Work Overview

1. Work Overview Mohammad Malli Planete Project, INRIA - Sophia Antipolis France

2. Motivation Delay proximity does not satisfy the requirements of many applications March 1, 2006

3. Scalable estimation of network distances We propose a model for estimating scalably ABw and P March 1, 2006

4. Distance Reconstruction after Matrix Sampling • Construct a matrix A representing the network distances among a set of nodes (e.g., lms) in a large scale network • Apply dimensionality reduction on the constructed matrix • The mostly used technique for dimensionality reduction is Principle Component Analysis (PCA) • PCA consists of constructing a matrix with A’s eigen vectors representing an Euclidean space where all peers should be positioned • Using PCA for sampling network distances matrices is not consistent with network topology since (i) distances are almost asymmetric, and (ii) the triangle inequality could not be satisfied March 1, 2006

5. Singular Value Decomposition SVD permits to reduce dimensionality while considering the properties of network distances (asymmetric, no triangulation) A is an NxN ABw matrixS is the NxN diagonal matrix with singular values of A arranged in a decreased orderV is the NxN matrix with eigen vectors of A arranged in columns March 1, 2006

6. SVD Algorithm 1. Keep the d singular values of S that are appreciable in magnitude and delete the others2. Define Nxd matrices: 3. With the constraint of minimizing the squared error function4. Then, the new estimated matrix is:5. For each peer Pi, the model associates two vectors Xi (outgoing vector) and Yi (incoming vector)6. The estimated distance from Hi to Hj is the dot product between the O.V. of Hi and the I.V. of Hj March 1, 2006

7. Ongoing Work Accomplishing and publishing the works on (i) loss rate estimation, and(ii) dimensionality reduction Preparing my thesis manuscript as the defense will be on September March 1, 2006