What is a maximum ST flow?

The maximum value of an s-t flow (i.e., flow from source s to sink t) is equal to the minimum capacity of an s-t cut (i.e., cut severing s from t) in the network, as stated in the max-flow min-cut theorem.

What is a bottleneck path?

The bottleneck path problem is a graph optimization problem finding a path between two vertices with the maximum flow, in which the flow of a path is defined as the minimum capacity of edges on that path.

What is the capacity of the ST cut?

The minimum capacity of an s-t cut is 250 and the sum of the revenue of each project is 450; therefore the maximum profit g is 450 − 250 = 200, by selecting projects p2 and p3.

What is an st flow?

In a flow network, an s-t cut is a cut that requires the source ‘s’ and the sink ‘t’ to be in different subsets, and it consists of edges going from the source’s side to the sink’s side. The capacity of an s-t cut is defined by the sum of the capacity of each edge in the cut-set. ( Source: Wiki)

What is a bottleneck in a graph?

In mathematics, a minimum bottleneck spanning tree (MBST) in an undirected graph is a spanning tree in which the most expensive edge is as cheap as possible. A bottleneck edge is the highest weighted edge in a spanning tree.

What is maximum spanning tree?

A maximum spanning tree is a spanning tree with weight greater than or equal to the weight of every other spanning tree. Such a tree can be found with algorithms such as Prim’s or Kruskal’s after multiplying the edge weights by -1 and solving the MST problem on the new graph.

What is a Minimax path?

Undirected graphs In an undirected graph, a widest path may be found as the path between the two vertices in the maximum spanning tree of the graph, and a minimax path may be found as the path between the two vertices in the minimum spanning tree.

What is maximum flow graph?

A flow in a graph is a function and it satisfies a capacity constraint: for each edge . Net flow in the edges follows skew-symmetric property: . A maximum flow is defined as the maximum amount of flow that the graph or network would allow to flow from the source node to its sink node.

Is every minimum bottleneck tree a minimum spanning tree?

3.2. Hence, not all the minimum bottleneck spanning trees are minimum spanning trees. An MST is always an MBST. By the definition of an MBST, the bottleneck edge should belong to an MST.