Approximating the generalized terminal backup problem via half-integral multiflow relaxation

TL;DR

This paper introduces a 4/3-approximation algorithm for the generalized terminal backup problem with both edge- and node-connectivity constraints, based on a novel half-integral LP relaxation and multiflow formulation.

Contribution

It develops a strongly polynomial-time approximation algorithm for a complex network design problem using half-integral LP relaxation and multiflow techniques.

Findings

The LP relaxation is half-integral.

The half-integral solution can be rounded to a 4/3-approximate solution.

The LP relaxation with edge-connectivity constraints is equivalent to a multiflow problem.

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.