An Efficient Algorithm for Solving Minimum Cost Flow Problem with Complementarity Slack Conditions

Algorithm 1

	Initialization: initialize node potential . Let , be an initial optimal solution with a flow valued 0. Label source node . Set .
	While or cannot be found
	While
	For
	End
	If then
	End
	If then
	For
	If and
	Label node with a label , where ,.
	End
	If and then
	Label node with a label , where .
	End
	End
	End
	End
	End