We address the fundamental network design problem of constructing approximate minimum spanners. Our contributions are for the distributed setting, providing both algorithmic and hardness results. Our main hardness result shows that an α-approximation for the minimum directed kspanner problem for k ≥ 5 requires Ω(n/ √ α log n) rounds using deterministic algorithms or Ω( √ n/ √ α log n) rounds us...

This thesis consists of two papers studying online inference in general hidden Markov models using sequential Monte Carlo methods. The first paper present an novel algorithm, the particle-based, rapid incremental smoother (PaRIS), aimed at efficiently perform online approximation of smoothed expectations of additive state functionals in general hidden Markov models. The algorithm has, under wea...

Many practical applications are related to frequent sequential pattern mining, ranging from Web Usage Mining to Bioinformatics. To ensure an appropriate extraction cost for useful mining tasks, a key issue is to push the user-defined constraints deep inside the mining algorithms. In this paper, we study the search for frequent sequential patterns that are also similar to an user-defined referen...

Making an early classification in longitudinal data is highly desirable. For this purpose, a sequential classifier that incorporates a neutral zone framework is proposed. The classification procedure evaluates each subject sequentially at each longitudinal time point. If there is not adequate confidence in making a classification at a given time point, the decision will wait until the next time...

The process of finding interesting, novel, and useful patterns from data is now commonly known as Knowledge Discovery and Data mining (KDD). In this paper, we examine closely the problem of mining sequential patterns and propose a general evaluation method to assess the quality of the mined results. We propose four evaluation criteria, namely (1) recoverability, (2) the number of spurious patte...

The problem of finding the nearest positive semidefinite Hankel matrix of a given rank to an arbitrary matrix is considered. The problem is formulated as a nonlinear minimization problem with positive semidefinite Hankel matrix as constraints. Then an algorithm with rapid convergence is obtained by the Sequential Quadratic Programming (SQP) method. A second approach is to formulate the problem ...

Given a set S of n points in the plane, an -strongly convex -hull of S is de0ned as a convex polygon P with the vertices taken from S such that no point of S lies farther than outside P and such that even if the vertices of P are perturbed by as much as , P remains convex. This paper presents the 0rst parallel robust method for this generalized convex hull problem (note that the convex hull of ...