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The.Algorithm.Design.Manual.Springer-Verlag.1998

The.Algorithm.Design.Manual.Springer-Verlag.1998

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1.4.5 Transitive Closure and Reduction<br />

1.4.5 Transitive Closure and Reduction<br />

INPUT OUTPUT<br />

Input Description: A directed graph G=(V,E) .<br />

Problem: For transitive closure, construct a graph G'=(V,E') with edge (i,j) \in E' iff there is a directed<br />

path from i to j in G . For transitive reduction, construct a small graph G'=(V,E') with a directed path<br />

from i to j in G' iff (i,j) \in E .<br />

Implementations<br />

● LEDA - A Library of Efficient Data Types and <strong>Algorithm</strong>s (C++) (rating 6)<br />

● Combinatorica (Mathematica) (rating 4)<br />

Related Problems<br />

● Connected Components<br />

● Shortest Path<br />

file:///E|/WEBSITE/FILES/TRANSURE.HTM (1 of 2) [19/1/2003 1:36:47]

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