Состояние и перспективы развития рынка лакокрасочных материалов Украины

Целью статьи является рассмотрение состояние рынка лакокрасочных материалов Украины и мира на сегодняшний день, анализ объемов поставок и производства ЛКМ,а также разработка предложений по улучшению этой отрасли

Placing Arrows in Directed Graph Drawings

We consider the problem of placing arrow heads in directed graph drawings without them overlapping other drawn objects. This gives drawings where edge directions can be deduced unambiguously. We show hardness of the problem, present exact and heuristic algorithms, and report on a practical study.Comment: Appears in the Proceedings of the 24th International Symposium on Graph Drawing and Network Visualization (GD 2016

A linear programming approach to rectangular cartograms

In [26], the first two authors of this paper presented the first algorithms to construct rectangular cartograms. The first step is to determine a representation of all regions by rectangles and the second—most important—step is to get the areas of all rectangles correct. This paper presents a new approach to the second step. It is based on alternatingly solving linear programs on the x-coordinates and the y-coordinates of the sides of the rectangles. Our algorithm gives cartograms with considerably lower error and better visual qualities than previous approaches. It also handles countries that cannot be present in any purely rectangular cartogram and it introduces a new way of controlling incorrect adjacencies of countries. Our implementation computes aesthetically pleasing rectangular and nearly rectangular cartograms, for instance depicting the 152 countries of the World that have population over one million

Topologically correct subdivision simplification using the bandwidth criterion

The line simplification problem is an old and well studied problem in cartography. Although there are several algorithms to compute a simplification there seem to be no algorithms that perform line simplification in the context of other geographical objects. This paper presents a nearly quadratic time algorithm for the following line simplification problem: Given a polygonal line, a set of extra points, and a real ε> 0, compute a simplification that guarantees (i) a maximum error ; (ii) that the extra points remain on the same side of the simplified chain as of the original chain; and (iii) that the simplified chain has no self-intersections. The algorithm is applied as the main subroutine for subdivision simplification and guarantees that the resulting subdivision is topologically correct

Geometry and generation of a new graph planarity game

\u3cp\u3eWe introduce a new abstract graph game, Swap Planarity, where the goal is to reach a state without edge intersections and a move consists of swapping the locations of two vertices connected by an edge. We analyze this puzzle game using concepts from graph theory and graph drawing, computational geometry, and complexity. Furthermore, we specify quality criteria for puzzle instances, and describe a method to generate high-quality instances. We also report on experiments that show how well this generation process works.\u3c/p\u3

Geometry and generation of a new graph planarity game

We introduce a new abstract graph game, SWAP PLANARITY, where the goal is to reach a state without edge intersections and a move consists of swapping the locations of two vertices connected by an edge. We analyze this puzzle game using concepts from graph theory and graph drawing, computational geometry, and complexity. Furthermore, we specify what good levels look like and we show how they can be generated. We also report on experiments that show how well the generation works

Two-dimensional and three-dimensional point location in rectangular subdivisions

We apply van Emde Boas-type stratified trees to point location problems in rectangular subdivisions in 2 and 3 dimensions. In a subdivision with n rectangles having integer coordinates from [0, U - 1], we locate an integer query point in O((log log U)d) query time using O(n) space when d = 2 or O(n log log U) space when d = 3. Applications and extensions of this fixed universe approach include spatial point location using logarithmic time and linear space in rectilinear subdivisions having arbitrary coordinates, point location in c-oriented polygons or fat triangles in the plane, point location in subdivisions of space into fat prisms, and vertical ray shooting among horizontal fat objects. Like other results on stratified trees, our algorithms run on a RAM model and make use of perfect hashing

One-to-one point set matchings for grid map layout

We study several one-to-one point set matching problems which are motivated by layout problems for grid maps. We are given two sets A and B of n points in the plane, and we wish to compute an optimal one-to-one matching between A and B. We consider two optimisation criteria: minimising the sum of the L1-distances between matched points, and maximising the number of pairs of points in A for which the matching preserves the directional relation. We show how to minimise the total L1-distance under translation or scaling in O(n6 log3 n) time, and under both translation and scaling in O(n10 log3 n) time. We further give a 4-approximation for preserving directional relations by computing a minimum L1-distance matching in O(n2 log3 n) time