Vorstellungen und Mathematikunterricht

Die Unterrichtsforschung interessiert sich unter anderem dafür, wie Lernen mit Vorstellungen zusammenhängt. Aus ähnlichen Gründen können Vorstellungen auch für Unterrichtende aufschlussreich sein. Mit mathematischen Vorstellungsübungen liegt nun auch ein Unterrichtsinstrument vor, das im Unterricht die Vorstellungen aufgreift, die Schülerinnen und Schüler in der Auseinandersetzung mit mathematischen Fragen aufbauen

Speeding up SOR Solvers for Constraint-based GUIs with a Warm-Start Strategy

Many computer programs have graphical user interfaces (GUIs), which need good layout to make efficient use of the available screen real estate. Most GUIs do not have a fixed layout, but are resizable and able to adapt themselves. Constraints are a powerful tool for specifying adaptable GUI layouts: they are used to specify a layout in a general form, and a constraint solver is used to find a satisfying concrete layout, e.g.\ for a specific GUI size. The constraint solver has to calculate a new layout every time a GUI is resized or changed, so it needs to be efficient to ensure a good user experience. One approach for constraint solvers is based on the Gauss-Seidel algorithm and successive over-relaxation (SOR). Our observation is that a solution after resizing or changing is similar in structure to a previous solution. Thus, our hypothesis is that we can increase the computational performance of an SOR-based constraint solver if we reuse the solution of a previous layout to warm-start the solving of a new layout. In this paper we report on experiments to test this hypothesis experimentally for three common use cases: big-step resizing, small-step resizing and constraint change. In our experiments, we measured the solving time for randomly generated GUI layout specifications of various sizes. For all three cases we found that the performance is improved if an existing solution is used as a starting solution for a new layout