Preflow-push with excess scaling: Difference between revisions
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# All steps in the [[Preflow-push#Induction basis|induction basis]] of the [[Preflow-push|preflow push algorithm]]. | # All steps in the [[Preflow-push#Induction basis|induction basis]] of the [[Preflow-push|preflow push algorithm]]. | ||
# Set <math>\Delta</math> | # Set <math>\Delta:=2^L</math>, where <math>L:=<math>\lceil\log_2U\rceil</math> and <math>U:=\max\{u(a)|a\in A\}</math>. | ||
Revision as of 13:40, 29 October 2014
Abstract view
Algorithmic problem: max-flow problem (standard version)
Type of algorithm: loop.
Invariant: Before and after each iteration:
- The current flow is feasible.
- There is a nonnegative, integral value [math]\displaystyle{ \Delta }[/math].
- The excess of no node exceeds [math]\displaystyle{ \Delta }[/math].
Variant: [math]\displaystyle{ \Delta }[/math] is divided by two (integral division).
Break condition: [math]\displaystyle{ \Delta=0 }[/math].
Induction basis
- All steps in the induction basis of the preflow push algorithm.
- Set [math]\displaystyle{ \Delta:=2^L }[/math], where [math]\displaystyle{ L:=\lt math\gt \lceil\log_2U\rceil }[/math] and [math]\displaystyle{ U:=\max\{u(a)|a\in A\} }[/math].