In the network, the material flow which meets constraints below is called a feasible flow.

If there is a feasible flow [f.sub.ij] that meets the conditions [f.sub.ij[ < [c.sub.ij], the chain is an augmented chain of feasible flow [f.sub.ij].

Each time a feasible flow with minimum cost is found, we assume that there are numerous virtual routes.

Give an initial feasible flow [f.sub.0], which can be zero.

The necessary and sufficient condition of judging whether a quasi-blocking-cut is a real blocking cut is as follows [21]: for any feasible flow in the network, if entrance arcs from the feasible flow and positive arcs in the quasi-blocking-cut all are saturated arcs, this quasi-blocking-cut is a real blocking cut, and the blocking cut is obtained by the feasible flow which is defined between positive arcs and opposite arcs located on network flow.

In the directed shortest path tree, the node connected with positive arc just is the least common ancestor of the directed shortest path tree and the node connected with opposite arc just is the leaf node of the directed shortest path tree, and the feasible flow hugging coverage hole is equivalent to the shortest path between the node connected with positive arc and the node connected with opposite arc, as shown in Figure 1.

Al Bayati said in a statement today "we praise the high performance and morals that we sensed in the field from these systems that worked for three consecutive days and for long hours under the high temperature on security a safe and

feasible flow of visitors to the Holy city of Kadhimiya."

The system optimum

feasible flow in a network is a special case of the following non-linear program (denoted by SO, see [10])

Definition 3 (Feasible flow) Let G = (V, E, o) be a digraph with capacities u and l.

We remark that c is well-directed iff there is an [epsilon] > 0 such that [epsilon]c is a feasible flow.

Conversely, if c is a well-directed cycle on [RES.sup.b](f) with [delta]([gamma](c)) > 0, then [epsilon]c is a feasible flow on [RES.sup.b](f) for sufficiently small [epsilon] > 0.

The set of feasible directions in which to increase can be interpreted as the convex cone of feasible flows of an auxiliary network [RES.sup.b](f).