# Experimental Evaluation of Parametric Max-Flow Algorithms

@inproceedings{Babenko2007ExperimentalEO, title={Experimental Evaluation of Parametric Max-Flow Algorithms}, author={Maxim A. Babenko and Jonathan Derryberry and Andrew V. Goldberg and Robert Endre Tarjan and Yunhong Zhou}, booktitle={Workshop on Engineering Applications}, year={2007} }

The parametric maximum flow problem is an extension of the classical maximum flow problem in which the capacities of certain arcs are not fixed but are functions of a single parameter. Gallo et al. [6] showed that certain versions of the push-relabel algorithm for ordinary maximum flow can be extended to the parametric problem while only increasing the worst-case time bound by a constant factor. Recently Zhang et al. [14,13] proposed a novel, simple balancing algorithm for the parametric…

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## References

SHOWING 1-10 OF 16 REFERENCES

### Balancing Applied to Maximum Network Flow Problems

- Computer Science, MathematicsESA
- 2006

It is shown that a standard monotonic parametric maximum flow problem can be formulated as a problem of computing a particular maximum flow that is balanced in an appropriate sense, and a divide-and-conquer algorithm is presented to compute such a balanced flow in a logarithmic number of ordinary maximum-flow computations.

### A Fast Parametric Maximum Flow Algorithm and Applications

- Mathematics, Computer ScienceSIAM J. Comput.
- 1989

It is shown that the recent maximum flow algorithm of Goldberg and Tarjan can be extended to solve an important class of such parametric maximum flow problems, at the cost of only a constant factor in its worst-case time bound.

### A new approach to the maximum flow problem

- Computer ScienceSTOC '86
- 1986

By incorporating the dynamic tree data structure of Sleator and Tarjan, a version of the algorithm running in O(nm log(n'/m)) time on an n-vertex, m-edge graph is obtained, as fast as any known method for any graph density and faster on graphs of moderate density.

### The Pseudoflow Algorithm and the Pseudoflow-Based Simplex for the Maximum Flow Problem

- Computer ScienceIPCO
- 1998

This is the first known simplex algorithm for maximum flow that generates all possible breakpoints of parameter values in the same complexity as required to solve a single maximum flow instance and the fastest one.

### Beyond the flow decomposition barrier

- MathematicsProceedings 38th Annual Symposium on Foundations of Computer Science
- 1997

Borders are improved for the Gomory-Hu tree problem, the parametric flow problem, and the approximate s-t cut problem by introducing a new approach to the maximum flow problem.

### Simultaneous Parametric Maximum Flow Algorithm with Vertex Balancing

- Computer Science
- 2005

SPMF replaces the path-wise flow augmentation by flow-redistribution at each node, which provides a factor of ten speed-up for all the large datasets tested, and the new algorithms are monotone convergent.

### On Implementing the Push—Relabel Method for the Maximum Flow Problem

- Computer ScienceAlgorithmica
- 1997

Efficient implementations of the push—relabel method for the maximum flow problem are studied, showing that the highest-level selection strategy gives better results when combined with both global and gap relabeling heuristics.

### Algorithms - ESA 2006, 14th Annual European Symposium, Zurich, Switzerland, September 11-13, 2006, Proceedings

- Computer ScienceESA
- 2006

Invited Lectures.- Origami, Linkages, and Polyhedra: Folding with Algorithms.- Reliable and Efficient Geometric Computing.- Some Computational Challenges in Today's Bio-medicine.- Contributed Papers:…

### On Implementing Push-Relabel Method for the Maximum Flow Problem

- Computer ScienceIPCO
- 1995

The resulting codes are faster than the previous codes, and much faster on some problem families, due to the combination of heuristics used in the implementation of the push-relabel method.

### Improved Algorithms for Bipartite Network Flow

- Mathematics, Computer ScienceSIAM J. Comput.
- 1994

It is shown that several maximum flow algorithms can be substantially sped up when applied to unbalanced networks, and ideas are extended to dynamic tree implementations, parametric maximum flows, and minimum-cost flows.