Related papers: Randomized Triangle Algorithms for Convex Hull Mem…
The random triangular group $\Gamma(n,p)$ is the group given by a random group presentation with $n$ generators in which every relator of length three is present independently with probability $p$. We show that in the evolution of…
This paper aims to investigate the distributed stochastic optimization problems on compact embedded submanifolds (in the Euclidean space) for multi-agent network systems. To address the manifold structure, we propose a distributed…
A quadratically constrained quadratic program (QCQP) is an optimization problem in which the objective function is a quadratic function and the feasible region is defined by quadratic constraints. Solving non-convex QCQP to global…
Let $P\subset\mathbb{R}^{2}$ be a set of $n$ points. In this paper we show two new algorithms, one to compute the number of triangulations of $P$, and one to compute the number of pseudo-triangulations of $P$. We show that our algorithms…
We introduce a modified model of random walk, and then develop two novel clustering algorithms based on it. In the algorithms, each data point in a dataset is considered as a particle which can move at random in space according to the…
Linear optimization problems are investigated whose parameters are uncertain. We apply coherent distortion risk measures to capture the possible violation of a restriction. Each risk constraint induces an uncertainty set of coefficients,…
In this paper we study the statistical properties of convex hulls of $N$ random points in a plane chosen according to a given distribution. The points may be chosen independently or they may be correlated. After a non-exhaustive survey of…
Triangulation of a three-dimensional point from at least two noisy 2-D images can be formulated as a quadratically constrained quadratic program. We propose an algorithm to extract candidate solutions to this problem from its semidefinite…
What is the probability that a random triangle is acute? We explore this old question from a modern viewpoint, taking into account linear algebra, shape theory, numerical analysis, random matrix theory, the Hopf fibration, and much much…
Much prior work has been done on designing computational geometry algorithms that handle input degeneracies, data imprecision, and arithmetic round-off errors. We take a new approach, inspired by the noisy sorting literature, and study…
Triangle strips have been widely used for efficient rendering. It is NP-complete to test whether a given triangulated model can be represented as a single triangle strip, so many heuristics have been proposed to partition models into few…
We study the following metric distortion problem: there are two finite sets of points, $V$ and $C$, that lie in the same metric space, and our goal is to choose a point in $C$ whose total distance from the points in $V$ is as small as…
This thesis is divided in two parts. The first presents an overview of known results in statistical mechanics of disordered systems and its approach to random combinatorial optimization problems. The second part is a discussion of two…
We have developed a general Bayesian algorithm for determining the coordinates of points in a three-dimensional space. The algorithm takes as input a set of probabilistic constraints on the coordinates of the points, and an a priori…
We present a novel recursive algorithm for reducing a symmetric matrix to a triangular factorization which reveals the rank profile matrix. That is, the algorithm computes a factorization $\mathbf{P}^T\mathbf{A}\mathbf{P} =…
We analyze a simple randomized subgradient method for approximating solutions to stochastic systems of convex functional constraints, the only input to the algorithm being the size of minibatches. By introducing a new notion of what is…
We introduce the notion of quadratic hull of a linear code, and give some of its properties. We then show that any symmetric bilinear multiplication algorithm for a finite-dimensional algebra over a field can be obtained by…
Without randomization, escaping the saddle points of $f \colon \mathbb{R}^d \to \mathbb{R}$ requires at least $\Omega(d)$ pieces of information about $f$ (values, gradients, Hessian-vector products). With randomization, this can be reduced…
We developed a corporative stochastic approximation (CSA) type algorithm for semi-infinite programming (SIP), where the cut generation problem is solved inexactly. First, we provide general error bounds for inexact CSA. Then, we propose two…
In this article, a new solution for the convex hull problem has been presented. The convex hull is a widely known problem in computational geometry. As nature is a rich source of ideas in the field of algorithms, the solution has been…