Eecient Transitive Closure Computation

We present two new transitive closure algorithms that are based on strong component detection. The algorithms scan the input graph only once without generating partial successor sets for each node. The new algorithms eliminate the redundancy caused by strong components more e ciently than previous transitive closure algorithms. We present statistically sound simulation experiments showing that the new algorithms are more e cient than previous ones. We also describe a compact representation for the successor sets of the transitive closure that can be used together with the new algorithms. The new representation saves much space and reduces the number of operations needed in successor set construction. We show that the representation often eliminates redundant computations caused by multiple paths between pairs of nodes.

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