# A new approach to the maximum flow problem

@inproceedings{Goldberg1986ANA,
title={A new approach to the maximum flow problem},
author={Andrew V. Goldberg and Robert Endre Tarjan},
booktitle={Symposium on the Theory of Computing},
year={1986}
}
• Published in
Symposium on the Theory of…
1 November 1986
• Computer Science
All previously known efftcient maximum-flow algorithms work by finding augmenting paths, either one path at a time (as in the original Ford and Fulkerson algorithm) or all shortest-length 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…
1,644 Citations

## Tables from this paper

• Computer Science
JACM
• 1988
An alternative method based on the preflow concept of Karzanov, which runs as fast as any other known method on dense graphs, achieving an O(n) time bound on an n-vertex graph and faster on graphs of moderate density.
• Computer Science
• 2020
The algorithm for Edmonds-Karp is a modified version of the algorithm for Ford-Fulkerson, a highly polynomial time algorithm that uses BFS to find augmenting paths.
• Computer Science
• 1991
This article develops two distance-directed augmenting path algorithms for the maximum flow problem and improves the complexity of these algorithms to O(nm log U), where U denotes the largest arc capacity.
• Computer Science
Networks
• 2017
This article adopts a technique to construct a strongly polynomial time algorithm for solving the minimum cost flow problem and runs in O ( n m 2 ( log n ) 2 ) time, where n and m are the numbers of nodes and arcs, respectively.
• Computer Science
Algorithmica
• 2005
The ideas from [10] to show that the faster bounds hold even when the capacity changes are not “in order,” provided the authors only need the minimum cuts are applied; if the flows are required then the times are respectively O(n3+km) and O( n2√m).
• Computer Science
SIAM J. Comput.
• 1989
Possible improvements to the Ahuja-Orlin algorithm are explored and it is shown that the use of dynamic trees in the latter algorithm reduces the running time to $O(nm\log (({n / m})(\log U)^{{1 / 2}} + 2))$.
• Computer Science
JEAL
• 2005
This paper implements the 2-approximation algorithm of Dinitz et al.
• Computer Science
• 1988
This paper proposes new scaling algorithms for the assignment and minimum cycle mean problems and shows that by using ideas of the assignment algorithm in an approximate binary search procedure, the minimum mean cycle problem can also be solved in O(J-nm log nC) time.
A faster push-relabel algorithm for the maximum flow problem on bounded-degree networks with n vertices and m arcs is presented and an algorithm incorporating some or all of the techniques may be a promising avenue towards an O(mn)-time algorithm for all edge densities.

## References

SHOWING 1-10 OF 45 REFERENCES

• Computer Science
JACM
• 1988
An alternative method based on the preflow concept of Karzanov, which runs as fast as any other known method on dense graphs, achieving an O(n) time bound on an n-vertex graph and faster on graphs of moderate density.
This thesis presents a new algorithm for the maximum network flow problem that finds a maximum flow in O(nmlog n) time, which is a factor of log n faster than the previous fastest algorithm.
This thesis proves lower bounds on the parallel complexity of the maximal independent set problem and the problem of 2-coloring a rooted tree, and introduces a frame work that allows the generalization of the maximum flow techniques to the minimum-cost flow problem.
• H. Gabow
• Computer Science
24th Annual Symposium on Foundations of Computer Science (sfcs 1983)
• 1983
This work presents efficient algorithms for network problems that work by scaling the numeric parameters, and gives simple algorithms that match the best time bounds for shortest paths on a directed graph with nonnegative lengths and maximum value network flow.
A new algorithm to find a maximum flow in a flow-network which has n vertices and m edges in time of O($n\cdot I \log^2 I$), where I = M+n is the input size (up to a constant factor) and this result improves the previous upper bound of Z.
• Computer Science
TOPL
• 1983
A distributed algorithm is presented that constructs the minimum weight spanning tree in a connected undirected graph with distinct edge weights that can be initiated spontaneously at any node or at any subset of nodes.
• Computer Science
JACM
• 1985
The splay tree, a self-adjusting form of binary search tree, is developed and analyzed and is found to be as efficient as balanced trees when total running time is the measure of interest.