7.14
Undergraduate based.
We have to consider it recursively to find a flormula for the number of saturating and nonsaturating pushes/relabel.
Ordered by distancer label and then the lexcicographic order of the nodes label.
23 Matching Annotations
- Mar 2023
-
www.dl.behinehyab.com www.dl.behinehyab.com
-
-
Thus the maximum capacity augmenting path has residual capacity atleast (v* - v)/m. Now consider a sequence of 2m consecutive maximum capacityaugmentations starting with the flow x. If each of these augmentations augments atleast (v* - v)/2m units of flow, then within 2m or fewer iterations we will establisha maximum flow.
Why is this \(2m\) what the fuck dude.
Ok, check: here for more information.
-
This argument shows that within 2m consecutive iterations, thealgorithm either establishes a maximum flow or reduces the residual capacity of themaximum capacity augmenting path by a factor of at least 2.
This is an unstated claim where, the proof comes before this paragraph.
-
this result would imply that the al-gorithm could saturate any arc at most k/2 times.
2 relabeling is required to saturate one arc once.
-
7.4
Undergraduaet based.
Show the distance labels and excesses at each step. Verify you have the maximum flow by exhibiting an appropriate cut.
There is double arcs on here again what the hell.
-
7.2
Undergraduate based, algorithm.
Show your residual Δ network after each augmentation. Verify you have the maximum flow by exhibiting an appropriate cut.
Why is there a double arc for the graph 7.21(b)? Is it a lower bound for the flow on the network?
-
Lemma 7.12.
Upper bound for the distance label of the preflow push algorithm
-
Lemma 7.11.
dipath connection for all nodes in the graph.
-
active
A node is active in the preflow push algorithm when its excess is strictly positive, during the operations of the preflow push algorithm.
-
An augmentation on arc (i, j) might, however,create an additional arc (j, i) with rji > 0 and therefore also create an additionalinequality d(j) ~ d(i) + 1 that the distanceJabels must satisfy.
This is just using the inductive hypothesis. The indecutive hypothesis hold for all the neighbours of the curren node \(i\), after the delection of the arcs, the neigboring vertices decreased, therefore, valid distance label condition still holds.
-
Lemma 7.5
The shortest augmenting path matains a correct distance label for all the vertices during the iterations. By valid, we mean that there exists some way such that \(d(j) = d(i) + 1\), where \((i, j)\in A\), for all \(i\in N\).
-
Property 7.2.
-
admissible arc
\((i, j)\) is an admissible arc when \(d(j) = d(i) + 1\), whre \(d\) is the distance label from the algorithm, and \(r_{i, j} > 0\).
-
Property 7.7.
The complexity of the memeroized shortest aug path max flow.
-
7.4 SHORTEST AUGMENTING PATH ALGORITHM
Not quite Dinic, Not quite Edmonds Karp. It's something in between.
-
blocking flows
-
Theorem 7.10
-
Dinic's algorithm
The BFS for max flow with retreat.
-
Theorem 7.4
-
Property 7.1
-
Property 7.3
-
7.13
Graudate based.
-
- Feb 2023
-
Local file Local file
-
Floyd-Warshall Algorithm,
floyd warshall algorithm
-