max_flow - maximum flow between two nodes

Calling Sequence

[v,phi,flag] = max_flow(i,j,g)

Parameters

• i : integer, number of start node
• j : integer, number of end node
• g : graph list
• v : value of the maximum flow it is exists
• phi : row vector of the value of the flow on the arcs
• flag : feasible problem flag (0 or 1)

Description

max_flow returns the value of maximum flow v from node number i to node number j if it exists, and the value of the flow on each arc as a row vector phi. All the computations are made with integer numbers. The graph must be directed. If the problem is not feasible, flag is equal to 0, otherwise it is equal to 1.

The bounds of the flow are given by the elements edge_min_cap and edge_max_cap of the graph list. The value of the maximum capacity must be greater than or equal to the value of the minimum capacity. If the value of edge_min_cap or edge_max_cap is not given (empty row vector []), it is assumed to be equal to 0 on each edge.

Examples

ta=[1 1 2 2 3 3 4 4 5 5 5 5 6 6 6 7 7 15 15 15 15 15 15];
ta=[ta, 15 8 9 10 11 12 13 14];
he=[10 13 9 14 8 11 9 11 8 10 12 13 8 9 12 8 11 1 2 3 4];
he=[he, 5 6 7 16 16 16 16 16 16 16];
n=16;
g=make_graph('foo',1,n,ta,he);
g('node_x')=[42 615 231 505 145 312 403 233 506 34 400 312 142 614 260 257];
g('node_y')=[143 145 154 154 147 152 157 270 273 279 269 273 273 274 50 376];
ma=edge_number(g);
g('edge_max_cap')=ones(1,ma);
g('edge_min_cap')=zeros(1,ma);
source=15; sink=16;
nodetype=0*ones(1,n); nodetype(source)=2; nodetype(sink)=1;
g('node_type')=nodetype;
nodecolor=0*ones(1,n); nodecolor(source)=11; nodecolor(sink)=11;
g('node_color')=nodecolor;
show_graph(g);
[v,phi,ierr]=max_flow(source,sink,g);
ii=find(phi<>0); edgecolor=phi; edgecolor(ii)=11*ones(ii);
g('edge_color')=edgecolor;
edgefontsize=8*ones(1,ma); edgefontsize(ii)=18*ones(ii);
g('edge_font_size')=edgefontsize;
g('edge_label')=string(phi);
show_graph(g);