A novel method for solving the multi-commodity flow problem on evolving networks

Abstract

The minimum cost multi-commodity flow (MMCF) problem on evolving networks is the latest challenge to solving the min-cost network flow problem of multi-commodity flowing from multi-source and multi-sink on an evolving network. Previous researches primarily focus on the solution of MMCF problem within static networks. However, researchers ignored the MMCF problem within networks where the structure dynamically changes over time. Evolving networks have a dynamically changing and unpredictable network structure. The existing methods must recalculate when the network structure changes, leading to high computational complexity. This manuscript proposes a dynamic graph computing model for adaptive dynamic path selection and optimization. First, the model selects the path with the least cost for each commodity, assuming the route can transport a specified number of such commodities to find the optimal path faster. Second, we design path selection and flow update strategies for each node in the graph to adapt to changes in the graph structure. At the same time, we can prevent multiple commodity conflicts from exceeding the marginal capacity limit. Finally, the optimal path of each commodity is dynamically pruned based on the original optical path to obtain the tree structure and determine the absolute path to meet the specified transportation quantity of each commodity. Performance analysis results show that our method can efficiently cope with the dynamic changes of the network structure, which provides ideas for solving the multi-commodity network flow problem in dynamic networks.