Parameters

Description

min_qcost_flow computes the minimum quadratic cost flow in the network g. It returns the total cost of the flows on the arcs c and the row vector of the flows on the arcs phi. eps is the precision of the iterative algorithm. If the problem is not feasible (impossible to find a compatible flow for instance), flag is equal to 0, otherwise it is equal to 1.

The bounds of the flow are given by themin_cap and max_cap fielgs of the graph edges_data_structure. The value of the maximum capacity must be greater than or equal to the value of the minimum capacity. If the value of min_cap or max_cap is not given , it is assumed to be equal to 0 on each edge.

The costs on the edges are given by the elements q_orig and q_weight of the graph edges_data_structure. The cost on arc u is given by:

(1/2)*q_weight[u](phi[u]-q_orig[u])^2

The costs must be non negative. If the value of q_orig or q_weight is not given, it is assumed to be equal to 0 on each edge.

This function uses an algorithm due to M. Minoux.

Examples

ta=[1 1 2 2 2 3 4 4 5 6 6 6 7 7 7 8 9 10 12 12 13 13 13 14 15 14 9 11 10 1 8];
he=[2 6 3 4 5 1 3 5 1 7 10 11 5 8 9 5 8 11 10 11 9 11 15 13 14 4 6 9 1 12 14];
g=make_graph('foo',1,15,ta,he);
g.nodes.graphics.x=[155,153,85,155,237,244,244,334,338,346,442,440,439,333,438];
g.nodes.graphics.y=[45,177,253,254,253,114,171,257,174,101,172,64,264,350,351];
show_graph(g);

ma=edge_number(g)
g=add_edge_data(g,'min_cap',[0,1,5,5,0,3,3,5,4,1,4,3,3,1,3,1,1,4,1,3,1,4,5,4,4,2,1,4,2,3,2]);
g=add_edge_data(g,'max_cap',[38,37,42,41,34,49,35,36,43,43,43,48,37,..
                                 36,42,48,44,36,30,31,30,41,32,42,34,48,32,36,36,36,30]);
g=add_edge_data(g,'q_weight',ones(1,ma));
[c,phi,flag]=min_qcost_flow(0.001,g);flag

g.edges.graphics.foreground(find(phi<>0))=color('red');
g=add_edge_data(g,'flow',phi)
g.edges.graphics.display='flow';
show_graph(g);


 
  

See Also