We prove that any two-pass graph streaming algorithm for the $s$-$t$ reachability problem in $n$-vertex directed graphs requires near-quadratic space of $n^{2-o(1)}$ bits. As a corollary, we also obtain near-quadratic space lower bounds for several other fundamental problems including maximum bipartite matching and (approximate) shortest path in undirected graphs. Our results collectively imply that a wide range of graph problems admit essentially no non-trivial streaming algorithm even when two passes over the input is allowed. Prior to our work, such impossibility results were only known for single-pass streaming algorithms, and the best two-pass lower bounds only ruled out $o(n^{7/6})$ space algorithms, leaving open a large gap between (trivial) upper bounds and lower bounds.

中文翻译：

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两遍图流算法的近二次下界

我们证明了 $n$-顶点有向图中 $s$-$t$ 可达性问题的任何两遍图流算法都需要 $n^{2-o(1)}$ 位的近二次空间。作为推论，我们还获得了其他几个基本问​​题的近二次空间下界，包括无向图中的最大二部匹配和（近似）最短路径。我们的结果共同表明，即使允许两次通过输入，广泛的图问题也基本上不承认非平凡的流算法。在我们的工作之前，这种不可能的结果只适用于单通道流算法，而最好的双通道下界只排除了 $o(n^{7/6})$ 空间算法，在两者之间留下了很大的差距（平凡的）上限和下限。