Approximating the Minimum Equivalent Digraph
<|reference_start|>Approximating the Minimum Equivalent Digraph: 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.<|reference_end|>
@article{khuller2002approximating,
    title={Approximating the Minimum Equivalent Digraph},
    author={Samir Khuller, Balaji Raghavachari, Neal E. Young},
    journal={SIAM J. Computing 24(4):859-872 (1995)},
    year={2002},
    doi={10.1137/S0097539793256685},
    archivePrefix={arXiv},
    eprint={cs/0205040},
    primaryClass={cs.DS cs.DM}
}