Primal-dual algorithms for computing weight-constrained shortest paths and weight-constrained minimum spanning trees

In the QoS shortest path problem, we want to find a path connecting two given vertices u and v to minimize path cost subject to the constraint that the path weight is no greater than a given bound. In the QoS minimum spanning tree problem, we want to find a spanning tree to minimize tree cost subject to the constraint that the tree weight is no greater than a given bound. Both problems are NP-hard and have important applications in computer and communication networks. We present simple but effective primal-dual algorithms for computing approximate solutions for both problems. Computational results show that our algorithm find optimal solutions in more than 80% of the cases and find close to optimal solutions in all other cases, while using much less time.