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Approximating the Minimum Equivalent Digraph

Samir Khuller·Balaji Raghavachari·Neal E. Young
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Abstract

The MEG (minimum equivalent graph) problem is, given a directed graph, to find a small subset of the edges that maintains all reachability relations between nodes. The problem is NP-hard. This paper gives an approximation algorithm with performance guarantee of pi^2/6 ~ 1.64. The algorithm and its analysis are based on the simple idea of contracting long cycles. (This result is strengthened slightly in ``On strongly connected digraphs with bounded cycle length'' (1996).) The analysis applies directly to 2-Exchange, a simple ``local improvement'' algorithm, showing that its performance guarantee is 1.75.

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Samir Khuller, Balaji Raghavachari, Neal E. Young. 2002-05-18. Approximating the Minimum Equivalent Digraph. https://doi.org/10.1137/s0097539793256685

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