相关论文: Areal Optimization of Polygons

Compacting orthogonal drawings is a challenging task. Usually algorithms try to compute drawings with small area or edge length while preserving the underlying orthogonal shape. We present a one-dimensional compaction algorithm that alters…

Consider an arrangement of $k$ lines intersecting the unit square. There is some minimum scaling factor so that any placement of a rectangle with aspect ratio $1 \times p$ with $p\geq 1$ must non-transversely intersect some portion of the…

Let $A_1,A_2,...,A_n$ be the vertices of a polygon with unit perimeter, that is $\sum_{i=1}^n |A_i A_{i+1}|=1$. We derive various tight estimates on the minimum and maximum values of the sum of pairwise distances, and respectively sum of…

This paper deals with the accomplishment of total area coverage of an arbitrary region using sensors with a finite sensing radius of rs. For a given region, we aim to obtain a deterministic placement of sensors which, apart from ensuring…

Finding an optimal alignment connecting two end-points in a specified corridor is a complex problem that requires solving three interrelated sub-problems, namely the horizontal alignment, vertical alignment and earthwork optimization…

The polygon $P$ is small if its diameter equals one. When $n=2^s$, it is still an open problem to find the maximum perimeter or the maximum width of a small $n$-gon. Motivated by Bingane's series of works, we improve the lower bounds for…

A convex polygon Q is circumscribed about a convex polygon P if every vertex of P lies on at least one side of Q. We present an algorithm for finding a maximum area convex polygon circumscribed about any given convex n-gon in O(n^3) time.…

This second part on polygons in the hyperbolic plane is based on the first part which deals with uniqueness and existence of cocyclic polygons with prescribed sidelengths. The topic here is the maximum question for the area of these…

A rectilinear polygon is a polygon whose edges are axis-aligned. Walking counterclockwise on the boundary of such a polygon yields a sequence of left turns and right turns. The number of left turns always equals the number of right turns…

Partitioning and grouping of similar objects plays a fundamental role in image segmentation and in clustering problems. In such problems a typical goal is to group together similar objects, or pixels in the case of image processing. At 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…

New algorithms are devised for finding the maxima of multidimensional point samples, one of the very first problems studied in computational geometry. The algorithms are very simple and easily coded and modified for practical needs. The…

We analyze the asymptotic properties of a Euclidean optimization problem on the plane. Specifically, we consider a network with three bins and $n$ objects spatially uniformly distributed, each object being allocated to a bin at a cost…

The paper deals with optimality issues in connection with updating beliefs in networks. We address two processes: triangulation and construction of junction trees. In the first part, we give a simple algorithm for constructing an optimal…

Detecting polygons defined by a set of line segments in a plane is an important step in analyzing vector drawings. This paper presents an approach combining several algorithms to detect basic polygons from arbitrary line segments. The…

We analyze the structure of networks minimizing the global resistance to flow (or dissipated energy) with respect to two different constraints: fixed total channel volume and fixed total channel surface area. First, we determine the shape…

Given $n$ pairs of points, $\mathcal{S} = \{\{p_1, q_1\}, \{p_2, q_2\}, \dots, \{p_n, q_n\}\}$, in some metric space, we study the problem of two-coloring the points within each pair, red and blue, to optimize the cost of a pair of…

This paper discusses the problem of covering and hitting a set of line segments $\cal L$ in ${\mathbb R}^2$ by a pair of axis-parallel squares such that the side length of the larger of the two squares is minimized. We also discuss the…

Coupled-wire constructions have proven to be useful tools to characterize Abelian and non-Abelian topological states of matter in two spatial dimensions. In many cases, their success has been complemented by the vast arsenal of other…

We consider the problem of packing rectangles into bins that are unit squares, where the goal is to minimize the number of bins used. All rectangles have to be packed non-overlapping and orthogonal, i.e., axis-parallel. We present an…