Nearly Work-Efficient Parallel DFS in Undirected Graphs

04/19/2023

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by   Mohsen Ghaffari, et al.

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We present the first parallel depth-first search algorithm for undirected graphs that has near-linear work and sublinear depth. Concretely, in any n-node m-edge undirected graph, our algorithm computes a DFS in Õ(√(n)) depth and using Õ(m+n) work. All prior work either required Ω(n) depth, and thus were essentially sequential, or needed a high poly(n) work and thus were far from being work-efficient.