Related papers: Two New Algorithms for Line Clipping in E2 and The…
In this paper we consider several instances of the k-center on a line problem where the goal is, given a set of points S in the plane and a parameter k >= 1, to find k disks with centers on a line l such that their union covers S and the…
Considering a 2D matrix of positive and negative numbers, how might one draw a rectangle within it whose contents sum higher than all other rectangles'? This fundamental problem, commonly known the maximum rectangle problem or subwindow…
An efficient computer algorithm is described for the perspective drawing of a wide class of surfaces. The class includes surfaces corresponding lo single-valued, continuous functions which are defined over rectangular domains. The algorithm…
Let $P$ be a set of $n$ points in the plane. We consider a variation of the classical Erd\H{o}s-Szekeres problem, presenting efficient algorithms with $O(n^3)$ running time and $O(n^2)$ space complexity that compute: (1) A subset $S$ of $P$…
We present a novel 2D convex hull peeling algorithm for outlier detection, which repeatedly removes the point on the hull that decreases the hull's area the most. To find k outliers among n points, one simply peels k points. The algorithm…
Acceleration of algorithms is becoming a crucial problem, if larger data sets are to be processed. Evaluation of algorithms is mostly done by using computational geometry approach and evaluation of computational complexity. However in…
Many classical algorithms are known for computing the convex hull of a set of $n$ point in $\mathbb{R}^2$ using $O(n)$ space. For large point sets, whose size exceeds the size of the working space, these algorithms cannot be directly used.…
In this paper we aim to bring new approach into usage of Shoelace Algorithm for area calculation in convex polygons on Cartesian coordinate system, with concentration on point in polygon concept. Generalization of usage of the concept will…
We study a class of integer bilevel programs with second-order cone constraints at the upper-level and a convex-quadratic objective function and linear constraints at the lower-level. We develop disjunctive cuts (DCs) to separate…
Sum-of-squares (SOS) optimization provides a computationally tractable framework for certifying polynomial nonnegativity. If the considered problem is convex, the SOS problem can be transcribed into and solved by semi-definite programs.…
Linear regression is a basic and widely-used methodology in data analysis. It is known that some quantum algorithms efficiently perform least squares linear regression of an exponentially large data set. However, if we obtain values of the…
There is an existing exact algorithm that solves DC programming problems if one component of the DC function is polyhedral convex (Loehne, Wagner, 2017). Motivated by this, first, we consider two cutting-plane algorithms for generating an…
Thinning is the removal of contour pixels/points of connected components in an image to produce their skeleton with retained connectivity and structural properties. The output requirements of a thinning procedure often vary with…
We propose a new framework for deriving screening rules for convex optimization problems. Our approach covers a large class of constrained and penalized optimization formulations, and works in two steps. First, given any approximate point,…
Man-made environments such as households, offices, or factory floors are typically composed of linear structures. Accordingly, polylines are a natural way to accurately represent their geometry. In this paper, we propose a novel…
Cutting plane methods are a fundamental approach for solving integer linear programs (ILPs). In each iteration of such methods, additional linear constraints (cuts) are introduced to the constraint set with the aim of excluding the previous…
We survey the main formulations and solution methods for two-dimensional orthogonal cutting and packing problems, where both items and bins are rectangles. We focus on exact methods and relaxations for the four main problems from the…
Higher-dimensional orthogonal packing problems have a wide range of practical applications, including packing, cutting, and scheduling. Combining the use of our data structure for characterizing feasible packings with our new classes of…
We study the problem of finding neck-like features on a surface. Applications for such cuts include robotics, mesh segmentation, and algorithmic applications. We provide a new definition for a surface bottleneck -- informally, it is the…
We introduce a computational origami problem which we call the segment folding problem: given a set of $n$ line-segments in the plane the aim is to make creases along all segments in the minimum number of folding steps. Note that a folding…