Mixed Map Labeling

Point feature map labeling is a geometric problem, in which a set of input points must be labeled with a set of disjoint rectangles (the bounding boxes of the label texts). Typically, labeling models either use internal labels, which must touch their feature point, or external (boundary) labels, which are placed on one of the four sides of the input points' bounding box and which are connected to their feature points by crossing-free leader lines. In this paper we study polynomial-time algorithms for maximizing the number of internal labels in a mixed labeling model that combines internal and external labels. The model requires that all leaders are parallel to a given orientation $\theta \in [0,2\pi)$, whose value influences the geometric properties and hence the running times of our algorithms.Comment: Full version for the paper accepted at CIAC 201

Agglomerative Clustering of Growing Squares

We study an agglomerative clustering problem motivated by interactive glyphs in geo-visualization. Consider a set of disjoint square glyphs on an interactive map. When the user zooms out, the glyphs grow in size relative to the map, possibly with different speeds. When two glyphs intersect, we wish to replace them by a new glyph that captures the information of the intersecting glyphs. We present a fully dynamic kinetic data structure that maintains a set of $n$ disjoint growing squares. Our data structure uses $O(n (\log n \log\log n)^2)$ space, supports queries in worst case $O(\log^3 n)$ time, and updates in $O(\log^7 n)$ amortized time. This leads to an $O(n\alpha(n)\log^7 n)$ time algorithm to solve the agglomerative clustering problem. This is a significant improvement over the current best $O(n^2)$ time algorithms.Comment: 14 pages, 7 figure

Dynamic Data Structures for k-Nearest Neighbor Queries

Our aim is to develop dynamic data structures that support $k$-nearest neighbors ($k$-NN) queries for a set of $n$ point sites in the plane in $O(f(n) + k)$ time, where $f(n)$ is some polylogarithmic function of $n$. The key component is a general query algorithm that allows us to find the $k$-NN spread over $t$ substructures simultaneously, thus reducing an $O(tk)$ term in the query time to $O(k)$. Combining this technique with the logarithmic method allows us to turn any static $k$-NN data structure into a data structure supporting both efficient insertions and queries. For the fully dynamic case, this technique allows us to recover the deterministic, worst-case, $O(\log^2n/\log\log n +k)$ query time for the Euclidean distance claimed before, while preserving the polylogarithmic update times. We adapt this data structure to also support fully dynamic \emph{geodesic} $k$-NN queries among a set of sites in a simple polygon. For this purpose, we design a shallow cutting based, deletion-only $k$-NN data structure. More generally, we obtain a dynamic planar $k$-NN data structure for any type of distance functions for which we can build vertical shallow cuttings. We apply all of our methods in the plane for the Euclidean distance, the geodesic distance, and general, constant-complexity, algebraic distance functions

Effects of fermentable starch and straw-enriched housing on energy partitioning of growing pigs

Both dietary fermentable carbohydrates and the availability of straw bedding potentially affect activity patterns and energy utilisation in pigs. The present study aimed to investigate the combined effects of straw bedding and fermentable carbohydrates (native potato starch) on energy partitioning in growing pigs. In a 2 × 2 factorial arrangement, 16 groups of 12 pigs (approximately 25 kg) were assigned to either barren housing or housing on straw bedding, and to native or pregelatinised potato starch included in the diet. Pigs were fed at approximately 2.5 times maintenance. Nitrogen and energy balances were measured per group during a 7-day experimental period, which was preceded by a 30-day adaptation period. Heat production and physical activity were measured during 9-min intervals. The availability of straw bedding increased both metabolisable energy (ME) intake and total heat production (P <0.001). Housing conditions did not affect total energy retention, but pigs on straw bedding retained more energy as protein (P <0.01) and less as fat (P <0.05) than barren-housed pigs. Average daily gain (P <0.001), ME intake (P <0.001) and energy retention (P <0.01) were lower in pigs on the native potato starch diet compared to those on the pregelatinised potato starch diet. Pigs on the pregelatinised potato starch diet showed larger fluctuations in heat production and respiration quotient over the 24-h cycle than pigs on the native potato starch diet, and a higher activity-related energy expenditure. The effect of dietary starch type on activity-related heat production depended, however, on housing type (P <0.05). In barren housing, activity-related heat production was less affected by starch type (16.1% and 13.7% of total heat production on the pregelatinised and native potato starch diet, respectively) than in straw-enriched housing (21.1% and 15.0% of the total heat production on the pregelatinised and native potato starch diet, respectively). In conclusion, the present study shows that the availability both of straw bedding and of dietary starch type, fermentable or digestible, affects energy utilisation and physical activity of pigs. The effects of housing condition on protein and fat deposition suggest that environmental enrichment with long straw may result in leaner pigs. The lower energy expenditure on the physical activity of pigs on the native potato starch diet, which was the most obvious in straw-housed pigs, likely reflects a decrease in foraging behaviour related to a more gradual supply of energy from fermentation processes

Homotopy Measures for Representative Trajectories

An important task in trajectory analysis is defining a meaningful representative for a cluster of similar trajectories. Formally defining and computing such a representative r is a challenging problem. We propose and discuss two new definitions, both of which use only the geometry of the input trajectories. The definitions are based on the homotopy area as a measure of similarity between two curves, which is a minimum area swept by all possible deformations of one curve into the other. In the first definition we wish to minimize the maximum homotopy area between r and any input trajectory, whereas in the second definition we wish to minimize the sum of the homotopy areas between r and the input trajectories. For both definitions computing an optimal representative is NP-hard. However, for the case of minimizing the sum of the homotopy areas, an optimal representative can be found efficiently in a natural class of restricted inputs, namely, when the arrangement of trajectories forms a directed acyclic graph

Развитие финансово-кредитной инфраструктуры национальной экономики

We introduce a variation of unit-distance graphs which we call emph clear unit-distance graphs. They require the pairwise distances of the representing points to be either exactly 1 or not close to 1. We discuss properties and applications of clear unit-distance graphs