Lexicographically Maximum Contraflow Problem with Vertex Capacities

Algorithm 3

LexMDCF algorithm for multinetwork.

(1)	Given a dynamic multinetwork , with , for all and integer inputs.
(2)	Transform into undirected multinetwork as in Algorithm 2 and set .
(3)	Label each parallel arcs as such that for ; .
(4)	Compute LexMDF on network using algorithm in [14].
(5)	Perform flow decomposition into path and cycle flows of maximum flows obtained from step 4 and remove all cycle flows.
(6)	Arc is reversed if and only if the flow along arc is greater than or if there is non-negative flow along arc .
(7)	Obtain LexMDCF solution for multinetwork .