RECOGNIZING WEIGHTED AND SEEDED DISK GRAPHS

Disk intersection representations realize graphs by mapping vertices bijectively to disks in the plane such that two disks intersect each other if and only if the corresponding vertices are adjacent in the graph. If intersections are restricted to touching points of the boundaries, we call them disk contact representations. Deciding whether a vertex-weighted planar graph can be realized such that the disks\u27 radii coincide with the vertex weights is known to be NP-hard for both contact and intersection representations. In this work, we reduce the gap between hardness and tractability by analyzing the problem for special graph classes. We show that in the contact scenario it remains NP-hard for outerplanar graphs with unit weights and for stars with arbitrary weights, strengthening the previous hardness results. On the positive side, we present a constructive linear-time recognition algorithm for embedded stars with arbitrary weights. We also consider a version of the problem in which the disks of a representation are supposed to cover preassigned points, called seeds. We show that both for contact and intersection representations this problem is NP-hard for unit weights even if the given graph is a path. If the disks\u27 radii are not prescribed, the problem remains NP-hard for trees in the contact scenario

The effect of high speed rotation on the performance of hydrostatic thrust bearings.

Hydrostatic bearings have been the subject of many theoretical and experimental investigations. Some investigations have confirmed that increasing the speed of rotation of a hydrostatic thrust bearing reduces the load carrying capacity. Previous theoretical predictions of the pressure distribution, during rotation, have not taken into account the radial inertia effects, with the result that the predicted values of pressure near the vicinity of the air inlet, have been much higher than those measured under test. In this investigation radial and rotational inertia effects have been considered theoretically and experimentally for both 'parallel' and 'stepped' bearings using air as the lubricant. The relevance of compressibility has also been assessed

On Embeddability of Buses in Point Sets

Set membership of points in the plane can be visualized by connecting corresponding points via graphical features, like paths, trees, polygons, ellipses. In this paper we study the \emph{bus embeddability problem} (BEP): given a set of colored points we ask whether there exists a planar realization with one horizontal straight-line segment per color, called bus, such that all points with the same color are connected with vertical line segments to their bus. We present an ILP and an FPT algorithm for the general problem. For restricted versions of this problem, such as when the relative order of buses is predefined, or when a bus must be placed above all its points, we provide efficient algorithms. We show that another restricted version of the problem can be solved using 2-stack pushall sorting. On the negative side we prove the NP-completeness of a special case of BEP.Comment: 19 pages, 9 figures, conference version at GD 201

Structure of mixed ombrophyllous forests with Araucaria angustifolia (Araucariaceae) under external stress in Southern Brazil.

This study is part of the Floristic and Forest Inventory of Santa Catarina, conceived to evaluate forest resources, species composition and structure of forest remnants, providing information to update forest conservation and land use policy in Southern Brazilian State of Santa Catarina (95 000km²). In accordance to the Brazilian National Forest Inventory (IFN-BR), the inventory applies systematic sampling, with 440 clusters containing four crosswise 1 000m² plots (20x50m) each, located on a 10x10km grid overlaid to land use map based on classification of SPOT-4 images from 2005. Within the sample units, all woody individuals of the main stratum (DBH?10cm) are measured and collected (fertile and sterile), if not undoubtedly identified in field. Regeneration stratum (height>1.50m; DBH<10cm) is registered in 100m² in each sample unit. Floristic sampling includes collection of all fertile trees, shrubs and herbs within the sample unit and in its surroundings. This study performs analysis based on 92 clusters measured in 2008 within an area of 32 320km² of mixed ombrophyllous forests with Araucaria angustifolia located at the state’s high plateau (500m to 1 560m above sea level at 26º00’-28º30’ S and 49º13’-51º23’ W). Mean density (DBH?10cm) is 578 individuals/ha (ranging from 85/ha to 1 310/ha), mean species richness in measured remnants is 35 (8 to 62), Shannon and Wiener diversity index (H’) varies between 1.05 and 3.48. Despite high total species diversity (364 Magnoliophyta, five Coniferophyta and one tree fern) and relatively high mean basal area (25.75m²/ha, varying from 3.87 to 68.85m²/ ha), the overwhelming majority of forest fragments are considered highly impacted and impoverished, mostly by logging, burning and extensive cattle farming, turning necessary more efficient protection measures. Basal area was considered an appropriate indicator for stand quality and conservation status

Constraint Generation Algorithm for the Minimum Connectivity Inference Problem

Given a hypergraph $H$, the Minimum Connectivity Inference problem asks for a graph on the same vertex set as $H$ with the minimum number of edges such that the subgraph induced by every hyperedge of $H$ is connected. This problem has received a lot of attention these recent years, both from a theoretical and practical perspective, leading to several implemented approximation, greedy and heuristic algorithms. Concerning exact algorithms, only Mixed Integer Linear Programming (MILP) formulations have been experimented, all representing connectivity constraints by the means of graph flows. In this work, we investigate the efficiency of a constraint generation algorithm, where we iteratively add cut constraints to a simple ILP until a feasible (and optimal) solution is found. It turns out that our method is faster than the previous best flow-based MILP algorithm on random generated instances, which suggests that a constraint generation approach might be also useful for other optimization problems dealing with connectivity constraints. At last, we present the results of an enumeration algorithm for the problem.Comment: 16 pages, 4 tables, 1 figur

Extending Upward Planar Graph Drawings

In this paper we study the computational complexity of the Upward Planarity Extension problem, which takes in input an upward planar drawing $\Gamma_H$ of a subgraph $H$ of a directed graph $G$ and asks whether $\Gamma_H$ can be extended to an upward planar drawing of $G$. Our study fits into the line of research on the extensibility of partial representations, which has recently become a mainstream in Graph Drawing. We show the following results. First, we prove that the Upward Planarity Extension problem is NP-complete, even if $G$ has a prescribed upward embedding, the vertex set of $H$ coincides with the one of $G$, and $H$ contains no edge. Second, we show that the Upward Planarity Extension problem can be solved in $O(n \log n)$ time if $G$ is an $n$-vertex upward planar $st$-graph. This result improves upon a known $O(n^2)$-time algorithm, which however applies to all $n$-vertex single-source upward planar graphs. Finally, we show how to solve in polynomial time a surprisingly difficult version of the Upward Planarity Extension problem, in which $G$ is a directed path or cycle with a prescribed upward embedding, $H$ contains no edges, and no two vertices share the same $y$-coordinate in $\Gamma_H$

AN OPTION OF HIGH CHARGE OPERATION FOR THE EUROPEAN XFEL

Abstract The 1.3 GHz superconducting accelerator developed in the framework of TESLA and the European XFEL project holds the potential to accelerate high charge electron beams. This feature has been successfully demonstrated during the first run of the free electron laser at the TESLA Test Facility with lasing driven by electron bunches with a charge of up to 4 nC. Currently DESY and the European XFEL GmbH perform revision of the baseline parameters for the electron beam. In this report we discuss a potential option of operation of the European XFEL driven by high charge (1 nC to 3 nC) electron beams. We present the results of the production and characterization of high charge electron bunches. Experiments have been performed at PITZ and demonstrated good properties of the electron beam in terms of emittance. Simulations of the radiation properties of SASE FELs show that application of high charge electron beams will open up the possibility to generate radiation pulse energies up to the few hundred milli-Joule level