The Maximum Flow Problem with flow width constraints is an NP-hard problem. Two models are proposed: the first model is a compact node-arc model using two flow conservation blocks per path. For each path, one block defines the path while the other one sends the right amount of flow on it. The second model is an extended arc-path model, obtained from the first model after a Dantzig-Wolfe reformulation. It is an extended model as it relies on the set of all the paths between the source and the sink nodes. Some symmetry breaking constraints are used to improve the model. A Branch and Price algorithm is proposed to solve the problem. The column generation procedure reduces to the computation of a shortest path whose cost depends on weights on the arcs and on the path capacity. A polynomial-time algorithm is proposed to solve this subproblem. Computational results are shown on a set of medium-sized instances to show the effectiveness of our approach.
Routing problems, which include a QoS-based path control, play a key role in broadband communication networks. We analyze here an algorithmic procedure based on branch-and-price algorithm and on the flow deviation method to solve a nonlinear k -splittable flow problem. The model can support end-to-end delay bounds on each path and we compare the behavior of the algorithm with and without these constraints. The trade-off between QoS guarantees and CPU time is clearly established and we show that minimizing the average delay on all arcs will yield solutions close to the optimal one at a significant computational saving.
Routing problems, which include a QoS-based path control, play a key role in broadband communication networks. We analyze here an algorithmic procedure based on branch-and-price algorithm and on the flow deviation method to solve a nonlinear k-splittable flow problem. The model can support end-to-end delay bounds on each path and we compare the behavior of the algorithm with and without these constraints. The trade-off between QoS guarantees and CPU time is clearly established and we show that minimizing the average delay on all arcs will yield solutions close to the optimal one at a significant computational saving.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.