Dynamic Multicommodity Contraflow Problem with Asymmetric Transit Times

Algorithm 2

An FPTAS algorithm for maximum DMCCF with asymmetric transit times on arcs.

Input: Given dynamic multicommodity flow network

 1. The auxiliary network is transformed to -condensed auxiliary network with

 2. Compute the MSMCF on the auxiliary network .

 3. Decompose along the paths and cycles, remove cycle flows and update .

 4. Reverse up to the capacity iff , replaced by whenever where and .

 5. For each , if is reversed, and . If neither nor is reversed, , where is the saved capacity of .

Output: The maximum DMCCF