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Kaczmarz Algorithm with Soft Constraints for User Interface Layout

机译：用户界面布局的具有软约束的Kaczmarz算法

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摘要

The Kaczmarz method is an iterative method for solving large systems of equations that projects iterates orthogonally onto the solution space of each equation. In contrast to direct methods such as Gaussian elimination or QR-factorization, this algorithm is efficient for problems with sparse matrices, as they appear in constraint-based user interface (UI) layout specifications. However, the Kaczmarz method as described in the literature has its limitations: it considers only equality constraints and does not support soft constraints, which makes it inapplicable to the UI layout problem. In this paper we extend the Kaczmarz method for solving specifications containing soft constraints, using the prioritized IIS detection algorithm. Furthermore, the performance and convergence of the 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.
机译：Kaczmarz方法是一种用于求解大型方程组的迭代方法，该系统将迭代正交投影到每个方程的解空间上。与诸如高斯消除或QR分解之类的直接方法相比，该算法对于稀疏矩阵的问题非常有效，因为它们出现在基于约束的用户界面（UI）布局规范中。但是，文献中描述的Kaczmarz方法有其局限性：它仅考虑相等约束，不支持软约束，这使其不适用于UI布局问题。在本文中，我们使用优先的IIS检测算法扩展了Kaczmarz方法，以解决包含软约束的规范。此外，使用随机生成的各种大小的UI布局规范，经验地评估了所提出算法的性能和收敛性。结果表明，与诸如Matlab的LINPROG（一种著名的高效线性编程求解器）之类的标准方法相比，这些方法可提供更高的性能。

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