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- ...</math>-path in <math>G</math> with respect to <math>\ell</math> among all paths that have at most <math>|V|</math> arcs. # The last arc (pointing to <math>w</math>) of one of these paths.1 KB (259 words) - 12:56, 22 October 2014
- == Negative cost factors == The case that some arcs have negative cost factors, may be transformed as follows into the above version, in whic2 KB (348 words) - 14:31, 1 December 2014
- File:V12 negative Kostenfaktoren Beispiel.jpg|negative Kostenfaktoren Beispiel File:V12 negative Kostenfaktoren konzeptionell.jpg|negative Kostenfaktoren konzeptionell5 KB (732 words) - 09:07, 13 February 2016
- # The '''length''' of an [[Basic graph definitions#Paths|ordinary path]] (incl. [[Basic graph definitions#Cycles|ordinary cycles]]) ...ons#Cycles|generalized cycles]]) is either defined identically to ordinary paths or, alternatively, the lengths of the backward arcs are not added but subtr11 KB (2,059 words) - 14:34, 5 December 2014
- ...''' There is no more [[Basics of shortest paths#Path lengths and distances|negative cycle]] in the residual network. # If all arcs <math>(s,v)</math> are [[Basic flow definitions#Flow-augmenting paths and saturated arcs|saturated]], return the restriction of this flow to the7 KB (1,256 words) - 15:18, 5 February 2015
- ...ts of the invariant of the [[Successive shortest paths|successive shortest paths]] algorithm. ...ep|induction step]] of the [[Successive shortest paths|successive shortest paths algorithm]]. The essential modification is that <math>c</math> is replaced4 KB (757 words) - 14:39, 20 February 2015
- # There is no negative cycle in the [[Basic flow definitions#Residual network|residual network]] ...[Dijkstra|Dijkstra's]] are not an option. However, a [[Successive shortest paths with reduced costs|variant]] of the algorithm works on a nonnegative variat6 KB (1,107 words) - 10:08, 6 May 2015
- * [[Shortest Paths Problems]] ** [[All pairs shortest paths]]4 KB (380 words) - 15:13, 30 November 2020
- ...enting paths and saturated arcs|flow-augmenting paths]] <math>(s,t)</math>-paths, always choose one with smallest number of arcs. Consequently, a [[Breadth- .../math> according to [[Ford-Fulkerson]] does not create new flow-augmenting paths of length <math>k</math> or less than <math>k</math>.4 KB (790 words) - 12:34, 1 December 2015
- [[Category:All Pairs Shortest Paths]] [[Category:Shortest Paths Problems]]10 KB (1,765 words) - 08:35, 14 January 2021
- ...d by <math>f(a)\geq\ell(a)</math>. In particular, <math>f(a)</math> may be negative if <math>\ell(a)</math> is so. == Flow-augmenting paths and saturated arcs ==11 KB (2,126 words) - 13:42, 17 November 2015