Sequential algorithms for the Stable Matching Problem are often too slow in the context of some large scale applications like switch scheduling. Parallel architectures can offer a notable decrease in runtime complexity. We propose a stable matching algorithm using n^2 processors that converges in O(nlog(n)) average runtime. The algorithm is structurally based on the Parallel Iterative Improvement (PII) algorithm, where we improve the convergence from 90% to 100%. We suggest alternative selection methods for pairs in the PII algorithm, called Right-Minimum and Dynamic Selection, resulting in full convergence over 3.3 million trials and generally much faster termination.

翻译：针对大规模应用（如交换机调度）中的稳定匹配问题，传统串行算法往往效率不足。并行架构可显著降低运行时复杂度。本文提出一种使用n²个处理器的稳定匹配算法，其平均运行时间复杂度为O(nlog(n))。该算法基于并行迭代改进（Parallel Iterative Improvement, PII）算法框架，通过优化将收敛率从90%提升至100%。我们提出了PII算法中两种替代性配对选择方法——右最小值选择（Right-Minimum）与动态选择（Dynamic Selection），使得在330万次试验中实现完全收敛，且算法终止速度显著加快。