相关论文: A Simple Circle Discretization Algorithm With Appl…

We consider methods for finding a simple polygon of minimum (Min-Area) or maximum (Max-Area) possible area for a given set of points in the plane. Both problems are known to be NP-hard; at the center of the recent CG Challenge, practical…

Gradient-based optimization methods are commonly used to identify local optima in high-dimensional spaces. When derivatives cannot be evaluated directly, stochastic estimators can provide approximate gradients. However, these estimators'…

Solutions of partial differential equations can often be written as surface integrals having a kernel related to a singular fundamental solution. Special methods are needed to evaluate the integral accurately at points on or near the…

Motivated by automated junction recognition in tracking data, we study a problem of placing a square or disc of fixed size in an arrangement of lines or line segments in the plane. We let distances among the intersection points of the lines…

We study the generalization of split, k-branch split, and intersection cuts from Mixed Integer Linear Programming to the realm of Mixed Integer Nonlinear Programming. Constructing such cuts requires calculating the convex hull of the…

This paper deals with exploiting symmetry for solving linear and integer programming problems. Basic properties of linear representations of finite groups can be used to reduce symmetric linear programming to solving linear programs of…

In this book chapter we survey known approaches and algorithms to compute discrepancy measures of point sets. After providing an introduction which puts the calculation of discrepancy measures in a more general context, we focus on the…

Applying dimensionality reduction (DR) to large, high-dimensional data sets can be challenging when distinguishing the underlying high-dimensional data clusters in a 2D projection for exploratory analysis. We address this problem by first…

Clustering a graph when the clusters can overlap can be seen from three different angles: We may look for cliques that cover the edges of the graph with bounded overlap, we may look to add or delete few edges to uncover the cluster…

Many problems of theoretical and practical interest involve finding an optimum over a family of convex functions. For instance, finding the projection on the convex functions in $H^k(\Omega)$, and optimizing functionals arising from some…

Distributed computation is a framework used to break down a complex computational task into smaller tasks and distributing them among computational nodes. Erasure correction codes have recently been introduced and have become a popular…

In this paper, we analyze the convergence of several discretize-then-optimize algorithms, based on either a second-order or a fourth-order finite difference discretization, for solving elliptic PDE-constrained optimization or optimal…

A trademark of nonlinear, time-dependent, convection-dominated problems is the spontaneous formation of non-smooth macro-scale features, like shock discontinuities and non-differentiable kinks, which pose a challenge for high-resolution…

The problem deals with an exact calculation of the intersection area of a circle arbitrary placed on a grid of square shaped elements with gaps between them (finite fill factor). Usually an approximation is used for the calculation of the…

Introduction of curvilinear coordinates might be very convenient in many cases. Theoretically, tensor analysis would be most suited. However, tensor notation can't be used in numerical procedure. For example, the strict discrimination of…

In this paper we study formulations and algorithms for the cycle clustering problem, a partitioning problem over the vertex set of a directed graph with nonnegative arc weights that is used to identify cyclic behavior in simulation data…

The set of all error-correcting codes C over a fixed finite alphabet F of cardinality q determines the set of code points in the unit square with coordinates (R(C), delta (C)):= (relative transmission rate, relative minimal distance). The…

In this paper we propose a generic algorithm to calculate the rotation parameters of CORDIC angles required for the Discrete Cosine Transform algorithm (DCT). This leads us to increase the precision of calculation meeting any accuracy.Our…

We consider the problem of solving a large-scale Quadratically Constrained Quadratic Program. Such problems occur naturally in many scientific and web applications. Although there are efficient methods which tackle this problem, they are…

A hierarchical scheme for clustering data is presented which applies to spaces with a high number of dimension ($N_{_{D}}>3$). The data set is first reduced to a smaller set of partitions (multi-dimensional bins). Multiple clustering…