Constraints have played an important role in the construction of GUIs, where they are mainly used to define the layout of the widgets. Resizing behavior is very important in GUIs because areas have domain specific parameters such as form the resizing of windows. If linear objective function is used and window is resized then error is not distributed equally. To distribute the error equally, a quadratic objective function is introduced. Different algorithms are widely used for solving linear constraints and quadratic problems in a variety of different scientific areas. The linear relxation, Kaczmarz, direct and linear programming methods are common methods for solving linear constraints for GUI layout. The interior point and active set methods are most commonly used techniques to solve quadratic programming problems. Current constraint solvers designed for GUI layout do not use interior point methods for solving a quadratic objective function subject to linear equality and inequality constraints. In this paper, performance aspects and the convergence speed of interior point and active set methods are compared along with one most commonly used linear programming method when they are implemented for graphical user interface layout. The performance and convergence of the proposed algorithms are evaluated empirically using randomly generated UI layout specifications of various sizes. The results show that the interior point algorithms perform significantly better than the Simplex method and QOCA-solver, which uses the active set method implementation for solving quadratic optimization.
Linear equality and inequality constraints arise naturally in specifying many aspects of user interfaces, such as requiring that onewindowbe to the left of another, requiring that a pane occupy the leftmost 1 3 of a window, or preferring that an object be contained within a rectangle if possible. Current constraint solvers designed for UI applications cannot efficiently handle simultaneous linear equations and inequalities. This is amajor limitation. We describe incremental algorithms based on the dual simplex and active set methods that can solve such systems of constraints efficiently. Linear equality and inequality constraints arise naturally in specifying many aspects of user interfaces, such as requiring that one window be to the left of another, requiring that a pane occupy the leftmost third of a window, or preferring that an object be contained within a rectangle if possible. Previous constraint solvers designed for user interface applications cannot handle simultaneous linear equations and inequalities efficiently. This is a major limitation, as such systems of constraints arise often in natural declarative specifications. We describe Cassowary---an incremental algorithm based on the dual simplex method, which can solve such systems of constraints efficiently. We have implemented the algorithm as part of a constraint-solving toolkit. We discuss the implementation of the toolkit, its application programming interface, and its performance. We propose a scalable algorithm called HiRise2 for incrementally solving soft linear constraints over real domains. It is based on a framework for soft constraints, known as constraint hierarchies, to allow effective modeling of user interface applications by using hierarchical preferences for constraints. HiRise2 introduces LU decompositions to improve the scalability of an incremental simplex method. Using this algorithm, we implemented a constraint solver. We also show the results of experiments on the performance of the solver. 