Approximating the Minimum Equivalent Digraph
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 NPhard. 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 2Exchange, a simple ``local improvement'' algorithm, showing that its performance guarantee is 1.75.
 Publication:

arXiv eprints
 Pub Date:
 May 2002
 arXiv:
 arXiv:cs/0205040
 Bibcode:
 2002cs........5040K
 Keywords:

 Computer Science  Data Structures and Algorithms;
 Computer Science  Discrete Mathematics;
 F.2.2;
 G.2.2
 EPrint:
 conference version in ACMSIAM Symposium on Discrete Algorithms (1994)