ContraMST: A unified framework for dynamic MST maintenance

Abstract

Dynamic graphs, characterized by frequent changes in their topological structure through the addition or deletion of edges or vertices, present significant challenges for algorithm design. This work introduces ContraMST, a suite of algorithms for efficiently processing dynamic graphs in a batched setting. We employ a tree contraction mechanism to create a hierarchical representation of the input graph, facilitating the identification of localized updates. This approach enables the maintenance of critical graph primitives, such as the minimum spanning tree (MST), without requiring recomputation from scratch. Experimental results demonstrate the effectiveness of ContraMST on real-world graphs, where batch-dynamic algorithms are crucial for efficiently handling updates in different batch processing scenarios.

Specifically, our technique highlights ContraMST’s performance across various update scenarios: IMB (Incremental), DMB (Decremental), and FDM (Fully Batch Dynamic) MST. For IMB, we demonstrate experimental validations on GPUs, where our proposed technique achieves up to 3.43$\times$ speedup compared to equivalent parallel implementations on shared-memory CPUs. Additionally, it provides up to 4.23$\times$ speedup over conventional parallel computation from scratch. For DMB, experimental results show that ContraMST achieves up to 4.98$\times$ speedup on GPUs compared to equivalent parallel implementations on shared-memory CPUs, with an additional 5.12$\times$ speedup over conventional parallel computation from scratch. For FDM, our experimental validations demonstrate that ContraMST achieves up to 6.56$\times$ speedup on GPUs over shared-memory CPU implementations and up to 7.31$\times$ speedup compared to conventional parallel computation from scratch. This significant improvement is attributed to ContraMST’s ability to process IMB and DMB operations together, reducing redundant computations and fully utilizing GPU parallelism. These results underscore ContraMST’s efficiency in managing dynamic graph updates in a batch setting, leveraging GPU parallelism to enhance performance across all update scenarios.