max_cap_path - maximum capacity path

Calling Sequence

[p,cap] = max_cap_path(i,j,g)

Parameters

• i,j : integers, node numbers
• g : graph list
• p : row vector of integer numbers of the arcs of the path if it exists
• cap : value of the capacity of the path

Description

max_cap_path returns the path with maximum capacity from node i to node j for the graph g if it exists and returns the empty vector [] otherwise.

The capacities of the edges are given by the element edge_max_cap of the graph list. If its value is not given (empty vector []), max_cap_path returns the empty vector []. The capacities must be strictly positive, i.e negative capacities are considered as equal to 0 (no capacity at all).

Examples

ta=[1 1 2 2 2 3 4 5 5 7 8 8 9 10 10 10 11 12 13 13 13 14 15 16 16 17 17];
he=[2 10 3 5 7 4 2 4 6 8 6 9 7 7 11 15 12 13 9 10 14 11 16 1 17 14 15];
g=make_graph('foo',1,17,ta,he);
g('node_x')=[283 163 63 57 164 164 273 271 339 384 504 513 439 623 631 757 642];
g('node_y')=[59 133 223 318 227 319 221 324 432 141 209 319 428 443 187 151 301];
show_graph(g);
ma=edge_number(g);
g('edge_max_cap')=int(rand(1,ma)*16)+5;
[p,cap]=max_cap_path(1,14,g);
edgecolor=1*ones(1,ma); edgecolor(p)=11*ones(p); g('edge_color')=edgecolor;
x_message(['The maximum capacity is: '+string(cap);
           'Showing the corresponding path']);
show_graph(g); show_arcs(p);