On the Complexity of the Asymmetric VPN Problem

We give the first constant factor approximation algorithm for the asymmetric Virtual Private Network (VPN) problem with arbitrary concave costs. We even show the stronger result, that there is always a tree solution of cost at most 2 OPT and that a tree solution of (expected) cost at most 49.84 OPT can be determined in polynomial time. Furthermore, we answer an outstanding open question about the complexity status of the so called balanced VPN problem by proving its NP-hardness

The VPN problems with concave costs

Only recently Goyal, Olver and Shepherd (Proc. STOC, 2008) proved that the symmetric Virtual Private Network Design (sVPN) problem has the tree routing property, namely, that there always exists an optimal solution to the problem whose support is a tree. Combining this with previous results by Fingerhut, Suri and Turner (J. Alg., 1997) and Gupta, Kleinberg, Kumar, Rastogi and Yener (Proc. STOC, 2001), sVPN can be solved in polynomial time. In this paper we investigate an APX-hard generalization of sVPN, where the contribution of each edge to the total cost is proportional to some non-negative, concave and non-decreasing function of the capacity reservation. We show that the tree routing property extends to the new problem, and give a constant-factor approximation algorithm for it. We also show that the undirected uncapacitated single-source minimum concave-cost flow problem has the tree routing property when the cost function has some property of symmetry

Dynamic vs Oblivious Routing in Network Design

Consider the robust network design problem of finding a minimum cost network with enough capacity to route all traffic demand matrices in a given polytope. We investigate the impact of different routing models in this robust setting: in particular, we compare \emph{oblivious} routing, where the routing between each terminal pair must be fixed in advance, to \emph{dynamic} routing, where routings may depend arbitrarily on the current demand. Our main result is a construction that shows that the optimal cost of such a network based on oblivious routing (fractional or integral) may be a factor of \BigOmega(\log{n}) more than the cost required when using dynamic routing. This is true even in the important special case of the asymmetric hose model. This answers a question in \cite{chekurisurvey07}, and is tight up to constant factors. Our proof technique builds on a connection between expander graphs and robust design for single-sink traffic patterns \cite{ChekuriHardness07}

Performance Analytics of Cloud Networks

As the world becomes more inter-connected and dependent on the Internet, networks become ever more pervasive, and the stresses placed upon them more demanding. Similarly, the expectations of networks to maintain a high level of performance have also increased. Network performance is highly important to any business that operates online, depends on web traffic, runs any part of their infrastructure in a cloud environment, or even hosts their own network infrastructure. Depending upon the exact nature of a network, whether it be local or wide-area, 10 or 100 Gigabit, it will have distinct performance characteristics and it is important for a business or individual operating on the network to understand those performance characteristics and how they affect operations. To better understand our networks, it is necessary that we test them to measure their performance capabilities and track these metrics over time. In our work, we provide an in-depth analysis of how best to run cloud benchmarks to increase our network intelligence and how we can use the results of those benchmarks to predict future performance and identify performance anomalies. To achieve this, we explain how to effectively run cloud benchmarks and propose a scheduling algorithm for running large numbers of cloud benchmarks daily. We then use the performance data gathered from this method to conduct a thorough analysis of the performance characteristics of a cloud network, train neural networks to forecast future throughput based on historical results and detect performance anomalies as they occur

Tax mix corners and other kinks

This paper models the local tax mix determination process in the presence of state-wide tax limitations and shows how excess sensitivity of local public spending to grants (the conventionally and somewhat misleadingly called flypaper effect) arises in the endogenously generated constrained tax mix and cannot in general be taken as a symptom of local government overspending. By means of a panel data switching regression approach that allows for fixed effects and endogenous selection, the paper exploits the clustering of Italian Provinces at the corners produced by upper and lower tax limitations, and provides evidence of considerable cap-generated excess sensitivity