Solving linear arithmetic constraints for user interface applications

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 l/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 a major limitation. We describe incremental algorithms based on the dual simplex and active set methods that can solve such systems of constraints efficiently.