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We present the first GPU-based parallel algorithm to efficiently update vertex coloring on large dynamic networks. For single GPU, we introduce the concept of loosely maintained vertex color update that reduces computation and memory requirements. For multiple GPUs, in distributed environments, we propose priority-based ordering of vertices to reduce the communication time. We prove the correctness of our algorithms and experimentally demonstrate that for graphs of over 16 million vertices and over 134 million edges on a single GPU, our dynamic algorithm is as much as 20x faster than state-of-the-art algorithm on static graphs. For larger graphs with over 130 million vertices and over 260 million edges, our distributed implementation with 8 GPUs produces updated color assignments within 160 milliseconds. In all cases, the proposed parallel algorithms produce comparable or fewer colors than state-of-the-art algorithms.
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Anti-Section Transitive Closure
The transitive closure of a graph is a new graph where every vertex is directly connected to all vertices to which it had a path in the original graph. Transitive closures are useful for reachability and relationship querying. Finding the transitive closure can be computationally expensive and requires a large memory footprint as the output is typically larger than the input. Some of the original research on transitive closures assumed that graphs were dense and used dense adjacency matrices. We have since learned that many real-world networks are extremely sparse, and the existing methods do not scale. In this work, we introduce a new algorithm called Anti-section Transitive Closure (ATC) for finding the transitive closure of a graph. We present a new parallel edges operation – anti-sections – for finding new edges to reachable vertices. ATC scales to massively multithreaded systems such as NVIDIA’s GPU with tens of thousands of threads. We show that the anti-section operation shares some traits with the triangle counting intersection operation in graph analysis. Lastly, we view the transitive closure problem as a dynamic graph problem requiring edge insertions. By doing this, our memory footprint is smaller. We also show a method for creating the batches in parallel using two different techniques: dual-round and hash. Using these techniques and the Hornet dynamic graph data structure, we show our new algorithm on an NVIDIA Titan V GPU. We compare with other packages such as NetworkX, SEI-GBTL, SuiteSparse, and cuSparse.
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- Award ID(s):
- 2109988
- PAR ID:
- 10311655
- Date Published:
- Journal Name:
- The 28th IEEE International Conference on High Performance Computing, Data, and Analytics (HiPC)
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Accepted Manuscript1.0
- Conference Paper:
- The DOI is not currently available.
