Solving linear arithmetic constraints for user interface applications

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Abstract
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 1/3 of a window, or preferring that an ob- ject be contained within a rectangle if possible. Current con- straint 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.

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