1 research outputs found
The Hildreth's Algorithm with Applications to Soft Constraints for User Interface Layout
The Hildreth's algorithm is a row action method for solving large systems of
inequalities. This algorithm is efficient for problems with sparse matrices, as
opposed to direct methods such as Gaussian elimination or QR-factorization. We
apply the Hildreth's algorithm, as well as a randomized version, along with
prioritized selection of the inequalities, to efficiently detect the highest
priority feasible subsystem of equations. We prove convergence results and
feasibility criteria for both cyclic and randomized Hildreth's algorithm, as
well as a mixed algorithm which uses Hildreth's algorithm for inequalities and
Kaczmarz algorithm for equalities. These prioritized, sparse systems of
inequalities commonly appear in constraint-based user interface (UI) layout
specifications. The performance and convergence of these proposed algorithms
are evaluated empirically using randomly generated UI layout specifications of
various sizes. The results show that these methods offer improvements in
performance over standard methods like Matlab's LINPROG, a well-known efficient
linear programming solver, and the recent developed Kaczmarz algorithm with
prioritized IIS detection.Comment: 16 pages, 3 figures. arXiv admin note: substantial text overlap with
arXiv:1309.700