Maximal Matching (MM) is a fundamental graph problem with diverse applications. While state-of-the-art parallel MM algorithms have a total expected work linear in number of edges, they require randomization, iterative graph processing, and contraction after each iteration. These overheads increase execution time and demand additional memory, reducing applicability to large-scale graphs. In this paper, we introduce Skipper, an asynchronous Maximal Matching algorithm that resolves conflicts instantaneously using a parallel reservation strategy, which merges both reservation and committing steps into a single step. Skipper processes each edge only once, definitively determining whether the edge is selected as a match. Skipper does not require graph contraction and minimizes memory space utilization, requiring only a single byte of memory space per vertex. Furthermore, Skipper operates in the asynchronous parallel random access machine (APRAM) model, relaxing synchronization between threads, and facilitating better parallelization gains. Our evaluation, conducted on real-world and synthetic graphs with up to 224 billion edges, shows that Skipper achieves a speedup of 4.9--15.6 times, with a geometric mean of 8.0 times.

翻译：最大匹配（MM）是一个具有多样化应用的基础图论问题。尽管当前最先进的并行MM算法在总期望工作量上与边数呈线性关系，但它们需要随机化、迭代式图处理以及每次迭代后的图收缩操作。这些开销增加了执行时间并需要额外的内存，降低了对大规模图数据的适用性。本文提出Skipper，一种基于并行预留策略的异步最大匹配算法，该策略通过将预留与提交步骤合并为单一步骤来实现即时冲突消解。Skipper对每条边仅处理一次即可确定性地判断该边是否被选为匹配边。算法无需进行图收缩，并最小化内存空间占用，每个顶点仅需1字节存储空间。此外，Skipper在异步并行随机存取机（APRAM）模型下运行，放宽了线程间的同步要求，从而获得更优的并行化收益。我们在包含高达2240亿条边的真实世界图与合成图上进行的评估表明，Skipper实现了4.9至15.6倍的加速比，几何平均加速比为8.0倍。