Orientation-Constrained Rectangular Layouts

We construct partitions of rectangles into smaller rectangles from an input consisting of a planar dual graph of the layout together with restrictions on the orientations of edges and junctions of the layout. Such an orientation-constrained layout, if it exists, may be constructed in polynomial time, and all orientation-constrained layouts may be listed in polynomial time per layout.Comment: To appear at Algorithms and Data Structures Symposium, Banff, Canada, August 2009. 12 pages, 5 figure

Combinatorial Properties of Triangle-Free Rectangle Arrangements and the Squarability Problem

We consider arrangements of axis-aligned rectangles in the plane. A geometric arrangement specifies the coordinates of all rectangles, while a combinatorial arrangement specifies only the respective intersection type in which each pair of rectangles intersects. First, we investigate combinatorial contact arrangements, i.e., arrangements of interior-disjoint rectangles, with a triangle-free intersection graph. We show that such rectangle arrangements are in bijection with the 4-orientations of an underlying planar multigraph and prove that there is a corresponding geometric rectangle contact arrangement. Moreover, we prove that every triangle-free planar graph is the contact graph of such an arrangement. Secondly, we introduce the question whether a given rectangle arrangement has a combinatorially equivalent square arrangement. In addition to some necessary conditions and counterexamples, we show that rectangle arrangements pierced by a horizontal line are squarable under certain sufficient conditions.Comment: 15 pages, 13 figures, extended version of a paper to appear at the International Symposium on Graph Drawing and Network Visualization (GD) 201

Threat of allergenic airborne grass pollen in Szczecin, NW Poland: the dynamics of pollen seasons, effect of meteorological variables and air pollution

The dynamics of Poaceae pollen season, in particularly that of the Secale genus, in Szczecin (western Poland) 2004–2008 was analysed to establish a relationship between the meteorological variables, air pollution and the pollen count of the taxa studied. Consecutive phases during the pollen season were defined for each taxon (1, 2.5, 5, 25, 50, 75, 95, 97.5, 99% of annual total), and duration of the season was determined using the 98% method. On the basis of this analysis, the temporary differences in the dynamics of the seasons were most evident for Secale in 2005 and 2006 with the longest main pollen season (90% total pollen). The pollen season of Poaceae started the earliest in 2007, when thermal conditions were the most favourable. Correlation analysis with meteorological factors demonstrated that the relative humidity, mean and maximum air temperature, and rainfall were the factors influencing the average daily pollen concentrations in the atmosphere; also, the presence of air pollutants such as ozone, PM10 and SO2 was statistically related to the pollen count in the air. However, multiple regression models explained little part of the total variance. Atmospheric pollution induces aggravation of symptoms of grass pollen allergy