Oblivious Routing: Static Routing Prepared Against Network Traffic and Link Failures

International audienceNetwork routing considers the problem of finding one or multiple paths to transfer packets from their source to their destination, ideally making the best use of the available resources (for instance, by minimising the congestion in the network). Oblivious routing is a technique that generates static routing schemes that are independent of the traffic, but still have strong theoretical guarantees about its performance (for instance, measured by link congestion). This work presents a numerical study of oblivious routing, in both synthetic and realistic networks. It also contains a novel extension to link failures, to which the routing should be immunised

The Multilayer Capacitated Survivable IP Network Design Problem : valid inequalities and Branch-and-Cut

Telecommunication networks can be seen as the stacking of several layers like, for instance, IP-over-Optical networks. This infrastructure has to be sufficiently survivable to restore the traffic in the event of a failure. Moreover, it should have adequate capacities so that the demands can be routed between the origin-destinations. In this paper we consider the Multilayer Capacitated Survivable IP Network Design problem. We study two variants of this problem with simple and multiple capacities. We give two multicommodity flow formulations for each variant of this problem and describe some valid inequalities. In particular, we characterize valid inequalities obtained using Chvatal-Gomory procedure from the well known Cutset inequalities. We show that some of these inequalities are facet defining. We discuss separation routines for all the valid inequalities. Using these results, we develop a Branch-and-Cut algorithm and a Branch-and-Cut-and-Price algorithm for each variant and present extensive computational results

Network coding and multi-terminal flow problems

Given a telecommunication network with non-negative arc capacities, a special vertex called source, and a set of vertices called terminals, we want to send as much information as possible simultaneously from the source to each terminal. We compare the classical routing scheme modeled by the maximum concurrent fl ow problem and a network coding approach within a multicast network. Multicast protocols allow an intermediate node to replicate its input data towards several output interfaces, and network coding refers to the ability for an intermediate node to perform coding operations on its inputs (for example, bit-wise XOR or linear combinations) releasing a coded information ow on its outputs. It can be show that the maximum quantity of information that can be routed from the source to each terminal using multicast with network coding is the minimum over all terminals of the value of a maximum fl ow between the source and the terminal. This means that we compare the maximum concurrent fl ow with the superposition of independent maximum fl ows, one for each terminal

Comparing Oblivious and Robust Routing Approaches

National audienceNetwork routing is an already well-studied problem: the routers in the network know which path a packet must follow in order to reach its destination. Traffic engineering attempts to tune the routing to meet some requirements, such as avoiding congestion or a reducing end-to-end delays. Several approaches have been devised to perform these adaptations, but only few of them deal with the uncertainty in some parameters. Mostly, the uncertainty lies in the demand, the total amount of traffic that goes through the network; however, links and nodes may also fail.Robust routing approaches have been proposed to tackle this issue: indeed, they consider that traffic matrices are not know precisely but that they lie in an uncertainty space that can be analytically described [1].Oblivious routing is the extreme case where the uncertainty space is the whole set of possible traffic matrices and the prescribed routing must be as close as p ossible to the optimum routing, whatever traffic matrix effectively occurs. It has been proved that oblivious routing achieves a polylogarithmic competitive ratio with respect to congestion [2].Several variants of robust or oblivious routing approaches will be considered and compared on series of realistic instances, some of which are based on Orange network topologies. Future works include dealing with other sources of uncertainty (for instance, survivability to failures [3]) within a common robustness framework.[1] Sözüer, S., and Thiele, A. C. (2016). The State of Robust Optimization. In Robustness Analysis in Decision Aiding, Optimization, and Analytics.[2] Räcke, H. (2002). Minimizing congestion in general networks. In Foundations of Computer Science, 2002.[3] Li, L., Buddhikot, M. M., Chekuri, C., and Guo, K. (2005). Routing bandwidth guaranteed paths with local restoration in label switched networks. IEEE Journal on Selected Areas in Communications, 23(2), 437-449

A Branch and Cut Algorithm for Hub Location Problems with Single Assignment

The hub location problem with single assignment is the problem of locating hubs and assigning the terminal nodes to hubs in order to minimize the cost of hub installation and the cost of routing the traffic in the network. There may also be capacity restrictions on the amount of traffic that can transit by hubs. The aim of this paper is to investigate polyhedral properties of these problems and to develop a branch and cut algorithm based on these results

Statistically Efficient, Polynomial-Time Algorithms for Combinatorial Semi-Bandits

International audienceWe consider combinatorial semi-bandits over a set X ⊂ {0, 1} d where rewards are uncorrelated across items. For this problem, the algorithm ESCB yields the smallest known regret bound R(T) = O d (ln m) 2 (ln T) ∆ min after T rounds, where m = max x ∈X 1 ⊤ x. However, ESCB has computational complexity O(|X|), which is typically exponential in d, and cannot be used in large dimensions. We propose the first algorithm that is both computationally and statistically efficient for this problem with regret R(T) = O d (ln m) 2 (ln T) ∆ min and computational asymptotic complexity O(δ −1 T poly(d)), where δ T is a function which vanishes arbitrarily slowly. Our approach involves carefully designing AESCB, an approximate version of ESCB with the same regret guarantees. We show that, whenever budgeted linear maximization over X can be solved up to a given approximation ratio, AESCB is implementable in polynomial time O(δ −1 T poly(d)) by repeatedly maximizing a linear function over X subject to a linear budget constraint, and showing how to solve these maximization problems efficiently. Additional algorithms, proofs and numerical experiments are given in the complete version of this work