Éric Gourdin

• PhD Applied Mathematics
• Head of Department at Orange Gardens, Chatillon

Given a bi‐directed graph modeling a telecommunication network, and a set of origin‐destination pairs representing traffic requests (commodities) along with their associated Service Function Chains (SFCs), the Virtual Network Function Placement and Routing Problem (VNFPRP) aims to find, for each commodity, one latency‐constrained routing path that...

We 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 (łn m)2 (łn T) øver Δmin) after T rounds, where m = maxx ∈ X 1Tx. However, ESCB has computational complexity O(|X|), which is typically exponential in d, a...

We consider combinatorial semi-bandits over a set of arms X \subset \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 (łn m)^2 (łn T) / Δ_\min ) after T rounds, where m = \max_x \in X 1^\top x. However, ESCB it has computational complexity O(|X|), which is t...

We consider combinatorial semi-bandits with uncorrelated Gaussian rewards. In this article, we propose the first method, to the best of our knowledge, that enables to compute the solution of the Graves-Lai optimization problem in polynomial time for many combinatorial structures of interest. In turn, this immediately yields the first known approach...

In this paper we study a problem faced by network service providers in which a set of Virtual Network Functions (VNFs) has to be installed in a telecommunication network at minimum cost. For each given origin-destination pair of nodes (commodities), a latency-constrained routing path has to be found that visits the required VNFs in a pre-defined or...

This chapter gives an insight into some challenging combinatorial optimization problems that have to be tackled to deliver efficient and appropriate decision algorithms to manage future networks. The first part of the chapter is dedicated to variants of routing optimization problems in future IP networks, and the second part is dedicated to two opt...

Network Functions Virtualization (NFV) and Software Defined Networking (SDN) are two promising techniques for the next generation telecommunication networks. Their introduction allows time, energy and cost minimization. Placing Virtual Network Functions (VNFs) on network nodes and routing data through these nodes is a very challenging combinatorial...

Modifying the topology of a network to mitigate the spread of an epidemic with epidemiological constant \(\lambda \) amounts to the NP-hard problem of finding a partial subgraph with maximum number of edges and spectral radius bounded above by \(\lambda \). A software-defined network capable of real-time topology reconfiguration can then use an alg...

We consider combinatorial semi-bandits over a set of arms ${\cal X} \subset \{0,1\}^d$ where rewards are uncorrelated across items. For this problem, the algorithm ESCB yields the smallest known regret bound $R(T) = {\cal O}\Big( {d (\ln m)^2 (\ln T) \over \Delta_{\min} }\Big)$, but it has computational complexity ${\cal O}(|{\cal X}|)$ which is ty...

Network 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 traf...

The exponential growth in networks' traffic accompanied by the multiplication of new services like those promised by the 5G led to a huge increase in the infrastructures' energy consumption. All over the world, many telecom operators are facing the problem of energy consumption and Green networking since many years and they all convey today that it...

Network 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 adaptati...

We consider several extensions of the fractional bin packing problem, a relaxation of the traditional bin packing problem where the objects may be split across multiple bins. In these extensions, we introduce load-balancing constraints imposing that the share of each object which is assigned to a same bin must be equal. We propose a Mixed-Integer P...

This chapter gives an insight into some challenging combinatorial optimization problems that have to be tackled to deliver efficient and appropriate decision algorithms to manage future networks. The first part of the chapter is dedicated to variants of routing optimization problems in future IP networks, and the second part is dedicated to two opt...

We consider several extensions of the fractional bin packing problem, a relaxation of the traditional bin packing problem where the objects may be split across multiple bins. In these extensions, we introduce load-balancing constraints imposing that the share of each object which is assigned to a same bin must be equal. We propose a Mixed-Integer P...

Telecommunication networks can be seen as the stacking of several layers like, for instance, IP-over-Optical networks. This infrastructure should have sufficient capacities to route some demands between their origin-destination nodes. In this paper we consider the Capacitated Multi-Failure Survivable Network Design problem. We study two variants of...

Software Defined Networking and Network Function Virtualization are two paradigms that offer a flexible software-based network management. Service providers are instantiating Virtualized Network Functions - e.g., firewalls, DPIs, gateways - to highly facilitate the deployment and reconfiguration of network services with reduced time-to-value. They...

Software Defined Networking and Network Function Virtualization are two paradigms that offer flexible software-based network management. Service providers are instantiating Virtualized Network Functions - e.g., firewalls, DPIs, gateways - to highly facilitate the deployment and reconfiguration of network services with reduced time-to-value. They em...

Content delivery networks (CDNs) have become key telecommunication actors. They contribute to improve significantly the quality of services delivering content to end users. However, their impact on the ecosystem raises concerns about their “fairness,” and therefore the question of their inclusion in the neutrality debates, becomes relevant. This pa...

This book is the proceedings of the 12th International Conference on the Design of Reliable Communication Networks, namely DRCN 2016. DRCN 2016 was held on March 14-16, 2016 in Paris, France. The individual papers can be obtained through IEEE Xplore at: http://ieeexplore.ieee.org/xpl/mostRecentIssue.jsp?punumber=7467375

Despite an intensive and long-lasting effort from the scientific community, the dynamic behavior of a single cache is still hard to model and work around hierarchy or federation of caches has barely started. As a result, it is very difficult to predict the potential benefit that one could gain from a cache in a real setting and network operators la...

In this article, we propose a generic decomposition scheme for the maximum concurrent flow problem. This decomposition scheme encompasses many models, including, among many others, the classical path formulation and the less studied tree formulation, where the flows of commodities sharing a same source vertex are routed on a set of trees. The prici...

To ensure the robust delivery of video streams, a network must emit additional data that will replace the missing ones in case of a failure of some server. One key issue is then to keep this so-called redundancy as low as possible while still ensuring some quality of service. In this paper, we provide protectionoriented models to compute the minimu...

We address survivability considerations for telecommunication networks where a part of the network may fail. We focus on single arc failures in multicast networks, with or without network coding. The problem is to compute a routing such that, if any single arc failure occurs, the remaining throughput is as large as possible. In the case of multicas...

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 appr...

In this paper, a new decomposition approach is proposed to solve large size instances of Multicommodity Flow problems. Instead of generating paths, we generate trees in a convenient way. Numerical results show that the new approach is much more efficient than the classical paths generation approach. Moreover, we propose a combinatorial polynomial-t...

We consider the problem of introducing network coding in a network in a manner that balances the benefits obtained from coding with the costs of providing coding, where such costs depend both on the number of nodes performing coding and the volume of traffic that is coded. Previous work has envisaged either the minimization of the number of nodes p...

Given a telecommunication network, modelled by a capacitated digraph, we are interested in comparing the behaviour and usefulness of two information propagation schemes, namely multicast and network coding, when the aforementioned network is subject to simple arc failure. We consider the case with a single source node and a set of terminal nodes. T...

This chapter examines several flow and multicommodity-flow problems in graphs and shows that they can be modeled as either linear or convex problems, with continuous variables or integers. The vast amount of literature and numerous results for these problems allow us to treat them, for the most part, very effectively. This results in flow models, r...

Network coding has been shown to be the solution that allows to reach the theoretical maximum throughput in a capacitated telecommunication network. It has also been shown to be a very appealing and practical alternative to routing-based approaches to send traffic from sources (servers) to terminals (clients) for many different applications. Howeve...

The effect of virus spreading in a telecommunication network, where a certain curing strategy is deployed, can be captured by epidemic models. In the N-intertwined model proposed and studied in [1], [2], the probability of each node to be infected depends on the curing and infection rate of its neighbors. In this paper, we consider the case where a...

One popular approach to overcome the expected congestions due to the spectacular development of various multimedia applications consists in installing transparent caches at strategically chosen places inside telecommunication networks. The problem of locating caches is a difficult optimization problem, closely related to the p-median problem. In th...

We introduce the Partitioning-Hub-Location-Routing Problem (PHLRP), a hub location problem involving graph partitioning and routing features. The PHLRP consists of partitioning a given network into sub-networks, locating at least one hub in each sub-network and routing the traffic within the network at minimum cost. This problem finds applications...

In grid systems, users compete for different types of resources such that they may execute their applications. Traditional grid systems are formed of organisations that join together for the purpose of collaborative projects. Resources of each of the participating organisation are pooled such that members of individual organisations may access the...

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 w...

Let G=(V,A) be a directed graph and F be a set of items. The Location-Dispatching Problem consists of determining subsets Li⊆F,i∈V, minimizing the sum of two costs: an installation cost associated with nodes i of V such that Li≠∅ and an access cost to each item of F. We formulate this problem as an integer linear program and propose a facial study...

In a capacitated graph with a set of commodities, the sparsity of a cut is the ratio between the capacity of the cut and the demand of the commodities separated by the cut. The Sparsest Cut (SC) is often introduced as a weak dual of the Maximum Concurrent Flow problem (MCF). Contrarily to MCF, problem SC is, in general, NP-hard. This problem has be...

In distributed network settings, where nodes are not under the control of a single administrative entity, the fulfillment of fundamental network operations is heavily dependent on their cooperation. Nevertheless, individual interests in combination with resource constraints do not always encourage cooperative behavior. In this work, we focus on sta...

The Grid is a promising concept to solve the dilemma of increasingly complex and demanding applications being confronted with the need for a more efficient and flexible use of existing computer resources. Even though Grid technologies have made progress within the context of large enterprises and academic projects, there has not yet been a widespre...

The Internet is a huge world-wide packet switching network comprised of more than 13,000 distinct subnetworks, referred to as Autonomous Systems (ASs) . They all rely on the Internet Protocol (IP) for transport of packets across the network. And most of them use shortest path routing protocols , such as OSPF or IS-IS, to control the routing of IP p...

In this paper, we discuss applications of max–min fairness (MMF) in survivable networks. We focus on two specific applications intended to face failure situations and provide several computational results for each of them. The first application, called simple robust routing, generalizes the multipath routing in order to achieve acceptable levels of...

This work deals with a multi-period capacitated location problem inspired by telecommunication access network planning problems, where demands and costs vary from one period to another. On each concentrator site, several capacitated concentrators can be installed at each period. Similarly, several capacitated modules can be installed at each period...

This paper considers the problem of aggregating several multicast sessions. A multicast session is defined as a subset of clients requiring the same information. Besides, each client can require several multicast sessions. A telecommunication network cannot manage many multicast sessions at the same time. It is hence necessary to group the sessions...

In this paper, we present the max-min fair (MMF) rerouting computation problem for different end-to-end rerouting strategies with respect to simple link failures. This work is in continuation of our earlier works on MMF [4, 5]. We present a general iterative algorithm for the MMF rerouting problem, as well as the associated mathematical formulation...

In this paper, we consider the max-min fair resource allocation problem as applied to elastic flows. We are interested in computing the optimal max-min fair rate allocation. The proposed approach is a linear programming based one and allows the computation of optimal routing paths with regard to max-min fairness, in stable and known traffic conditi...

In this paper, we consider the max-min fair resource allocation problem as applied to elastic flows. We are interested in computing the optimal max-min fair rate allocation. The proposed approach is a linear programming based one and allows the computation of optimal routing paths with regard to max-min fairness, in stable and known traffic conditi...

In the past years, telecommunications networks have seen an important evolution with the advances in optical technologies and the explosive growth of the Internet. Several optical systems allow a very large transport capacity, and data traffic has dramatically increased. Telecommunications networks are now moving towards a model of high-speed route...

We consider the general planning problem of decid- ing how to route "optimally" several commodities in a network (the topology and the capacities are given). Such decisions are essentially driven by the expected QoS that will be experienced by users under estimated traffic conditions. The choice of a suitable objective function is hence a crucial i...

Abstract 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 trac,in the network. There may,also be capacity restrictions on the amount,of trac,that can transit by hubs. The aim of this paper is to inves...

In most domains of the Internet network, the traffic demands are routed on a single-path defined as the shortest one according to a set of administrative weights. Most of the time, the values set by the administrator (or the default ones) are such that there are many paths of the same length between the extremities of some demands. However, if the...

In order to face the explosion of traffic in the Internet, the administrators who had a tendency to oversize their network have turned to new protocols aiming at better control of the routing and a better distribution of the traffic. New routing paradigms (MPLS) allowing explicit tunnel definitions are slowly emerging in the Internet community. How...

We review the models for telecommunication network design where there is a location problem involved. We classify the models into three classes as uncapacitated, capacitated and dynamic models. For each class, we discuss the core problem, its generalizations and the solution methods in the literature.

This work addresses the problem of static routing complexity and performance for best effort traffic in a data network and more specifically an Internet network running an IGP (Interior Gateway protocol), and MPLS if necessary. We first give a short presentation of the various routing strategies (single-path and multi-path) and their possible reali...

TheUncapacitated Facility Location Problem with Client Matching (LCM) is an extension of theUncapacitated Facility Location Problem (UFLP), where two clients allocated to a facility can be matched. As in the UFLP, facilities can be opened at any ofm predefined locations with given fixed costs, andn clients have to be allocated to the open facilitie...

: Network design problems are deceptively easy to describe, but are often very difficult to solve. Given a set of available (perhaps capacitated) edges, the problem seeks a least cost network, composed of both variable flow costs and edge fixed costs, that meets prescribed multicommodity flow requirements. Several decades ago, applied mathematician...

This paper proposes an extention of the Uncapacitated Facility Location Problem (UFLP) where the clients allocated to the facility can be matched in pairs in order to reduce the cost of serving them. As in the usual UFLP, facilities can be opened on anyone ofmpredefined locations with a given fixed cost, andnclients have to be allocated to opened f...

We propose a branch-and-bound framework for the global optimization of unconstrained Hölder functions. The general framework is used to derive two algorithms. The first one is a generalization of Piyavskii's algorithm for univariate Lipschitz functions. The second algorithm, using a piecewise constant upper-bounding function, is designed for multiv...

Much work has been devoted to the problem of finding maximum likelihood estimators for the three-parameter Weibull distribution. This problem has not been clearly recognized as a global optimization one and most methods from the literature occasionally fail to find a global optimum. We develop a global optimization algorithm which uses first order...

There has been much recent statistical research in the area of inference under constraints. The problem considered here is that of bounded parameter estimation, in particular that of normal and Poisson means, using minimaxity as the criterion of evaluation. Because of the ease of calculation of linear minimax rules, the ratio of these risks to the...

Abstract We introduce the Partitioning-Hub-Location-Routing Problem (PHLRP), a hub location problem involving graph partitioning and routing features. PHLRP consists of partitioning a given network into sub-networks, locating at least one hub in each sub-network and routing the trac,within the network at minimum cost. This problem finds application...

Nonparametric estimation of smooth functions that are members of Sobolev classes is closely related to the problem of estimating the (infinite dimensional) mean of a standard Gaussian shift when the mean is known to lie in an ℓ p body. D.L. Donoho, R.C. Liu and B. MacGibbon [Ann. Stat. 18, No. 3, 1416-1437 (1990; Zbl 0705.62018)] obtained exact res...

Résumé additionnel en anglais. Thèse (Ph. D.)--École polytechnique, 1994. "Thèse présentée en vue de l'obtention du grade de Philosophiæ Doctor (Ph. D.) (Mathématiques).'