# 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} }

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

### A new approach to the maximum-flow problem

- Computer ScienceJACM
- 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.

### A NEW APPROACH TO MAXIMUM FLOW OF MIN CUT THEOREM BY PROPOSED ALGORITHM

- 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.

### Distance-Directed Augmenting Path Algorithms for Maximum Flow and Parametric Maximum Flow Problems

- 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.

### Cancel‐and‐tighten algorithm for quickest flow problems

- Computer ScienceNetworks
- 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.

### A faster parametric minimum-cut algorithm

- Computer ScienceAlgorithmica
- 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).

### Improved Time Bounds for the Maximum Flow Problem

- Computer ScienceSIAM 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 $O(nm\log (({n / m})(\log U)^{{1 / 2}} + 2))$.

### Implementing approximation algorithms for the single-source unsplittable flow problem

- Computer ScienceJEAL
- 2005

This paper implements the 2-approximation algorithm of Dinitz et al.

### New scaling algorithms for the assignment and minimum cycle mean problems

- 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 New Push-Relabel Algorithm for the Maximum Flow Problem

- Computer ScienceArXiv
- 2013

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

### A new approach to the maximum-flow problem

- Computer ScienceJACM
- 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.

### An 0 (nm log n) algorithm for maximum network flow

- Computer Science
- 1980

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.

### Efficient graph algorithms for sequential and parallel computers

- Computer Science
- 1987

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.

### Scaling algorithms for network problems

- Computer Science24th 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.

### An O($n\cdot I \log^2 I$) maximum-flow algorithm

- Computer Science
- 1978

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.

### A Distributed Algorithm for Minimum-Weight Spanning Trees

- Computer ScienceTOPL
- 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.

### Self-adjusting binary search trees

- Computer ScienceJACM
- 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.