Distributed Connectivity Decomposition

We present time-efficient distributed algorithms for decomposing graphs with large edge or vertex connectivity into multiple spanning or dominating trees, respectively. As their primary applications, these decompositions allow us to achieve information flow with size close to the connectivity by parallelizing it along the trees. More specifically, our distributed decomposition algorithms are as follows: (I) A decomposition of each undirected graph with vertex-connectivity $k$ into (fractionally) vertex-disjoint weighted dominating trees with total weight $\Omega(\frac{k}{\log n})$, in $\widetilde{O}(D+\sqrt{n})$ rounds. (II) A decomposition of each undirected graph with edge-connectivity $\lambda$ into (fractionally) edge-disjoint weighted spanning trees with total weight $\lceil\frac{\lambda-1}{2}\rceil(1-\varepsilon)$, in $\widetilde{O}(D+\sqrt{n\lambda})$ rounds. We also show round complexity lower bounds of $\tilde{\Omega}(D+\sqrt{\frac{n}{k}})$ and $\tilde{\Omega}(D+\sqrt{\frac{n}{\lambda}})$ for the above two decompositions, using techniques of [Das Sarma et al., STOC'11]. Moreover, our vertex-connectivity decomposition extends to centralized algorithms and improves the time complexity of [Censor-Hillel et al., SODA'14] from $O(n^3)$ to near-optimal $\tilde{O}(m)$. As corollaries, we also get distributed oblivious routing broadcast with $O(1)$-competitive edge-congestion and $O(\log n)$-competitive vertex-congestion. Furthermore, the vertex connectivity decomposition leads to near-time-optimal $O(\log n)$-approximation of vertex connectivity: centralized $\widetilde{O}(m)$ and distributed $\tilde{O}(D+\sqrt{n})$. The former moves toward the 1974 conjecture of Aho, Hopcroft, and Ullman postulating an $O(m)$ centralized exact algorithm while the latter is the first distributed vertex connectivity approximation

Sur l'utilisation du codage réseau et du multicast pour améliorer la performance dans les réseaux filaires

La popularité de la grande variété de l'utilisation d'Internet entraîne une croissance significative du trafic de données dans les réseaux de télécommunications. L'efficacité de la transmission de données sera contestée en vertu du principe de la capacité actuelle du réseau et des mécanismes de contrôle de flux de données. En plus d'augmenter l'investissement financier pour étendre la capacité du réseau, améliorer les techniques existantes est plus rationnel et éconmique.Diverses recherches de pointe pour faire face aux besoins en évolution des réseaux ont vu le jour, et l'une d'elles est appelée codage de réseau. Comme une extension naturelle dans la théorie du codage, il permet le mélange de différents flux réseau sur les noeuds intermédiaires, ce qui modifie la façon d'éviter les collisions de flux de données. Il a été appliqué pour obtenir un meilleur débit, fiabilité, sécurité et robustesse dans différents environnements et applications réseau. Cette thèse porte sur l'utilisation du réseau de codage pour le multicast dans les réseaux maillés fixes et systèmes de stockage distribués. Nous avons d'abord des modèles de différentes stratégies de routage multicast dans un cadre d'optimisation, y compris de multicast à base d'arbres et de codage de réseau; nous résolvons les modèles avec des algorithmes efficaces et comparons l'avantage de codage, en termes de gain de débit de taille moyenne graphique généré aléatoirement. Basé sur l'analyse numérique obtenue à partir des expériences précédentes, nous proposons un cadre révisé de routage multicast, appelé codage de réseau stratégique, qui combine transmission muticast standard et fonctions de codage de réseau afin d'obtenir le maximum de bénéfice de codage réseau au moindre coût lorsque ces coûts dépendent à la fois sur le nombre de noeuds à exécuter un codage et le volume de trafic qui est codé. Enfin, nous étudions le problème révisé de transport qui est capable de calculer un système de routage statique entre les serveurs et les clients dans les systèmes de stockage distribués où nous appliquons le codage pour soutenir le stockage de contenu. Nous étendons l'application à un problème d'optimisation général, nommé problème de transport avec des contraintes de degré, qui peut être largement utilisé dans divers domaines industriels, y compris les télécommunications, mais n'a pas été étudié très souvent. Pour ce problème, nous obtenons quelques résultats théoriques préliminaires et nous proposons une approche de décomposition Lagrange raisonnableThe popularity of the great variety of Internet usage brings about a significant growth of the data traffic in telecommunication network. Data transmission efficiency will be challenged under the premise of current network capacity and data flow control mechanisms. In addition to increasing financial investment to expand the network capacity, improving the existing techniques are more rational and economical. Various cutting-edge researches to cope with future network requirement have emerged, and one of them is called network coding. As a natural extension in coding theory, it allows mixing different network flows on the intermediate nodes, which changes the way of avoiding collisions of data flows. It has been applied to achieve better throughput and reliability, security, and robustness in various network environments and applications. This dissertation focuses on the use of network coding for multicast in fixed mesh networks and distributed storage systems. We first model various multicast routing strategies within an optimization framework, including tree-based multicast and network coding; we solve the models with efficient algorithms, and compare the coding advantage, in terms of throughput gain in medium size randomly generated graphs. Based on the numerical analysis obtained from previous experiments, we propose a revised multicast routing framework, called strategic network coding, which combines standard multicast forwarding and network coding features in order to obtain the most benefit from network coding at lowest cost where such costs depend both on the number of nodes performing coding and the volume of traffic that is coded. Finally, we investigate a revised transportation problem which is capable of calculating a static routing scheme between servers and clients in distributed storage systems where we apply coding to support the storage of contents. We extend the application to a general optimization problem, named transportation problem with degree constraints, which can be widely used in different industrial fields, including telecommunication, but has not been studied very often. For this problem, we derive some preliminary theoretical results and propose a reasonable Lagrangian decomposition approachEVRY-INT (912282302) / SudocSudocFranceF

Vertex sparsification and universal rounding algorithms

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2011.Cataloged from PDF version of thesis.Includes bibliographical references (p. 125-129).Suppose we are given a gigantic communication network, but are only interested in a small number of nodes (clients). There are many routing problems we could be asked to solve for our clients. Is there a much smaller network - that we could write down on a sheet of paper and put in our pocket - that approximately preserves all the relevant communication properties of the original network? As we will demonstrate, the answer to this question is YES, and we call this smaller network a vertex sparsifier. In fact, if we are asked to solve a sequence of optimization problems characterized by cuts or flows, we can compute a good vertex sparsifier ONCE and discard the original network. We can run our algorithms (or approximation algorithms) on the vertex sparsifier as a proxy - and still recover approximately optimal solutions in the original network. This novel pattern saves both space (because the network we store is much smaller) and time (because our algorithms run on a much smaller graph). Additionally, we apply these ideas to obtain a master theorem for graph partitioning problems - as long as the integrality gap of a standard linear programming relaxation is bounded on trees, then the integrality gap is at most a logarithmic factor larger for general networks. This result implies optimal bounds for many well studied graph partitioning problems as a special case, and even yields optimal bounds for more challenging problems that had not been studied before. Morally, these results are all based on the idea that even though the structure of optimal solutions can be quite complicated, these solution values can be approximated by crude (even linear) functions.by Ankur Moitra.Ph.D

Vertex sparsification and universal rounding algorithms

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2011.Cataloged from PDF version of thesis.Includes bibliographical references (p. 125-129).Suppose we are given a gigantic communication network, but are only interested in a small number of nodes (clients). There are many routing problems we could be asked to solve for our clients. Is there a much smaller network - that we could write down on a sheet of paper and put in our pocket - that approximately preserves all the relevant communication properties of the original network? As we will demonstrate, the answer to this question is YES, and we call this smaller network a vertex sparsifier. In fact, if we are asked to solve a sequence of optimization problems characterized by cuts or flows, we can compute a good vertex sparsifier ONCE and discard the original network. We can run our algorithms (or approximation algorithms) on the vertex sparsifier as a proxy - and still recover approximately optimal solutions in the original network. This novel pattern saves both space (because the network we store is much smaller) and time (because our algorithms run on a much smaller graph). Additionally, we apply these ideas to obtain a master theorem for graph partitioning problems - as long as the integrality gap of a standard linear programming relaxation is bounded on trees, then the integrality gap is at most a logarithmic factor larger for general networks. This result implies optimal bounds for many well studied graph partitioning problems as a special case, and even yields optimal bounds for more challenging problems that had not been studied before. Morally, these results are all based on the idea that even though the structure of optimal solutions can be quite complicated, these solution values can be approximated by crude (even linear) functions.by Ankur Moitra.Ph.D

From classical to quantum machine learning: survey on routing optimization in 6G software defined networking

The sixth generation (6G) of mobile networks will adopt on-demand self-reconfiguration to fulfill simultaneously stringent key performance indicators and overall optimization of usage of network resources. Such dynamic and flexible network management is made possible by Software Defined Networking (SDN) with a global view of the network, centralized control, and adaptable forwarding rules. Because of the complexity of 6G networks, Artificial Intelligence and its integration with SDN and Quantum Computing are considered prospective solutions to hard problems such as optimized routing in highly dynamic and complex networks. The main contribution of this survey is to present an in-depth study and analysis of recent research on the application of Reinforcement Learning (RL), Deep Reinforcement Learning (DRL), and Quantum Machine Learning (QML) techniques to address SDN routing challenges in 6G networks. Furthermore, the paper identifies and discusses open research questions in this domain. In summary, we conclude that there is a significant shift toward employing RL/DRL-based routing strategies in SDN networks, particularly over the past 3 years. Moreover, there is a huge interest in integrating QML techniques to tackle the complexity of routing in 6G networks. However, considerable work remains to be done in both approaches in order to accomplish thorough comparisons and synergies among various approaches and conduct meaningful evaluations using open datasets and different topologies

Online Network Design under Uncertainty

Today, computer and information networks play a significant role in the success of businesses, both large and small. Networks provide access to various services and resources to end users and devices. There has been extensive research on de- signing networks according to numerous criteria such as cost-efficiency, availability, adaptivity, survivability, among others. In this dissertation, we revisit some of the most fundamental network design problems in the presence of uncertainty. In most realistic models, we are forced to make decisions in the presence of an incomplete input, which is the source of uncertainty for an optimization algorithm. There are different types of uncertainty. For example, in stochastic settings, we may have some random variables derived from some known/unknown distributions. In online settings, the complete input is not known in a-priori and pieces of the input become available sequentially; leaving the algorithm to make decisions only with partial data. In this dissertation, we consider network design and network optimization problems with uncertainty. In particular, we study online bounded-degree Steiner network design, online survivable network design, and stochastic k-server. We analyze their complexity and design competitive algorithms for them

A Polyhedral Study of Mixed 0-1 Set

We consider a variant of the well-known single node fixed charge network flow set with constant capacities. This set arises from the relaxation of more general mixed integer sets such as lot-sizing problems with multiple suppliers. We provide a complete polyhedral characterization of the convex hull of the given set

Distributed optimization algorithms for multihop wireless networks

Recent technological advances in low-cost computing and communication hardware design have led to the feasibility of large-scale deployments of wireless ad hoc and sensor networks. Due to their wireless and decentralized nature, multihop wireless networks are attractive for a variety of applications. However, these properties also pose significant challenges to their developers and therefore require new types of algorithms. In cases where traditional wired networks usually rely on some kind of centralized entity, in multihop wireless networks nodes have to cooperate in a distributed and self-organizing manner. Additional side constraints, such as energy consumption, have to be taken into account as well. This thesis addresses practical problems from the domain of multihop wireless networks and investigates the application of mathematically justified distributed algorithms for solving them. Algorithms that are based on a mathematical model of an underlying optimization problem support a clear understanding of the assumptions and restrictions that are necessary in order to apply the algorithm to the problem at hand. Yet, the algorithms proposed in this thesis are simple enough to be formulated as a set of rules for each node to cooperate with other nodes in the network in computing optimal or approximate solutions. Nodes communicate with their neighbors by sending messages via wireless transmissions. Neither the size nor the number of messages grows rapidly with the size of the network. The thesis represents a step towards a unified understanding of the application of distributed optimization algorithms to problems from the domain of multihop wireless networks. The problems considered serve as examples for related problems and demonstrate the design methodology of obtaining distributed algorithms from mathematical optimization methods