Successive shortest paths with reduced costs

Abstract view

Invariant:

1. All points of the invariant of the successive shortest paths algorithm.
2. For each node [math]\displaystyle{ v\in V }[/math], there is a real number [math]\displaystyle{ \pi(v) }[/math] such that, for each arc [math]\displaystyle{ a=(v,w)\in A }[/math], the reduced cost [math]\displaystyle{ c(a)-\pi(v)+\pi(w) }[/math] is nonnegative.