APPROXIMATING THE MINIMUM EQUIVALENT DIGRAPH
- Author(s): KHULLER, S
- RAGHAVACHARI, B
- YOUNG, N
- et al.
Published Web Locationhttps://doi.org/10.1137/S0097539793256685
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.