X-Blossom: Massive Parallelization of Graph Maximum Matching

The blossom algorithm computes maximum matchings in graphs and has been widely applied across diverse domains, including machine learning, economic analysis, and other essential data analytics applications. As data scales and the demand for real-time processing intensifies, high-performance computing solutions have become indispensable. Over the years, substantial research efforts have been dedicated to improving the sequential blossom algorithm. However, developing an efficient parallel solution remains highly challenging due to the algorithm's intricate execution patterns, sequential recursive dependencies, dynamic data structure modifications, and inefficient path search. By thoroughly analyzing existing solutions, we have identified critical issues and proposed a new parallel framework called X-Blossom. This framework eliminates recursion entirely, enables efficient searches for multiple disjoint paths, and employs a simple path table to trace paths, removing the need for dynamic graphs and trees. These efforts in algorithm development result in significant performance enhancement. Extensive experiments on real-world datasets show that X-Blossom outperforms all existing solutions, achieving up to 992x speedup compared to the fastest sequential baseline, and an average of 431x speedup over the state-of-the-art parallel solution using 8 cores. It also demonstrates excellent scalability, achieving an average speedup of 1.72x when threads double in scalability tests to 64 cores. To the best of our knowledge, X-Blossom is the fastest solution for this class of graph algorithms.