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.
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Berman, P., DasGupta, B., Karpinski, M. (2009). Approximating Transitive Reductions for Directed Networks. In: Dehne, F., Gavrilova, M., Sack, JR., Tóth , C.D. (eds) Algorithms and Data Structures. WADS 2009. Lecture Notes in Computer Science, vol 5664. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03367-4_7
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DOI: https://doi.org/10.1007/978-3-642-03367-4_7
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