libraryGraph_minCostFlow (ingressNode , egressNode , flowRate , linkTable , costVector , capacityVector)

%%% libraryGraph_minCostFlow
%
% Usage: [exitFlag , flowRoutingVector , cost] = libraryGraph_minCostFlow
% (ingressNode , egressNode , flowRate , linkTable , costVector , capacityVector)
%
% Abstract: This function solves the Minimum Cost Flow Problem. This
% problem consist of finding the traffic flow routing between two nodes
% (ingress node and egress node) with the minimum cost. It is allowed
% bifurcations. To solve the Min Cost Flow, we use the function
% 'libraryFR_optimalFlowAssignment', that model the problem of assign
% optimally flows using a Linear Programming (LP) formulation. The problem
% is solved with the linprog solver from MATLAB.
% The function provides the solution which minimizes a given cost function. 
% The cost function employed is the sum of the costs in each link. 
% The cost in each link is give by the product of the Gbps 
% carried and cost per Gbps in the link.
%
% Arguments:
% o	In: 
%    ingressNode: Origin Node of the flow.
%
%   . egressNode: Destination Node of the flow.
%
%    flowRate: Traffic flow offered between the ingress node and egress
%     node
%
%   . linkTable(M,2): M-by-2 integer matrix. Each row is a link in the graph. 
%     first column is the ingress node (1...N), second the egress node
%    ( 1...N)
%
%   . capacityVector(M,1): Capacity in Gbps of each link. This is the
%     maximum traffic that the link can carry.
%
%   . costVector(M,1): Cost of carrying 1 Gbps in each link. If the
%     vector is constant, the average number of hops is minimized. If the
%     vector contains a measure of link distance, the average distance
%     traversed by the carried traffic is minimized
%
% o	Out:
%  . exitFlag: 
%           0, if the solution to the Minimun Cost Flow is feasible.
%           1, if the solution to the Minimun Cost Flow is not feasible.
%
%  . flowRoutingVector (1,L): 1-by-L integer matrix where  L is the number
%    of links. An element (l) means the Gbps belonging to flow that
%    traverse link l
%
%   cost: value of the cost function at optimum  

function [exitFlag , flowRoutingVector , cost] = libraryGraph_minCostFlow (ingressNode , egressNode , flowRate , linkTable , costVector , capacityVector)

NUMBERNODES = max(linkTable(:,1:2));
NUMBERNODES = max ([NUMBERNODES ingressNode egressNode]);
traff_trafficMatrix = zeros (NUMBERNODES,NUMBERNODES);

traff_trafficMatrix (ingressNode , egressNode) = flowRate;
    
[exitFlagFA flowTable flowRoutingVector cost] = libraryFR_optimalFlowAssignment(traff_trafficMatrix, linkTable , capacityVector , costVector);
    
if (size (flowTable,1) ~= 1)
    exitFlag =  1;
    return;
end

if (exitFlagFA ~= 0)
    exitFlag = 1;
else
    exitFlag = 0;
end