Related papers: Natural Way of Solving a Convex Hull Problem
The safe linear bandit problem is a version of the classical stochastic linear bandit problem where the learner's actions must satisfy an uncertain constraint at all rounds. Due its applicability to many real-world settings, this problem…
In applications throughout science and engineering one is often faced with the challenge of solving an ill-posed inverse problem, where the number of available measurements is smaller than the dimension of the model to be estimated. However…
In this study, a geometric version of an NP-hard problem ("Almost $2-SAT$" problem) is introduced which has potential applications in clustering, separation axis, binary sensor networks, shape separation, image processing, etc. Furthermore,…
Convex hulls are fundamental geometric tools used in a number of algorithms. This paper presents a fast, simple to implement and robust Smart Convex Hull (S-CH) algorithm for computing the convex hull of a set of points in E3. This…
A set in the Euclidean plane is said to be biconvex if, for some angle $\theta\in[0,\pi/2)$, all its sections along straight lines with inclination angles $\theta$ and $\theta+\pi/2$ are convex sets (i.e, empty sets or segments).…
Motivated by the desire to cope with data imprecision, we study methods for taking advantage of preliminary information about point sets in order to speed up the computation of certain structures associated with them. In particular, we…
We describe an algorithm for solving an important geometric problem arising in computer-aided manufacturing. When cutting away a region from a solid piece of material -- such as steel, wood, ceramics, or plastic -- using a rough tool in a…
This paper investigates the transformation of a convex hull, derived from a d-dimensional point cloud, into a concave surface. Our primary focus is on the development of a methodology that ensures all points in the point cloud are…
We prove that the combinatorial optimization problem of determining the hull number of a partial cube is NP-complete. This makes partial cubes the minimal graph class for which NP-completeness of this problem is known and improves some…
Let $P$ be a set of $n$ points in $\mathbb{R}^3$ in general position, and let $RCH(P)$ be the rectilinear convex hull of $P$. In this paper we obtain an optimal $O(n\log n)$-time and $O(n)$-space algorithm to compute $RCH(P)$. We also…
The convex rope problem is to find a counterclockwise or clockwise convex rope starting at the vertex a and ending at the vertex b of a simple polygon P, where a is a vertex of the convex hull of P and b is visible from infinity. The convex…
Bounding hull, such as convex hull, concave hull, alpha shapes etc. has vast applications in different areas especially in computational geometry. Alpha shape and concave hull are generalizations of convex hull. Unlike the convex hull, they…
An incremental approach for computation of convex hull for data points in two-dimensions is presented. The algorithm is not output-sensitive and costs a time that is linear in the size of data points at input. Graham's scan is applied only…
We investigate robust optimization problems defined for maximizing convex functions. For finite uncertainty set, we develop a geometric branch-and-bound algorithmic approach to solve this problem. The geometric branch-and-bound algorithm…
A set $S \subset \mathbb{Z}^d$ is digital convex if $conv(S) \cap \mathbb{Z}^d = S$, where $conv(S)$ denotes the convex hull of $S$. In this paper, we consider the algorithmic problem of testing whether a given set $S$ of $n$ lattice points…
This paper develops a general framework for solving a variety of convex cone problems that frequently arise in signal processing, machine learning, statistics, and other fields. The approach works as follows: first, determine a conic…
A simple method for some class of inverse obstacle scattering problems is introduced. The observation data are given by a wave field measured on a known surface surrounding unknown obstacles over a finite time interval. The wave is…
It is well known that the convex hull of $\{(x,y,xy)\}$, where $(x,y)$ is constrained to lie in a box, is given by the Reformulation-Linearization Technique (RLT) constraints. Belotti {\em et al.\,}(2010) and Miller {\em et al.\,}(2011)…
Given a point set $P$ in the plane, we seek a subset $Q\subseteq P$, whose convex hull gives a smaller and thus simpler representation of the convex hull of $P$. Specifically, let $cost(Q,P)$ denote the Hausdorff distance between the convex…
A new approach to the local and global explanation is proposed. It is based on selecting a convex hull constructed for the finite number of points around an explained instance. The convex hull allows us to consider a dual representation of…