《快与静：基于自适应工作过滤的稀疏矩阵行列式积估计》
The Quick and the Dead: Estimating Sparse-Matrix Permanents with Adaptive Work Filtering
AI总结：
该研究针对拉斯穆森行列式积估计器的性能局限，采用最小度排序结合自适应调度，提出稀疏矩阵行列式积估计方法，在小型矩阵上性能与现有最优相当，可有效扩展至大型稀疏矩阵。
AI中文摘要：
拉斯穆森（Rasmussen）的行列式积估计器是针对二元矩阵行列式积的简单无偏估计器，但其实际性能会受在完成完美匹配前终止的轨迹限制。这些失败的轨迹，加上存活权重间的离散性，会大幅降低有效样本量。尽管现有文献利用矩阵缩放等技术提升提议平衡，以及支持过滤去除结构上不可行的选择，但在每一步应用这些技术会大幅增加轨迹成本，且无法直接解决下一个顶点的选择问题。本文采用稀疏矩阵算法中的经典最小度排序来选择下一个顶点，每条轨迹的总桶维护工作量为O(n + m)，其中n为矩阵的行/列数，m为非零元数量。所提估计器使用自适应调度，仅在需要时才调用成本更高的缩放与过滤操作。实验表明，其在测试的小型矩阵上可与现有最优方法媲美，且能有效扩展至大型稀疏矩阵。
英文摘要：
Rasmussen's permanent estimator is a simple and unbiased estimator for the permanent of a binary matrix, but its practical performance can be limited by trajectories that terminate before completing a perfect matching. These failed trajectories, together with dispersion among the surviving weights, can substantially reduce the effective sample size. Although the literature leverages techniques such as matrix scaling to improve proposal balance and support filtering to remove structurally infeasible choices, using these at every step can substantially increase the trajectory cost. Furthermore, they do not directly address the choice of the next vertex. This paper uses the classical minimum-degree ordering in sparse matrix algorithms to select the next vertex with O(n + m) total bucket-maintenance work per trajectory, where n is the number of rows/columns in the matrix and m is the number of nonzeros. The proposed estimator uses adaptive schedules to invoke the more expensive scaling and filtering operations only when needed. The experiments show that it is competitive with the state of the art on the tested small matrices and scales effectively to large sparse matrices.
