On the approximability of robust network design

Al-Najjar, Yacine; Ben‐Ameur, Walid; Leguay, Jérémie

doi:10.1016/j.tcs.2021.01.026

Cited by 2 publications

(3 citation statements)

References 51 publications

(80 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…FIGURE 2 An example with three commodities: h i with i = 1, 2 having the same source and sink as edges e i , and h 3 from source node s to sink node t. In this example we show that  + dominates formulation  = Proposition 2.  + is a valid formulation.…”

Section: Relaxing the Flow Conservation Constraintsmentioning

confidence: 74%

“…This should be done for each constraint. The main advantage of (3) is that the uncertainty appearing in the flow conservation constraints (1a) is already handled using (2). However, the other constraints (3b) and (3c) still need to be treated using the techniques briefly recalled in Section 7 and used for the numerical evaluation.…”

Section: Initial Node-arc Formulationmentioning

confidence: 99%

“…In the case where the objective function of minimizing congestion is considered, a well‐known

O (\log n)

approximation ratio was presented in [47]. In a recent study on the approximability of robust network design [2], we proved that the robust network design problem with minimum congestion or with linear reservation cost cannot be approximated within any constant factor. Using the ETH conjecture, we also obtained a

Ω (\frac{\log n}{\log \log n})

lower bound which implies that the

O (\log n)

approximation ratio [47] is tight.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Affine routing for robust network design

et al. 2021

Self Cite

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

Section: Relaxing the Flow Conservation Constraintsmentioning

confidence: 74%

Section: Initial Node-arc Formulationmentioning

confidence: 99%

“…In the case where the objective function of minimizing congestion is considered, a well‐known