Question: Suppose that we wish to maintain the transitive closure of a directed graph G = (V, E) as we insert edges into E. That is,

Suppose that we wish to maintain the transitive closure of a directed graph G = (V, E) as we insert edges into E. That is, after each edge has been inserted, we want to update the transitive closure of the edges inserted so far. Assume that the graph G has no edges initially and that the transitive closure is to be represented as a Boolean matrix.
a. Show how the transitive closure G* = (V, E*) of a graph G = (V, E) can be updated in O (V2) time when a new edge is added to G.

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a Let T be the V V matrix representing the transitive closure such that Ti j is 1 if there is a path from i to j and 0 if not Initialize I when there ... View full answer

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