Max flow problem and push relabel algorithem
Transcript of Max flow problem and push relabel algorithem
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Maximum FlowPush relabel algorithm By Waqas Shehzad Fast NU Pakistan
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Push-RelabelPush-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.
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Preflow-Basics• Preflow algorithm allow temporary imbalance
(excess) at nodes, and work towards feasibility.• push-relabel algorithms work on one vertex at a
time, looking only at the vertex’s neighbors.• “pushing” preflow and “relabeling” a vertex
relabeling• Formally, a preflow is a function ƒ: V×V → R that
satisfies capacity constraints and
• In preflow algorithm a graph is consider to have two special nodes Source and Sink
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Cont..
PPreflow :
A labeling h : V Z+ is compatible with a preflow if
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Code for Preflow-Push
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Run time• Generic Preflow-Push algorithm runs in worst-case
time 0 ).• The total number of saturating push operations is
at most m.• The total number of nonsaturating push
operations is at most 2nm.• The total number of relabeling operations is less
than 2.• This running time is farther improved with
Highest-label rule, Excess scaling,
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References
• 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