The document summarizes the push-relabel algorithm for solving maximum flow problems. It states that the push-relabel algorithm was described by Andrew Goldberg and Robert Tarjan and leads to better running times than previous network flow algorithms. It works by exploiting the fact that multiple augmentations may partially share paths. The push-relabel algorithm is considered the fastest maximum flow algorithm and is not difficult to code.

1. By Waqas Shehzad
Fast NU Pakistan

2. Push-relabel algorithm is described by Dr. Andrew
Goldberg and Robert E.Tarjan.
Leads to better running times, both in theory and
practice.
 All previous Network Flow related algorithms are related
to augmentation.
 A draw back of aug-based schemes: each augmentation
takes O(n) time. Multiple augmentations may partially
share paths, but it’s not exploited by algorithms.
Not very hard to code.
Push relabel is consider as the Fastest maximum-flow
algorithm.

3. •

4. PPreflow :
A labeling h : V  Z+ is compatible with a preflow if

11. •

12. • Lecturer: Julian Mestre Optimization II Lecture 3
• Andrew V. Goldberg and Robert E. Tarjan, A new
approach to the maximum-flow problem.
• Thomas H. Cormen, Charles E. Leiserson, Ronald L.
Rivest. Introduction to Algorithms.
• Algorithm Tutorial: MaximumFlow
• Algorithm Tutorial: Introduction to graphs and their data
structures
• http://iss.ices.utexas.edu/?p=projects/galois/benchmarks/
preflow_push