Related papers: Minimum Partition of Polygons under Width and Cut …
A planar point set is in convex position precisely when it has a convex polygonization, that is, a polygonization with maximum interior angle measure at most \pi. We can thus talk about the convexity of a set of points in terms of the…
We study the query version of constrained minimum link paths between two points inside a simple polygon $P$ with $n$ vertices such that there is at least one point on the path, visible from a query point. The method is based on partitioning…
The problem of minimizing convex functionals of probability distributions is solved under the assumption that the density of every distribution is bounded from above and below. A system of sufficient and necessary first-order optimality…
We prove that every unit area convex pentagon is contained in a convex quadrilateral of area no greater than $3/\sqrt{5}$, and that every unit area convex hexagon is contained in a convex pentagon of area no greater than $7/6$. Both results…
Counting Euclidean triangulations with vertices in a finite set $\C$ of the convex hull $\conv(\C)$ of $\C$ is difficult in general, both algorithmically and theoretically. The aim of this paper is to describe nearly convex polygons, a…
In a rectilinear dual of a planar graph vertices are represented by simple rectilinear polygons and edges are represented by side-contact between the corresponding polygons. A rectilinear dual is called a cartogram if the area of each…
There exist many variants of guarding an orthogonal polygon in an orthogonal fashion: sometimes a guard can see an entire rectangle, or along a staircase, or along an orthogonal path with at most $k$ bends. In this paper, we study all these…
We present a polynomial time dynamic programming algorithm for optimal partitions in the shortest path metric induced by a tree. This resolves, among other things, the exact complexity status of the optimal partition problems in one…
We describe an algorithm for computing the separating common tangents of two simple polygons using linear time and only constant workspace. A tangent of a polygon is a line touching the polygon such that all of the polygon lies to the same…
Given a set $P$ of $n$ points in the plane, its separability is the minimum number of lines needed to separate all its pairs of points from each other. We show that the minimum number of lines needed to separate $n$ points, picked randomly…
If an n-side unit regular polygon is divided into m equal sized parts, then what is the minimum length of the split line ${l_{m,n}}$? This problem has its practical application in real world. This paper proved that ${l_{2,3}} = \sqrt…
This article presents uniform random generators of plane partitions according to the size (the number of cubes in the 3D interpretation). Combining a bijection of Pak with the method of Boltzmann sampling, we obtain random samplers that are…
We will first solve the following problem analytically: given a piece of wire of specified length, we will find where the wire should be cut and bent to form two regular polygons not necessarily having the same number of sides, so that the…
Triangulation algorithms that conform to a set of non-intersecting input segments typically proceed in an incremental fashion, by inserting points first, and then segments. Inserting a segment amounts to: (1) deleting all the triangles it…
Bounds on the log partition function are important in a variety of contexts, including approximate inference, model fitting, decision theory, and large deviations analysis. We introduce a new class of upper bounds on the log partition…
Let $n$ be a positive integer, not a power of two. A \textit{Reinhardt polygon} is a convex $n$-gon that is optimal in three different geometric optimization problems: it has maximal perimeter relative to its diameter, maximal width…
The long-standing problem of minimal projections is addressed from a computational point of view. Techniques to determine bounds on the projection constants of univariate polynomial spaces are presented. The upper bound, produced by a…
Consider two axis-aligned rectilinear simple polygons in the domain consisting of axis-aligned rectilinear obstacles in the plane such that the bounding boxes, one for each obstacle and one for each polygon, are disjoint. We present an…
Since its inception, Benders Decomposition (BD) has been successfully applied to a wide range of large-scale mixed-integer (linear) problems. The key element of BD is the derivation of Benders cuts, which are often not unique. In this…
We prove that, among all convex hyperbolic polygons with given angles, the perimeter is minimized by the unique polygon with an inscribed circle. The proof relies on work of J.-M.\ Schlenker.