Robust Metric Inequalities for Network Loading Under Demand Uncertainty

Claßen, Grit; Koster, Arie M. C. A.; Kutschka, Manuel; Tahiri, Issam

doi:10.1142/s0217595915500384

Cited by 7 publications

(3 citation statements)

References 19 publications

(47 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…A stronger co-NP hardness result is given in [11] where the graph is undirected (this implies the directed case result). Some exact solution methods for robust network design have been considered in [12,13]. Some special cases where dynamic routing is easy to compute have been described in [14,15,16].…”

Section: Introductionmentioning

confidence: 99%

On the approximability of robust network design

Al-Najjar

Ben‐Ameur

Leguay

2021

Theoretical Computer Science

View full text Add to dashboard Cite

Section: Introductionmentioning

confidence: 99%

On the approximability of robust network design

Al-Najjar

Ben‐Ameur

Leguay

2021

Theoretical Computer Science

View full text Add to dashboard Cite

“…A stronger co‐NP‐hardness result is given in [21] where the graph is undirected (this implies the directed case result). Some exact solution methods for robust network design have been considered in [5, 22, 35, 50]. In the case where the objective function of minimizing congestion is considered, a well‐known

O (\log n)

approximation ratio was presented in [47].…”

Section: Introductionmentioning

confidence: 99%

Affine routing for robust network design

et al. 2021

View full text Add to dashboard Cite

Taking into account the dynamic nature of traffic in telecommunication networks, the robust network design problem is to fix the edge capacities so that all demand vectors belonging to a polytope can be routed. While a common heuristic for this co‐NP‐hard problem is to compute, in polynomial time, an optimal static routing, affine routing can be used to obtain better solutions. It consists in restricting the routing to affinely depend on the demands. We show that a node‐arc formulation is less conservative than an arc‐path formulation. We also provide a cycle‐based formulation that is equivalent to the node‐arc formulation. To further reduce the solution's cost, several new formulations are obtained by relaxing flow conservation constraints and aggregating demands. As might be expected, aggregation allows us to reduce the size of formulations. A more striking result is that aggregation reduces the solution's cost.

show abstract

“…A stronger co-NP hardness result is given in [12] where the graph is undirected (this implies the directed case result). Some exact solution methods for robust network design have been considered in [13,14]. In the case where minimum congestion is considered a well-known O(log n) approximation ratio was presented in [15].…”

Section: Introductionmentioning

confidence: 99%

On the Approximability of Robust Network Design

Al-Najjar¹,

Ben‐Ameur²,

Leguay³

2020

Preprint

View full text Add to dashboard Cite

Considering the dynamic nature of traffic, the robust network design problem consists in computing the capacity to be reserved on each network link such that any demand vector belonging to a polyhedral set can be routed. The objective is either to minimize congestion or a linear cost. And routing freely depends on the demand.We first prove that the robust network design problem with minimum congestion cannot be approximated within any constant factor. Then, using the ETH conjecture, we get a Ω( log n log log n ) lower bound for the approximability of this problem. This implies that the well-known O(log n) approximation ratio established by Räcke in 2008 is tight.Using Lagrange relaxation, we obtain a new proof of the O(log n) approximation. An important consequence of the Lagrange-based reduction and our inapproximability results is that the robust network design problem with linear reservation cost cannot be approximated within any constant ratio. This answers a long-standing open question of Chekuri.Finally, we show that even if only two given paths are allowed for each commodity, the robust network design problem with minimum congestion or linear costs is hard to approximate within some constant k.

show abstract

Robust Metric Inequalities for Network Loading Under Demand Uncertainty

Cited by 7 publications

References 19 publications

On the approximability of robust network design

On the approximability of robust network design

Affine routing for robust network design

On the Approximability of Robust Network Design

Contact Info

Product

Resources

About