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.
@article{arxiv.cs/0205040,
title = {Approximating the Minimum Equivalent Digraph},
author = {Samir Khuller and Balaji Raghavachari and Neal E. Young},
journal= {arXiv preprint arXiv:cs/0205040},
year = {2015}
}
Comments
conference version in ACM-SIAM Symposium on Discrete Algorithms (1994)