Skipper: Maximal Matching with a Single Pass over Edges

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 graph pruning 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 pruning 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.