and intuitive, yet the algorithm runs as fast as any other known method on dense. graphs, achieving an O(n³) time bound on an nvertex graph. By incorporating the dynamic tree data structure of Sleator and Tarjan, we obtain a version of the algorithm running in O(nm log(n²/m)) time on an nvertex, medge graph. This is as fast as any known method for any graph density and faster on graphs of moderate density. The algorithm also admits efticient distributed and parallel implementations. A parallel implementation running in O(n²log n) time using n processors and O(m) space is obtained. This time bound matches that of the ShiloachVishkin algorithm, which also uses n processors but requires O(n²) space.
New DistanceDirected Algorithms for Maximum Flow and Parametric Maximum Flow Problems
, 1987
"... ..."
Max flows in O(nm) time, or better
, 2012
"... In this paper, we present improved polynomial time algorithms for the max flow problem defined on a network with n nodes and m arcs. We show how to solve the max flow problem in O(nm) time, improving upon the best previous algorithm due to King, Rao, and Tarjan, who solved the max flow problem in O( ..."
Abstract

Cited by 7 (0 self)
 Add to MetaCart
In this paper, we present improved polynomial time algorithms for the max flow problem defined on a network with n nodes and m arcs. We show how to solve the max flow problem in O(nm) time, improving upon the best previous algorithm due to King, Rao, and Tarjan, who solved the max flow problem in O(nm log m/(n log n) n) time. In the case that m = O(n), we improve the running time to O(n 2 / log n). We further improve the running time in the case that U ∗ = Umax/Umin is not too large, where Umax denotes the largest finite capacity and Umin denotes the smallest nonzero capacity. If log(U ∗ ) = O(n 1/3 log −3 n), we show how to solve the max flow problem in O(nm / log n) steps. In the case that log(U ∗ ) = O(log k n) for some fixed positive integer k, we show how to solve the max flow problem in Õ(n8/3) time. This latter algorithm relies on a subroutine for fast matrix multiplication. 1
A NEW KARZANOVTYPE o(n3) MAXFLOW ALGORITHM
, 1991
"... AbstractA new algorithm is presented for finding maximal and maximum value flows in directed single commodity networks. The algorithm gradually converts a combination of blocking preflows and backflows to a maximal flow in the network. Unlike other maximal flow algorithms, the algorithm treats the ..."
Abstract
 Add to MetaCart
AbstractA new algorithm is presented for finding maximal and maximum value flows in directed single commodity networks. The algorithm gradually converts a combination of blocking preflows and backflows to a maximal flow in the network. Unlike other maximal flow algorithms, the algorithm treats the network more symmetrically by attempting to increase flow on both the ForwardStep and the BackwardStep. The algorithm belongs to the so called phase algorithms, and is applied to Dinictype layered networks. With an effort of at most 0(n3) for maximum value flow, the algorithm ties with the fastest maximum flow algorithms in dense networks, where m % n*, and can therefore be seen as a significant alternate technique. The algorithm is based on the Karsanov [l] algorithm, and shares features with the algorithm of Tarjan [2], The first version of this algorithm was presented by the author in [3].