Suppose a directed graph has its arcs stored in secondary memory, and we wish to compute its transitive closure, also storing the result in secondary memory. We assume that an amount of main memory capable of holding
In the dense case, where
We then consider a special kind of standard algorithm, in which paths are constructed only by concatenating arcs and old paths, never by concatenating two old paths. This restriction seems essential if we are to take advantage of sparseness. Unfortunately, we show that almost another factor of
假设有向图的弧线存储在辅助存储器中,我们希望计算其传递闭包,并将结果也存储在辅助存储器中。我们假定有一定容量的主存储器能够保存 在密集情况下,其中 然后,我们考虑一种特殊的标准算法,其中仅通过串联弧和旧路径来构造路径,而不是通过串联两个旧路径来构造路径。如果要利用稀疏性,此限制似乎必不可少。不幸的是,我们证明了
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