On the edge capacitated Steiner tree problem

Cédric Bentz, Marie-Christine Costa and Alain Hertz
submitted
Publication type:
Paper in peer-reviewed journals
arXiv:
images/icons/icon_arxiv.png 1607.07082
Keywords :
Mixed-integer programming, bilevel programming, survivable networks
Abstract:
We are interested in the design of survivable capacitated rooted Steiner networks. Given a graph G=(V,E), capacity and cost functions on E, a root r, a subset T of V of terminals and an integer k, we search for a minimum cost subset E' of E$, covering T and r, such that the network induced by E' is k-survivable: after the removal of any k edges, there still exists a feasible flow from r to T. We also consider the possibility of protecting a given number of edges. We propose three different formulations: a cut-set, a flow and a bi-level formulation where the second-level is a min-max problem (with an attacker and a defender). We propose algorithms for each problem formulation and compare their efficiency.
BibTeX:
@article{Ben-Cos-Her-2200,
    author={Cédric Bentz and Marie-Christine Costa and Alain Hertz },
    title={On the edge capacitated Steiner tree problem },
    year={submitted },
    pages={1--31},
}