Metric embeddings with relaxed guarantees

We consider the problem of embedding finite metrics with slack: We seek to produce embeddings with small dimension and distortion while allowing a (small) constant fraction of all distances to be arbitrarily distorted. This definition is motivated by recent research in the networking community, which achieved striking empirical success at embedding Internet latencies with low distortion into low-dimensional Euclidean space, provided that some small slack is allowed. Answering an open question of Kleinberg, Slivkins, and Wexler [in Proceedings of the 45th IEEE Symposium on Foundations of Computer Science, 2004], we show that provable guarantees of this type can in fact be achieved in general: Any finite metric space can be embedded, with constant slack and constant distortion, into constant-dimensional Euclidean space. We then show that there exist stronger embeddings into l 1 which exhibit gracefully degrading distortion: There is a single embedding into l 1 that achieves distortion at most O (log 1/∈) on all but at most an ∈ fraction of distances simultaneously for all ∈ > 0. We extend this with distortion O (log 1/∈) 1/p to maps into general l p, p ≥ 1, for several classes of metrics, including those with bounded doubling dimension and those arising from the shortest-path metric of a graph with an excluded minor. Finally, we show that many of our constructions are tight and give a general technique to obtain lower bounds for ∈-slack embeddings from lower bounds for low-distortion embeddings. © 2009 Society for Industrial and Applied Mathematics.published_or_final_versio

Reshaping the African Internet: From scattered islands to a connected continent

There is an increasing awareness amongst developing regions on the importance of localizing Internet traffic in the quest for fast, affordable, and available Internet access. In this paper, we focus on Africa, where 37 IXPs are currently interconnecting local ISPs, but mostly at the country level. An option to enrich connectivity on the continent and incentivize content providers to establish presence in the region is to interconnect ISPs present at isolated IXPs by creating a distributed IXP layout spanning the continent. The goal of this paper is to investigate whether such IXP interconnection would be possible, and if successful, to estimate the best-case benefits that could be realized in terms of traffic localization and performance. Our hope is that quantitatively demonstrating the benefits will provide incentives for ISPs to intensify their peering relationships in the region. However, it is challenging to estimate this best-case scenario, due to numerous economic, political, and geographical factors influencing the region. Towards this end, we begin with a thorough analysis of the environment in Africa. We then investigate a naive approach to IXP interconnection, which shows that a theoretically optimal solution would be infeasible in practice due to the prevailing socio-economic conditions in the region. We therefore provide an innovative, realistic four-step interconnection scheme to achieve the distributed IXP layout that considers and parameterizes external socio-economic factors using publicly available datasets. We demonstrate that our constrained solution doubles the percentage of continental intra-African paths, reduces their lengths, and drastically decreases the median of their RTTs as well as RTTs to ASes hosting the top 10 global and top 10 regional Alexa websites. Our approach highlights how, given real-world constraints, a solution requires careful considerations in order to be practically realizable.Rodérick Fanou was partially supported by IMDEA Networks Institute, US NSF grant CNS-1414177, and the project BRADE (P2013/ICE-2958) from the Directorate General of Universities and Research, Board of Education, Madrid Regional Governement. Francisco Valera was partially funded by the European Commission under FP7 project LEONE (FP7-317647). Amogh Dhamdhere was partially funded by US NSF grants CNS-1414177 and CNS-1513847.Publicad

On the Power of Robust Solutions in Two-Stage Stochastic and Adaptive Optimization Problems

We consider a two-stage mixed integer stochastic optimization problem and show that a static robust solution is a good approximation to the fully adaptable two-stage solution for the stochastic problem under fairly general assumptions on the uncertainty set and the probability distribution. In particular, we show that if the right-hand side of the constraints is uncertain and belongs to a symmetric uncertainty set (such as hypercube, ellipsoid or norm ball) and the probability measure is also symmetric, then the cost of the optimal fixed solution to the corresponding robust problem is at most twice the optimal expected cost of the two-stage stochastic problem. Furthermore, we show that the bound is tight for symmetric uncertainty sets and can be arbitrarily large if the uncertainty set is not symmetric. We refer to the ratio of the optimal cost of the robust problem and the optimal cost of the two-stage stochastic problem as the stochasticity gap. We also extend the bound on the stochasticity gap for another class of uncertainty sets referred to as positive. If both the objective coefficients and right-hand side are uncertain, we show that the stochasticity gap can be arbitrarily large even if the uncertainty set and the probability measure are both symmetric. However, we prove that the adaptability gap (ratio of optimal cost of the robust problem and the optimal cost of a two-stage fully adaptable problem) is at most four even if both the objective coefficients and the right-hand side of the constraints are uncertain and belong to a symmetric uncertainty set. The bound holds for the class of positive uncertainty sets as well. Moreover, if the uncertainty set is a hypercube (special case of a symmetric set), the adaptability gap is one under an even more general model of uncertainty where the constraint coefficients are also uncertain.National Science Foundation (U.S.) (NSF Grant DMI-0556106)National Science Foundation (U.S.) (NSF Grant EFRI-0735905

Guest Editorial: Special section on embracing artificial intelligence for network and service management

Artificial Intelligence (AI) has the potential to leverage the immense amount of operational data of clouds, services, and social and communication networks. As a concrete example, AI techniques have been adopted by telcom operators to develop virtual assistants based on advances in natural language processing (NLP) for interaction with customers and machine learning (ML) to enhance the customer experience by improving customer flow. Machine learning has also been applied to finding fraud patterns which enables operators to focus on dealing with the activity as opposed to the previous focus on detecting fraud

Hyperbolic Geometry of Complex Networks

We develop a geometric framework to study the structure and function of complex networks. We assume that hyperbolic geometry underlies these networks, and we show that with this assumption, heterogeneous degree distributions and strong clustering in complex networks emerge naturally as simple reflections of the negative curvature and metric property of the underlying hyperbolic geometry. Conversely, we show that if a network has some metric structure, and if the network degree distribution is heterogeneous, then the network has an effective hyperbolic geometry underneath. We then establish a mapping between our geometric framework and statistical mechanics of complex networks. This mapping interprets edges in a network as non-interacting fermions whose energies are hyperbolic distances between nodes, while the auxiliary fields coupled to edges are linear functions of these energies or distances. The geometric network ensemble subsumes the standard configuration model and classical random graphs as two limiting cases with degenerate geometric structures. Finally, we show that targeted transport processes without global topology knowledge, made possible by our geometric framework, are maximally efficient, according to all efficiency measures, in networks with strongest heterogeneity and clustering, and that this efficiency is remarkably robust with respect to even catastrophic disturbances and damages to the network structure

Recoverable Robustness by Column Generation

Real-life planning problems are often complicated by the occurrence of disturbances, which imply that the original plan cannot be followed anymore and some recovery action must be taken to cope with the disturbance. In such a situation it is worthwhile to arm yourself against common disturbances. Well-known approaches to create plans that take possible, common disturbances into account are robust optimization and stochastic programming. Recently, a new approach has been developed that combines the best of these two: recoverable robustness. In this paper, we apply the technique of column generation to find solutions to recoverable robustness problems. We consider two types of solution approaches: separate recovery and combined recovery. We show our approach on two example problems: the size robust knapsack problem, in which the knapsack size may get reduced, and the demand robust shortest path problem, in which the sink is uncertain and the cost of edges may increase

Guest Editorial: Special issue on data analytics and machine learning for network and service management-Part II

Network and Service analytics can harness the immense stream of operational data from clouds, to services, to social and communication networks. In the era of big data and connected devices of all varieties, analytics and machine learning have found ways to improve reliability, configuration, performance, fault and security management. In particular, we see a growing trend towards using machine learning, artificial intelligence and data analytics to improve operations and management of information technology services, systems and networks

Guest Editorial: Special issue on data analytics and machine learning for network and service management-Part II

Network and Service analytics can harness the immense stream of operational data from clouds, to services, to social and communication networks. In the era of big data and connected devices of all varieties, analytics and machine learning have found ways to improve reliability, configuration, performance, fault and security management. In particular, we see a growing trend towards using machine learning, artificial intelligence and data analytics to improve operations and management of information technology services, systems and networks

From mechatronics to the Cloud

At its conception mechatronics was viewed purely in terms of the ability to integrate the technologies of mechanical and electrical engineering with computer science to transfer functionality, and hence complexity, from the mechanical domain to the software domain. However, as technologies, and in particular computing technologies, have evolved so the nature of mechatronics has changed from being purely associated with essentially stand-alone systems such as robots to providing the smart objects and systems which are the building blocks for Cyber-Physical Systems, and hence for Internet of Things and Cloud-based systems. With the possible advent of a 4th Industrial Revolution structured around these systems level concepts, mechatronics must again adapt its world view, if not its underlying technologies, to meet this new challenge