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

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

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

Formulation and evaluation of Vasaka granules for asthma

Asthma is a chronic disease of bronchi which usually requires continuous medical care. Approaches for drug formulation that easy to administer especially for chronic diseases can form valuable therapy.Azathodavasica is a plant believed to have several therapeutic effects including antiasthmatic properties.It is the leaves,which are of great importance for asthma. Azathodavasicaneesbelonging to family Acanthaceae, it is found mainly in India It is also called as vasaka. vasaka herb is used for treating cold cough and asthma. It is a well-knownayurvedic medicine for expectorant and helps to ease out the phlegm.Vasaka leaves contain quinazoline alkaloids such as vasicinone, vasicine, vasicinol, vasicol granules can be used for the treatment of asthma as they offer advantages such as faster disintegration and dissolution as compare to tablet capsules.1 Keywords: vasicinone, vasicine, vasicol, Acanthaceae, Azathoda

Inferring persistent interdomain congestion

There is significant interest in the technical and policy communities regarding the extent, scope, and consumer harm of persistent interdomain congestion. We provide empirical grounding for discussions of interdomain congestion by developing a system and method to measure congestion on thousands of interdomain links without direct access to them. We implement a system based on the Time Series Latency Probes (TSLP) technique that identifies links with evidence of recurring congestion suggestive of an under-provisioned link. We deploy our system at 86 vantage points worldwide and show that congestion inferred using our lightweight TSLP method correlates with other metrics of interconnection performance impairment. We use our method to study interdomain links of eight large U.S. broadband access providers from March 2016 to December 2017, and validate our inferences against ground-truth traffic statistics from two of the providers. For the period of time over which we gathered measurements, we did not find evidence of widespread endemic congestion on interdomain links between access ISPs and directly connected transit and content providers, although some such links exhibited recurring congestion patterns. We describe limitations, open challenges, and a path toward the use of this method for large-scale third-party monitoring of the Internet interconnection ecosystem

Steering hyper-giants' traffic at scale

Large content providers, known as hyper-giants, are responsible for sending the majority of the content traffic to consumers. These hyper-giants operate highly distributed infrastructures to cope with the ever-increasing demand for online content. To achieve 40 commercial-grade performance of Web applications, enhanced end-user experience, improved reliability, and scaled network capacity, hyper-giants are increasingly interconnecting with eyeball networks at multiple locations. This poses new challenges for both (1) the eyeball networks having to perform complex inbound traffic engineering, and (2) hyper-giants having to map end-user requests to appropriate servers. We report on our multi-year experience in designing, building, rolling-out, and operating the first-ever large scale system, the Flow Director, which enables automated cooperation between one of the largest eyeball networks and a leading hyper-giant. We use empirical data collected at the eyeball network to evaluate its impact over two years of operation. We find very high compliance of the hyper-giant to the Flow Director’s recommendations, resulting in (1) close to optimal user-server mapping, and (2) 15% reduction of the hyper-giant’s traffic overhead on the ISP’s long-haul links, i.e., benefits for both parties and end-users alike.EC/H2020/679158/EU/Resolving the Tussle in the Internet: Mapping, Architecture, and Policy Making/ResolutioNe

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