Approximating the generalized terminal backup problem via half-integral multiflow relaxation
Abstract
We consider a network design problem called the generalized terminal backup problem. Whereas earlier work investigated the edge-connectivity constraints only, we consider both edge- and node-connectivity constraints for this problem. A major contribution of this paper is the development of a strongly polynomial-time 4/3-approximation algorithm for the problem. Specifically, we show that a linear programming relaxation of the problem is half-integral, and that the half-integral optimal solution can be rounded to a 4/3-approximate solution. We also prove that the linear programming relaxation of the problem with the edge-connectivity constraints is equivalent to minimizing the cost of half-integral multiflows that satisfy flow demands given from terminals. This observation presents a strongly polynomial-time algorithm for computing a minimum cost half-integral multiflow under flow demand constraints.
Cite
@article{arxiv.1409.5561,
title = {Approximating the generalized terminal backup problem via half-integral multiflow relaxation},
author = {Takuro Fukunaga},
journal= {arXiv preprint arXiv:1409.5561},
year = {2015}
}