Dynamic Multicommodity Contraflow Problem with Asymmetric Transit Times

Algorithm 1

Algorithm for maximum DMCCF.

Input: Given dynamic multicommodity flow network

 1. A given dynamic network is transformed into time-expanded network by

 2. An auxiliary network is constructed with

 3. Compute the MSMCF on the auxiliary network .

 4. Decompose along the paths and cycles and remove cycle flows and update .

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

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

Output: The Maximum DMCCF