Approximation Schemes for Maximum Weight Independent Set of Rectangles

In the Maximum Weight Independent Set of Rectangles (MWISR) problem we are given a set of n axis-parallel rectangles in the 2D-plane, and the goal is to select a maximum weight subset of pairwise non-overlapping rectangles. Due to many applications, e.g. in data mining, map labeling and admission control, the problem has received a lot of attention by various research communities. We present the first (1+epsilon)-approximation algorithm for the MWISR problem with quasi-polynomial running time 2^{poly(log n/epsilon)}. In contrast, the best known polynomial time approximation algorithms for the problem achieve superconstant approximation ratios of O(log log n) (unweighted case) and O(log n / log log n) (weighted case). Key to our results is a new geometric dynamic program which recursively subdivides the plane into polygons of bounded complexity. We provide the technical tools that are needed to analyze its performance. In particular, we present a method of partitioning the plane into small and simple areas such that the rectangles of an optimal solution are intersected in a very controlled manner. Together with a novel application of the weighted planar graph separator theorem due to Arora et al. this allows us to upper bound our approximation ratio by (1+epsilon). Our dynamic program is very general and we believe that it will be useful for other settings. In particular, we show that, when parametrized properly, it provides a polynomial time (1+epsilon)-approximation for the special case of the MWISR problem when each rectangle is relatively large in at least one dimension. Key to this analysis is a method to tile the plane in order to approximately describe the topology of these rectangles in an optimal solution. This technique might be a useful insight to design better polynomial time approximation algorithms or even a PTAS for the MWISR problem

A QPTAS for Maximum Weight Independent Set of Polygons with Polylogarithmically Many Vertices

The Maximum Weight Independent Set of Polygons problem is a fundamental problem in computational geometry. Given a set of weighted polygons in the 2-dimensional plane, the goal is to find a set of pairwise non-overlapping polygons with maximum total weight. Due to its wide range of applications, the MWISP problem and its special cases have been extensively studied both in the approximation algorithms and the computational geometry community. Despite a lot of research, its general case is not well-understood. Currently the best known polynomial time algorithm achieves an approximation ratio of n^(epsilon) [Fox and Pach, SODA 2011], and it is not even clear whether the problem is APX-hard. We present a (1+epsilon)-approximation algorithm, assuming that each polygon in the input has at most a polylogarithmic number of vertices. Our algorithm has quasi-polynomial running time. We use a recently introduced framework for approximating maximum weight independent set in geometric intersection graphs. The framework has been used to construct a QPTAS in the much simpler case of axis-parallel rectangles. We extend it in two ways, to adapt it to our much more general setting. First, we show that its technical core can be reduced to the case when all input polygons are triangles. Secondly, we replace its key technical ingredient which is a method to partition the plane using only few edges such that the objects stemming from the optimal solution are evenly distributed among the resulting faces and each object is intersected only a few times. Our new procedure for this task is not more complex than the original one, and it can handle the arising difficulties due to the arbitrary angles of the polygons. Note that already this obstacle makes the known analysis for the above framework fail. Also, in general it is not well understood how to handle this difficulty by efficient approximation algorithms

Nematicity, magnetism and superconductivity in FeSe

Iron-based superconductors are well known for their complex interplay between structure, magnetism and superconductivity. FeSe offers a particularly fascinating example. This material has been intensely discussed because of its extended nematic phase, whose relationship with magnetism is not obvious. Superconductivity in FeSe is highly tunable, with the superconducting transition temperature, $T_\mathrm{c}$, ranging from 8 K in bulk single crystals at ambient pressure to almost 40 K under pressure or in intercalated systems, and to even higher temperatures in thin films. In this topical review, we present an overview of nematicity, magnetism and superconductivity, and discuss the interplay of these phases in FeSe. We focus on bulk FeSe and the effects of physical pressure and chemical substitutions as tuning parameters. The experimental results are discussed in the context of the well-studied iron-pnictide superconductors and interpretations from theoretical approaches are presented.Comment: Topical Review submitted to Journal of Physics: Condensed Matte

Locational Conditions, Cooperation, and Innovativeness: Evidence from Research and Company Spin-offs

This paper has two goals. First, it analyzes the extent to which the innovativeness of spin-offs, either born from a research facility or from another company, is influenced by locational conditions. Second, it provides evidence on how important local cooperation links are in comparison to nonlocal ones. Using a sample of approximately 1,500 East German firms from knowledge-intensive sectors, we estimate a structural equation model applying the partial least squares method. We find that proximity to local research institutes and universities is the most influential factor for the cooperation intensity of spin-offs. Furthermore, the higher the cooperation intensity, the greater the innovativeness of a firm. Moreover, the results indicate that it is not the local but the nonlocal cooperation ties that are more conducive to innovativeness of research spin-offs. The findings also highlight that the innovativeness of research spin-offs with solely local links is strongly depends on support from various authorities and institutions.Research and Company Spin-Offs, Locational Conditions, Cooperation Intensity, Innovativeness, Structural Equation Modeling, Partial Least Squares Approach

Abundances and possible diffusion of elements in M67 stars

We present a spectroscopic study at high resolution, R~50,000, of 14 stars located on the main sequence, at the turn-off point and on the early subgiant branch in the cluster M67 in order to investigate its detailed chemical composition, for comparison with the Sun and solar twins in the solar neighbourhood, and to explore selective atomic diffusion of chemical elements as predicted by stellar-structure theory. We have obtained VLT/FLAMES-UVES spectra and analysed these strictly differentially in order to explore chemical-abundance similarities and differences between the M67 stars and the Sun, and among the M67 stars themselves. Individual abundances of 19 different chemical elements are obtained for the stars. They are found to agree very well with solar abundances, with abundance ratios closer to solar than those of most solar twins in the solar neighbourhood. An exception is Li which shows a considerable scatter among the cluster stars. There is a tendency for the cluster-star abundances to be depleted relative to the abundances in the field stars in correlation with the condensation temperature of the elements, a tendency earlier found also for the Sun. The results support the hypothesis that the gas of the proto-cluster was depleted by formation and cleansing of dust before the stars formed. They also add support to the proposal that the Sun was once formed in a dense stellar environment. Moreover, the observed minor reductions of heavy elements in the atmospheres of the dwarfs and turn-off point stars relative to our standard star M67-1194 and the subgiants seem to suggest that diffusion processes are at work in these stars, although the evidence is not compelling. Based on theoretical models the diffusion-corrected initial metallicity of M67 is estimated to be [Fe/H]=+0.06.Comment: 14 pages, 9 figures, 5 tables. Accepted for publication in section 8. Stellar atmospheres of Astronomy and Astrophysics. Minor language corrections and an update of section 4.1 as compared to previous publicatio

A Quality Model for Actionable Analytics in Rapid Software Development

Background: Accessing relevant data on the product, process, and usage perspectives of software as well as integrating and analyzing such data is crucial for getting reliable and timely actionable insights aimed at continuously managing software quality in Rapid Software Development (RSD). In this context, several software analytics tools have been developed in recent years. However, there is a lack of explainable software analytics that software practitioners trust. Aims: We aimed at creating a quality model (called Q-Rapids quality model) for actionable analytics in RSD, implementing it, and evaluating its understandability and relevance. Method: We performed workshops at four companies in order to determine relevant metrics as well as product and process factors. We also elicited how these metrics and factors are used and interpreted by practitioners when making decisions in RSD. We specified the Q-Rapids quality model by comparing and integrating the results of the four workshops. Then we implemented the Q-Rapids tool to support the usage of the Q-Rapids quality model as well as the gathering, integration, and analysis of the required data. Afterwards we installed the Q-Rapids tool in the four companies and performed semi-structured interviews with eight product owners to evaluate the understandability and relevance of the Q-Rapids quality model. Results: The participants of the evaluation perceived the metrics as well as the product and process factors of the Q-Rapids quality model as understandable. Also, they considered the Q-Rapids quality model relevant for identifying product and process deficiencies (e.g., blocking code situations). Conclusions: By means of heterogeneous data sources, the Q-Rapids quality model enables detecting problems that take more time to find manually and adds transparency among the perspectives of system, process, and usage.Comment: This is an Author's Accepted Manuscript of a paper to be published by IEEE in the 44th Euromicro Conference on Software Engineering and Advanced Applications (SEAA) 2018. The final authenticated version will be available onlin