MST in Incremental Graphs Through Tree Contractions

Dynamic graphs, characterized by rapid changes in their topological structure through adding or deleting edges or vertices, pose significant challenges for algorithm design. This paper presents a parallel algorithm for dynamic graphs in a batched setting. We employ a popular tree contraction mechanism to create a hierarchical representation of the input graph that allows the identification of localized areas that further enable maintaining a critical graph primitive such as the minimum spanning tree (MST) without requiring re-computation from scratch. We perform experiments to demonstrate the application of our algorithm in real-world graphs where batch-dynamic algorithms on large trees are essential for incremental updates. We show experimental validations on GPUs where our proposed technique can provide up to 3.43x speedup over equivalent parallel implementations on shared memory CPUs. Additionally, our methods can provide up to 4.23x speedup over conventional parallel computation from scratch.