Early Experiences in Traffic Engineering Exploiting Path Diversity: A Practical Approach

Recent literature has proved that stable dynamic routing algorithms have solid theoretical foundation that makes them suitable to be implemented in a real protocol, and used in practice in many different operational network contexts. Such algorithms inherit much of the properties of congestion controllers implementing one of the possible combination of AQM/ECN schemes at nodes and flow control at sources. In this paper we propose a linear program formulation of the multi-commodity flow problem with congestion control, under max-min fairness, comprising demands with or without exogenous peak rates. Our evaluations of the gain, using path diversity, in scenarios as intra-domain traffic engineering and wireless mesh networks encourages real implementations, especially in presence of hot spots demands and non uniform traffic matrices. We propose a flow aware perspective of the subject by using a natural multi-path extension to current congestion controllers and show its performance with respect to current proposals. Since flow aware architectures exploiting path diversity are feasible, scalable, robust and nearly optimal in presence of flows with exogenous peak rates, we claim that our solution rethinked in the context of realistic traffic assumptions performs as better as an optimal approach with all the additional benefits of the flow aware paradigm

An Analysis of Phase Transition in NK Landscapes

In this paper, we analyze the decision version of the NK landscape model from the perspective of threshold phenomena and phase transitions under two random distributions, the uniform probability model and the fixed ratio model. For the uniform probability model, we prove that the phase transition is easy in the sense that there is a polynomial algorithm that can solve a random instance of the problem with the probability asymptotic to 1 as the problem size tends to infinity. For the fixed ratio model, we establish several upper bounds for the solubility threshold, and prove that random instances with parameters above these upper bounds can be solved polynomially. This, together with our empirical study for random instances generated below and in the phase transition region, suggests that the phase transition of the fixed ratio model is also easy

Computing Expectations with Continuous P-Boxes: Univariate Case

Given an imprecise probabilistic model over a continuous space, computing lower/upper expectations is often computationally hard to achieve, even in simple cases. Because expectations are essential in decision making and risk analysis, tractable methods to compute them are crucial in many applications involving imprecise probabilistic models. We concentrate on p-boxes (a simple and popular model), and on the computation of lower expectations of non-monotone functions. This paper is devoted to the univariate case, that is where only one variable has uncertainty. We propose and compare two approaches : the first using general linear programming, and the second using the fact that p-boxes are special cases of random sets. We underline the complementarity of both approaches, as well as the differences.Comment: 31 pages, 6 figures, constitute an extended version of a small paper accepted in ISIPTA conference, and a preprint version of a paper accepted in IJA

Reconstruction of biological networks by supervised machine learning approaches

We review a recent trend in computational systems biology which aims at using pattern recognition algorithms to infer the structure of large-scale biological networks from heterogeneous genomic data. We present several strategies that have been proposed and that lead to different pattern recognition problems and algorithms. The strenght of these approaches is illustrated on the reconstruction of metabolic, protein-protein and regulatory networks of model organisms. In all cases, state-of-the-art performance is reported

Distributed Power Allocation with Rate Constraints in Gaussian Parallel Interference Channels

This paper considers the minimization of transmit power in Gaussian parallel interference channels, subject to a rate constraint for each user. To derive decentralized solutions that do not require any cooperation among the users, we formulate this power control problem as a (generalized) Nash equilibrium game. We obtain sufficient conditions that guarantee the existence and nonemptiness of the solution set to our problem. Then, to compute the solutions of the game, we propose two distributed algorithms based on the single user waterfilling solution: The \emph{sequential} and the \emph{simultaneous} iterative waterfilling algorithms, wherein the users update their own strategies sequentially and simultaneously, respectively. We derive a unified set of sufficient conditions that guarantee the uniqueness of the solution and global convergence of both algorithms. Our results are applicable to all practical distributed multipoint-to-multipoint interference systems, either wired or wireless, where a quality of service in terms of information rate must be guaranteed for each link.Comment: Paper submitted to IEEE Transactions on Information Theory, February 17, 2007. Revised January 11, 200

Aerodynamic design optimisation for complex geometries using unstructured grids

These lecture notes, prepared for the 1997 VKI Lecture Course on Inverse Design, discuss the use of unstructured grid CFD methods in the design of complex aeronautical geometries. The emphasis is on gradient-based optimisation approaches. The evaluation of approximate and exact linear sensitivities is described, as are different ways of formulating the adjoint equations to greatly reduce the computational cost when dealing with large numbers of design parameters. \ud \ud The current state-of-the-art is illustrated by two examples from turbomachinery and aircraft design

Normal, Abby Normal, Prefix Normal

A prefix normal word is a binary word with the property that no substring has more 1s than the prefix of the same length. This class of words is important in the context of binary jumbled pattern matching. In this paper we present results about the number $pnw(n)$ of prefix normal words of length $n$, showing that $pnw(n) =\Omega\left(2^{n - c\sqrt{n\ln n}}\right)$ for some $c$ and $pnw(n) = O \left(\frac{2^n (\ln n)^2}{n}\right)$. We introduce efficient algorithms for testing the prefix normal property and a "mechanical algorithm" for computing prefix normal forms. We also include games which can be played with prefix normal words. In these games Alice wishes to stay normal but Bob wants to drive her "abnormal" -- we discuss which parameter settings allow Alice to succeed.Comment: Accepted at FUN '1