I. Linear programming problems and their representations
For example:
Two. Maximum network flow problem
(1) Network
G is a simple forward graph, g= (v,e), v={1,2,...,n}. Specify a vertex s in V, called a source and another vertex T, called a sink. There is a ∈e of each edge (v,w) of the graph G, which should have a value cap (v,w) ≥0, called the capacity of the edge. This is referred to as a network of graph G.
(2) Network flow
A stream on a network is a nonnegative function Flow={flow (V,W)} that is defined on the edge set E of the network, and the Flow (V,W) is on the Edge (V,W).
(3) Ford-fulkerson algorithm
Ford_fulkerson (G, S, t) {for each
edge (U, v) ∈g.e
(U, v.). F = 0 while
GF exists an augmented path of S to T p{
CF (p) = MIN{CF (U, v ): (U, v) is in P}
for each edge (U, v) in p{
if (U, v) ∈e {
(U, v). F = = CF (p)
} else {
(V, u). F = CF (P)}}}}
(4) Edmonds-karp algorithm
To find an augmented path, you can use the EDMONDS-KARP algorithm to select the shortest path from S to T, where each edge has a weight of 1. That is, the range first traversal (BFS) with S as the starting point, the arrival of T is terminated.
