The algebraic structure of the densification and the sparsification tasks for CSPs

The tractability of certain CSPs for dense or sparse instances is known from the 90s. Recently, the densification and the sparsification of CSPs were formulated as computational tasks and the systematical study of their computational complexity was initiated. We approach this problem by introducing the densification operator, i.e. the closure operator that, given an instance of a CSP, outputs all constraints that are satisfied by all of its solutions. According to the Galois theory of closure operators, any such operator is related to a certain implicational system (or, a functional dependency) $\Sigma$. We are specifically interested in those classes of fixed-template CSPs, parameterized by constraint languages $\Gamma$, for which the size of an implicational system $\Sigma$ is a polynomial in the number of variables $n$. We show that in the Boolean case, $\Sigma$ is of polynomial size if and only if $\Gamma$ is of bounded width. For such languages, $\Sigma$ can be computed in log-space or in a logarithmic time with a polynomial number of processors. Given an implicational system $\Sigma$, the densification task is equivalent to the computation of the closure of input constraints. The sparsification task is equivalent to the computation of the minimal key. This leads to ${\mathcal O}({\rm poly}(n)\cdot N^2)$-algorithm for the sparsification task where $N$ is the number of non-redundant sparsifications of an original CSP. Finally, we give a complete classification of constraint languages over the Boolean domain for which the densification problem is tractable

BDGS: A Scalable Big Data Generator Suite in Big Data Benchmarking

Data generation is a key issue in big data benchmarking that aims to generate application-specific data sets to meet the 4V requirements of big data. Specifically, big data generators need to generate scalable data (Volume) of different types (Variety) under controllable generation rates (Velocity) while keeping the important characteristics of raw data (Veracity). This gives rise to various new challenges about how we design generators efficiently and successfully. To date, most existing techniques can only generate limited types of data and support specific big data systems such as Hadoop. Hence we develop a tool, called Big Data Generator Suite (BDGS), to efficiently generate scalable big data while employing data models derived from real data to preserve data veracity. The effectiveness of BDGS is demonstrated by developing six data generators covering three representative data types (structured, semi-structured and unstructured) and three data sources (text, graph, and table data)

Decision Support for Urban Regeneration - Using Multi Criteria Evaluation for Urban Green Space Development in Helsingborg

Urbanization and densification are two noticeable trends that imposes many challenges for urban planners. Fast growing cities comes with the need for incorporating publicly accessible green spaces to ensure public health and for creating an attractive city. Urban regeneration provides the possibilities of restructuring the urban environment according to desired needs. Helsingborg municipality did, in 2017, initiate one of the biggest renewal projects recorded in the municipality´s history. The H+ project, even though in an early stage, makes up a good example of how resource efficiency is growing in importance. Making the most out of limited resources implies demand for well-suiting planning strategies to base decisions on. Tools and methods for achieving this could be found in geographic information systems (GIS). More specifically for this study, the practicality of using multi criteria evaluation (MCE) for decision making is examined. In addition, an MCE is applied to find potentially suitable locations for new public green space within the H+ project area