Approximating Transitive Reductions for Directed Networks

Authors:
Piotr Berman;Bhaskar Dasgupta;Marek Karpinski
Affiliations:
Research partially done while visiting Dept. of Computer Science, University of Bonn and supported by DFG grant Bo 56/174-1, Pennsylvania State University, USA 16802;Supported by NSF grants DBI-0543365, IIS-0612044 and IIS-0346973, University of Illinois at Chicago, Chicago, USA 60607-7053;Supported in part by DFG grants, Procope grant 31022, and Hausdorff Center research grant EXC59-1, University of Bonn, Bonn, Germany 53117
Venue:
WADS '09 Proceedings of the 11th International Symposium on Algorithms and Data Structures
Year:
2009

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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 $\frac{3}{2}$-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 APX-hardness result for all those problems even if the length of all simple cycles is bounded by 5.