Related papers: CUDA implementation of Wagener's 2D convex hull PR…

We consider the problem of characterizing the convex hull of the graph of a bilinear function $f$ on the $n$-dimensional unit cube $[0,1]^n$. Extended formulations for this convex hull are obtained by taking subsets of the facets of the…

We describe an algorithm for computing the convex hull of a finite collection of points in the affine building of SL_d(K), for K a field with discrete valuation. These convex hulls describe the relations among a finite collection of…

Seeking the convex hull of an object is a very fundamental problem arising from various tasks. In this work, we propose two variational convex hull models using level set representation for 2-dimensional data. The first one is an exact…

This work puts forward a form finding problem of designing a least-volume vault that is a surface structure spanning over a plane region, which via pure compression transfers a vertically tracking load to the supporting boundary. Through a…

Efficient GPU execution of convolution operators is governed by memory-access efficiency, on-chip data reuse, and execution mapping rather than arithmetic throughput alone. This paper presents a controlled operator-level study of CUDA…

We consider polyhedral approximations of strictly convex compacta in finite dimensional Euclidean spaces (such compacta are also uniformly convex). We obtain the best possible estimates for errors of considered approximations in the…

We present sample CUDA programs for the GPU computing of the Swendsen-Wang multi-cluster spin flip algorithm. We deal with the classical spin models; the Ising model, the $q$-state Potts model, and the classical XY model. As for the…

In this paper, we propose a hybrid parallel programming approach for a numerical solution of a two-dimensional acoustic wave equation using an implicit difference scheme for a single computer. The calculations are carried out in an implicit…

The possibilities of exploiting the special structure of d.c. programs, which consist of optimizing the difference of convex functions, are currently more or less limited to variants of the DCA proposed by Pham Dinh Tao and Le Thi Hoai An…

We propose a cut-based algorithm for finding all vertices and all facets of the convex hull of all integer points of a polyhedron defined by a system of linear inequalities. Our algorithm DDM Cuts is based on the Gomory cuts and the dynamic…

We study the convex hulls of trajectories of polynomial dynamical systems. Such trajectories include real algebraic curves. The boundaries of the resulting convex bodies are stratified into families of faces. We present numerical algorithms…

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…

Convex hulls are useful as tight bounding proxies for a variety of tasks including collision detection, ray intersection, and distance computation. Unfortunately, the complexity of polyhedral convex hulls grows linearly with their input. We…

This paper introduces a parallel implementation in CUDA/C++ of the Gaussian process with a decomposed kernel. This recent formulation, introduced by Joukov and Kuli\'c (2022), is characterized by an approximated -- but much smaller --…

Two-dimensional patterns are used in many research areas in computer science, ranging from image processing to specification and verification of complex software systems (via scenarios). The contribution of this paper is twofold. First, we…

Globally non-positively curved, or CAT(0), polyhedral complexes arise in a number of applications, including evolutionary biology and robotics. These spaces have unique shortest paths and are composed of Euclidean polyhedra, yet many…

Using CUDA as programming language, we create a code named CuBA which is based on the CPU code "Boltzmann Approach for Many Parton Scattering (BAMPS)" developed in Frankfurt in order to study a system of many colliding particles resulting…

This paper reviews some recent applications of the theory of the compensated convex transforms or of the proximity hull as developed by the authors to image processing and shape interrogation with special attention given to the Hausdorff…

Arithmetic automata recognize infinite words of digits denoting decompositions of real and integer vectors. These automata are known expressive and efficient enough to represent the whole set of solutions of complex linear constraints…

These notes accompany the open-source code published in GitHub which implements a GPU-based line-segment, surface-triangle intersection algorithm in CUDA. It mentions some relevant works and discusses issues specific to this implementation.…