A new approach to the maximum-flow problem
Journal of the ACM (JACM)
An efficient algorithm for the minimum capacity cut problem
Mathematical Programming: Series A and B
Network flows: theory, algorithms, and applications
Network flows: theory, algorithms, and applications
A faster algorithm for finding the minimum cut in a directed graph
SODA selected papers from the third annual ACM-SIAM symposium on Discrete algorithms
The Steiner tree problem I: formulations, compositions and extension of facets
Mathematical Programming: Series A and B
Separation of partition inequalities for the (1,2)-survivable network design problem
Operations Research Letters
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The minimal Steiner tree problem is a classical NP-complete problem that has several applications in the communication and transportation sectors. It has recently emerged as a subproblem in decomposition techniques such as column generation and Lagrangian schemes. This has set new computational challenges to the state of the art solving approaches. Our goal is to improve on existing branch-and-cut algorithms so that our approach successfully serves as a fast subproblem solver in a decomposition context. Compared with existing literature, our technical contributions include 1) a new preflow-push cutting strategy, revisiting a little known graph algorithm, that halves the runtime of the separation step, and 2) a branching scheme that fairly balances the search tree and speeds up the search. An evaluation in a multicast design application shows that the algorithm enhances a column generation hybrid. Moreover, our approach offers a significant speedup factor on a publicly available set of challenging Steiner tree benchmarks.