Selection Improvements on the Parallel Iterative Algorithm for Stable Matching

Abstract: 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 $O(n log(n))$ average runtime. The algorithm is structurally based on the Parallel Iterative Improvement (PII) algorithm, where we improve the convergence rate from $90\%$ to $100\%$ over a large number of trials. We suggest alternative selection methods for pairs in the PII algorithm, called Right-Minimum and Dynamic Selection, as well as a faster preprocessing step, called Quick Initialization, resulting in full convergence over $3.6$ million trials and significantly improved runtime.