Parallel Maximum Cardinality Matching for General Graphs on GPUs

The matching problem formulated as Maximum Cardinality Matching in General Graphs (MCMGG) finds the largest matching on graphs without restrictions. The Micali-Vazirani algorithm has the best asymptotic complexity for solving MCMGG when the graphs are sparse. Parallelizing matching in general graphs on the GPU is difficult for multiple reasons. First, the augmenting path procedure is highly recursive, and NVIDIA GPUs use registers to store kernel arguments, which eventually spill into cached device memory, with a performance penalty. Second, extracting parallelism from the matching process requires partitioning the graph to avoid any overlapping augmenting paths. We propose an implementation of the Micali-Vazirani algorithm which identifies bridge edges using thread-parallel breadth-first search, followed by block-parallel path augmentation and blossom contraction. Augmenting path and Union-find methods were implemented as stack-based iterative methods, with a stack allocated in shared memory. Our experimentation shows that compared to the serial implementation, our approach results in up to 15-fold speedup for very sparse regular graphs, up to 5-fold slowdown for denser regular graphs, and finally a 50-fold slowdown for power-law distributed Kronecker graphs. This implementation has been open-sourced for further research on developing combinatorial graph algorithms on GPUs.