An Interactive Tool to Explore and Improve the Ply Number of Drawings

Given a straight-line drawing $\Gamma$ of a graph $G=(V,E)$, for every vertex $v$ the ply disk $D_v$ is defined as a disk centered at $v$ where the radius of the disk is half the length of the longest edge incident to $v$. The ply number of a given drawing is defined as the maximum number of overlapping disks at some point in $\mathbb{R}^2$. Here we present a tool to explore and evaluate the ply number for graphs with instant visual feedback for the user. We evaluate our methods in comparison to an existing ply computation by De Luca et al. [WALCOM'17]. We are able to reduce the computation time from seconds to milliseconds for given drawings and thereby contribute to further research on the ply topic by providing an efficient tool to examine graphs extensively by user interaction as well as some automatic features to reduce the ply number.Comment: Appears in the Proceedings of the 25th International Symposium on Graph Drawing and Network Visualization (GD 2017

Multi-Step Processing of Spatial Joins

Spatial joins are one of the most important operations for combining spatial objects of several relations. In this paper, spatial join processing is studied in detail for extended spatial objects in twodimensional data space. We present an approach for spatial join processing that is based on three steps. First, a spatial join is performed on the minimum bounding rectangles of the objects returning a set of candidates. Various approaches for accelerating this step of join processing have been examined at the last year’s conference [BKS 93a]. In this paper, we focus on the problem how to compute the answers from the set of candidates which is handled by the following two steps. First of all, sophisticated approximations are used to identify answers as well as to filter out false hits from the set of candidates. For this purpose, we investigate various types of conservative and progressive approximations. In the last step, the exact geometry of the remaining candidates has to be tested against the join predicate. The time required for computing spatial join predicates can essentially be reduced when objects are adequately organized in main memory. In our approach, objects are first decomposed into simple components which are exclusively organized by a main-memory resident spatial data structure. Overall, we present a complete approach of spatial join processing on complex spatial objects. The performance of the individual steps of our approach is evaluated with data sets from real cartographic applications. The results show that our approach reduces the total execution time of the spatial join by factors

Minimizing the stabbing number of matchings, trees, and triangulations

The (axis-parallel) stabbing number of a given set of line segments is the maximum number of segments that can be intersected by any one (axis-parallel) line. This paper deals with finding perfect matchings, spanning trees, or triangulations of minimum stabbing number for a given set of points. The complexity of these problems has been a long-standing open question; in fact, it is one of the original 30 outstanding open problems in computational geometry on the list by Demaine, Mitchell, and O'Rourke. The answer we provide is negative for a number of minimum stabbing problems by showing them NP-hard by means of a general proof technique. It implies non-trivial lower bounds on the approximability. On the positive side we propose a cut-based integer programming formulation for minimizing the stabbing number of matchings and spanning trees. We obtain lower bounds (in polynomial time) from the corresponding linear programming relaxations, and show that an optimal fractional solution always contains an edge of at least constant weight. This result constitutes a crucial step towards a constant-factor approximation via an iterated rounding scheme. In computational experiments we demonstrate that our approach allows for actually solving problems with up to several hundred points optimally or near-optimally.Comment: 25 pages, 12 figures, Latex. To appear in "Discrete and Computational Geometry". Previous version (extended abstract) appears in SODA 2004, pp. 430-43

Wavelength-selected Neutron Pulses Formed by a Spatial Magnetic Neutron Spin Resonator

AbstractWe present a novel type of spatial magnetic neutron spin resonator whose time and wavelength resolution can be de- coupled from each other by means of a travelling wave mode of operation. Combined with a pair of highly efficient polarisers such a device could act simultaneously as monochromator and chopper, able to produce short neutron pulses, whose wavelength, spectral width and duration could be varied almost instantaneously by purely electronic means with- out any mechanical modification of the experimental setup. To demonstrate the practical feasibility of this technique we have designed and built a first prototype resonator consisting of ten individually switchable modules which allows to produce neutron pulses in the microsecond regime. It was installed at a polarised 2.6Å neutron beamline at the 250kW TRIGA research reactor of the Vienna University of Technology where it could deliver pulses of 55μs duration, which is about three times less than the passage time of the neutrons through the resonator itself. In order to further improve the achievable wavelength resolution to about 3% a second prototype resonator, consisting of 48 individual modules with optimised field homogeneity and enlarged beam cross-section of 6 × 6cm2 was developed. We present the results of first measurements which demonstrate the successful operation of this device

Distributed rate allocation in switch-based multiparty videoconference

Multiparty videoconferences, or more generally multiparty video calls, are gaining a lot of popularity as they offer a rich communication experience. These applications have however, large requirements in terms of both network and computational resources and have to deal with sets of heterogenous clients. The multiparty videoconferencing systems can be grouped in two classes. They are based either on expensive central nodes, called multipoint control units (MCU), with transcoding capabilities, or, on a peer-to-peer strategy where users help each other to distribute the different video streams. Whereas the first one requires an expensive central hardware, the second one depends completely on the redistribution capacity of the users, which sometimes might neither provide sufficient bandwidth nor be reliable enough. In this work we propose an alternative solution where we use a central node to distribute the video streams but at the same time we maintain the hardware complexity and the computational requirements of this node as low as possible. The proposed solution uses a distributed algorithm to allocate the users' rates in a Quality of Service (QoS) aware manner. The allocation algorithm is also extremely fast and is able to quickly reallocate the rates in case the conditions change. We have further implemented our solution in a network simulator where we show that our rate allocation algorithm is able to properly optimize users' QoS and adapt to dynamic changes in the system. We also illustrate the benefits of our solution in terms network usage and average utility when compared to a baseline heuristic method operating on the same system architecture

Geometric matrix midranges

We define geometric matrix midranges for positive definite Hermitian matrices and study the midrange problem from a number of perspectives. Special attention is given to the midrange of two positive definite matrices before considering the extension of the problem to $N > 2$ matrices. We compare matrix midrange statistics with the scalar and vector midrange problem and note the special significance of the matrix problem from a computational standpoint. We also study various aspects of geometric matrix midrange statistics from the viewpoint of linear algebra, differential geometry and convex optimization.ECH2020 EUROPEAN RESEARCH COUNCIL (ERC) (670645

Comparing apples and oranges: assessment of the relative video quality in the presence of different types of distortions

<p>Abstract</p> <p>Video quality assessment is essential for the performance analysis of visual communication applications. Objective metrics can be used for estimating the relative quality differences, but they typically give reliable results only if the compared videos contain similar types of quality distortion. However, video compression typically produces different kinds of visual artifacts than transmission errors. In this article, we focus on a novel subjective quality assessment method that is suitable for comparing different types of quality distortions. The proposed method has been used to evaluate how well different objective quality metrics estimate the relative subjective quality levels for content with different types of quality distortions. Our conclusion is that none of the studied objective metrics works reliably for assessing the co-impact of compression artifacts and transmission errors on the subjective quality. Nevertheless, we have observed that the objective metrics' tendency to either over- or underestimate the perceived impact of transmission errors has a high correlation with the spatial and temporal activity levels of the content. Therefore, our results can be useful for improving the performance of objective metrics in the presence of both source and channel distortions.</p

Tree-based Partition Querying: A Methodology for Computing Medoids in Large Spatial Datasets

Besides traditional domains (e.g., resource allocation, data mining applications), algorithms for medoid computation and related problems will play an important role in numerous emerging fields, such as location based services and sensor networks. Since the k-medoid problem is NP-hard, all existing work deals with approximate solutions on relatively small datasets. This paper aims at efficient methods for very large spatial databases, motivated by: (1) the high and ever increasing availability of spatial data, and (2) the need for novel query types and improved services. The proposed solutions exploit the intrinsic grouping properties of a data partition index in order to read only a small part of the dataset. Compared to previous approaches, we achieve results of comparable or better quality at a small fraction of the CPU and I/O costs (seconds as opposed to hours, and tens of node accesses instead of thousands). In addition, we study medoid-aggregate queries, where k is not known in advance, but we are asked to compute a medoid set that leads to an average distance close to a user-specified value. Similarly, medoid-optimization queries aim at minimizing both the number of medoids k and the average distance. We also consider the max version for the aforementioned problems, where the goal is to minimize the maximum (instead of the average) distance between any object and its closest medoid. Finally, we investigate bichromatic and weighted medoid versions for all query types, as well as, maximum capacity and dynamic medoids