05.12.2007

We consider minimum equivalent digraph (directed network) problem (also known as the strong transitive reduction), its maximumoptimization variant, and some extensions of those two types of problems. We prove the existence of polynomial time approximation algorithms with ratios1.5 for all the minimization problems and 2 for all the maximization problems. We establish also approximation hardness result for those problems to within aconstant even if the length of cycles is bounded by 5.