Finding the maximum matching in bipartite graphs is a fundamental graph operation widely used in various fields. To expedite the acquisition of the maximum matching, Karp and Sipser introduced two data reduction rules aimed at decreasing the input size. However, the KaSi algorithm, which implements the two data reduction rules, has several drawbacks: a high upper bound on time complexity and inefficient storage structure. The poor upper bound on time complexity makes the algorithm lack robustness when dealing with extreme cases, and the inefficient storage structure struggles to balance vertex merging and neighborhood traversal operations, leading to poor performance on real-life graphs. To address these issues, we introduced MVM, an algorithm incorporating three novel optimization strategies to implement the data reduction rules. Our theoretical analysis proves that the MVM algorithm, even when using data structures with the worst search efficiency, can still maintain near-linear time complexity, ensuring the algorithm's robustness. Additionally, we designed an innovative storage format that supports efficient vertex merging operations while preserving the locality of edge sets, thus ensuring the efficiency of neighborhood traversals in graph algorithms. Finally, we conduct evaluations on both real-life and synthetic graphs. Extensive experiments demonstrate the superiority of our method.

翻译：在二分图中寻找最大匹配是一项基础的图操作，广泛应用于多个领域。为加速获取最大匹配，Karp与Sipser提出了两条旨在缩减输入规模的数据规约规则。然而，实现这两条规约规则的KaSi算法存在若干缺陷：时间复杂度上界较高且存储结构低效。较高的时间复杂度上界导致算法在处理极端情况时缺乏鲁棒性，而低效的存储结构难以平衡顶点合并与邻域遍历操作，致使算法在实际图数据上表现不佳。为解决这些问题，我们提出了MVM算法，该算法融合了三种新颖的优化策略以实现数据规约规则。理论分析证明，即使采用搜索效率最差的数据结构，MVM算法仍能保持近线性时间复杂度，从而确保算法的鲁棒性。此外，我们设计了一种创新的存储格式，该格式在支持高效顶点合并操作的同时，保持了边集的局部性特征，从而保障了图算法中邻域遍历的效率。最后，我们在真实图数据与合成图数据上进行了性能评估。大量实验结果表明，我们所提方法具有显著优越性。