A Scalable Linear Constraint Solver for User Interface Construction. This paper proposes an algorithm for satisfying systems of linear equality and inequality constraints with hierarchical strengths or preferences. Basically, it is a numerical method that incrementally obtains the LU decompositions of linear constraint systems. To realize this, it introduces a novel technique for analyzing hierarchical systems of linear constraints. In addition, it improves performance by adopting techniques that utilize the sparsity and disjointness of constraint systems. Based on this algorithm, the HiRise constraint solver has been designed and implemented for the use of constructing interactive graphical user interfaces. This paper shows that HiRise is scalable up to thousands of simultaneous constraints in real-time execution.