Transitive Closure (Strongly Connected Components)

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Description

In this problem, we also want to compute the transitive closure of a graph. (Perhaps this should be a separate problem?)

Related Problems

Related: Strongly Connected Components, Maximum Strongly Connected Component, Strong Connectivity (dynamic), 2 Strong Components (dynamic), Connected Subgraph

Parameters

V: number of vertices

E: number of edges

Table of Algorithms

Name Year Time Space Approximation Factor Model Reference
Paul Purdom 1970 $O(V^{2}+VE)$ $O(V^{2})$ Exact Deterministic Time & Space

Time Complexity Graph

Strongly Connected Components - Transitive Closure - Time.png

Space Complexity Graph

Strongly Connected Components - Transitive Closure - Space.png

Pareto Frontier Improvements Graph

Strongly Connected Components - Transitive Closure - Pareto Frontier.png