The paper proposes dynamic parallel algorithms for connectivity and bipartiteness of undirected graphs that require constant time and $O(n^{1/2+\epsilon})$ work on the CRCW PRAM model. The work of these algorithms almost matches the work of the $O(\log n)$ time algorithm for connectivity by Kopelowitz et al. (2018) on the EREW PRAM model and the time of the sequential algorithm for bipartiteness by Eppstein et al. (1997). In particular, we show that the sparsification technique, which has been used in both mentioned papers, can in principle also be used for constant time algorithms in the CRCW PRAM model, despite the logarithmic depth of sparsification trees.

翻译：本文提出了针对无向图连通性和二部性的动态并行算法，这些算法在CRCW PRAM模型上需要常数时间和$O(n^{1/2+\epsilon})$工作量。这些算法的工作量几乎与Kopelowitz等人（2018）在EREW PRAM模型上针对连通性提出的$O(\log n)$时间算法的工作量相匹配，也几乎与Eppstein等人（1997）针对二部性提出的顺序算法的时间相匹配。特别地，我们证明了稀疏化技术——在上述两篇论文中均有使用——尽管稀疏化树具有对数深度，但在原则上同样可用于CRCW PRAM模型中的常数时间算法。