Approximating Transitive Reductions for Directed Networks

Abstract. We consider minimum equivalent digraph problem, its maximum optimization variant and some non-trivial extensions of these two types of problems motivated by biological and social network applications. We provide 3 2 -approximation algorithms for all the minimization problems and 2-approximation algorithms for all the maximization problems using appropriate primal-dual polytopes. We also show lower bounds on the integrality gap of the polytope to provide some intuition on the final limit of such approaches. Furthermore, we provide APXhardness result for all those problems even if the length of all simple cycles is bounded by 5.

• Type: Conference
• Year: 2009
• Where: WADS
• Authors: Piotr Berman, Bhaskar DasGupta, Marek Karpinski
• Keywords: Algorithms, Appropriate Primal-dual Polytopes, Minimum Equivalent Digraph, Problems, WADS 2009