This paper investigates the following natural greedy procedure for clustering in the bi-criterion setting: iteratively grow a set of centers, in each round adding the center from a candidate set that maximally decreases clustering cost. In the case of k-medians and k-means, the key results are as follows. • When the method considers all data points as candidate centers, then selecting O(k log(1...

Given a directed graph with capacities on each arc and given a set of commodities, the QoS constrained Routing Problem (QCRP) consists in routing each commodity while respecting a endto-end upper bound on the delay for each packet. This problem is NP-hard and we propose an augmented Lagrangean approach to solve it. A flow deviation algorithm as well as a projected gradient method are proposed t...

We investigate the problem of estimating a random variable Y ∈ Y under a privacy constraint dictated by another correlated random variable X ∈ X , where estimation efficiency and privacy are assessed in terms of two different loss functions. In the discrete case, we use the Hamming loss function and express the corresponding utility-privacy tradeoff in terms of the privacy-constrained guessing ...

Kleinberg [17] proposed in 2000 the first random graph model achieving to reproduce small world navigability, i.e. the ability to greedily discover polylogarithmic routes between any pair of nodes in a graph, with only a partial knowledge of distances. Following this seminal work, a major challenge was to extend this model to larger classes of graphs than regular meshes, introducing the concept...

We present a new derivative-free trust-region (DFTR) algorithm to solve general nonlinear constrained problems with the use of an augmented Lagrangian method. No derivatives are used, neither for the objective function nor for the constraints. An augmented Lagrangian method, known as an effective tool to solve equality and inequality constrained optimization problems with derivatives, is exploi...

We consider the problem of maximizing the secure connectivity in wireless ad hoc networks, and analyze complexity of the postdeployment key establishment process constrained by physical layer properties such as connectivity, energy consumption and interference. Two approaches, based on graph augmentation problems with nonlinear edge costs, are formulated. The first one is based on establishing ...

This paper is aimed toward the definition of a new exact augmented Lagrangian function for two-sided inequality constrained problems. The distinguishing feature of this augmented Lagrangian function is that it employs only one multiplier for each two-sided constraint. We prove that stationary points, local minimizers and global minimizers of the exact augmented Lagrangian function correspond ex...

The first main result of this paper is a novel nonuniform discretization approximation method for the kinodynamic motion-planning problem. The kinodynamic motion-planning problem is to compute a collision-free, time-optimal trajectory for a robot whose accelerations and velocities are bounded. Previous approximation methods are all based on a uniform discretization in the time space. On the con...