Fast and memory-efficient minimum spanning tree on the GPU

The GPU is an efficient accelerator for regular data-parallel workloads, but GPU acceleration is more difficult for graph algorithms and other applications with irregular memory access patterns and large memory footprints. The minimum spanning tree MST problem arises in a variety of applications and its solution exemplifies the difficulties of mapping irregular algorithms to the GPU. In this paper, we present a memory-efficient parallel algorithm for finding the minimum spanning tree of very large graphs by introducing a data-parallel implementation of Kruskal's algorithm. We test scalability and performance on random and real-world graphs with up to 25 million vertices and 240 million edges on an Nvidia Tesla T10 GPU with 4GB of memory. Our method can process graphs 4X larger and up to 10X faster than was possible with the recently published implementation of Boruvka's MST algorithm for the GPU. We also demonstrate the performance advantage of the proposed method against the multi-core filter-Kruskal's MST algorithm on a dual quad-core CPU server with Nehalem X5550 processors.