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 O~(n) depth and using O~(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.
@article{arxiv.2304.09774,
title = {Nearly Work-Efficient Parallel DFS in Undirected Graphs},
author = {Mohsen Ghaffari and Christoph Grunau and Jiahao Qu},
journal= {arXiv preprint arXiv:2304.09774},
year = {2023}
}