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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Aho, A., Garey, M.R., Ullman, J.D.: The transitive reduction of a directed graph. SIAM Journal of Computing 1(2), 131–137 (1972)
Albert, R., DasGupta, B., Dondi, R., Sontag, E.: Inferring (Biological) Signal Transduction Networks via Transitive Reductions of Directed Graphs. Algorithmica 51(2), 129–159 (2008)
Albert, R., DasGupta, B., Dondi, R., Kachalo, S., Sontag, E., Zelikovsky, A., Westbrooks, K.: A Novel Method for Signal Transduction Network Inference from Indirect Experimental Evidence. Journal of Computational Biology 14(7), 927–949 (2007)
Berman, P., Karpinski, M., Scott, A.D.: Approximation Hardness of Short Symmetric Instances of MAX-3SAT, Electronic Colloquium on Computational Complexity, Report TR03-049 (2003), http://eccc.hpi-web.de/eccc-reports/2003/TR03-049/index.html
Dubois, V., Bothorel, C.: Transitive reduction for social network analysis and visualization. In: IEEE/WIC/ACM International Conference on Web Intelligence, pp. 128–131 (2005)
Edmonds, J.: Optimum Branchings. In: Dantzig, G.B., Veinott Jr., A.F. (eds.) Mathematics and the Decision Sciences. Amer. Math. Soc. Lectures Appl. Math., vol. 11, pp. 335–345 (1968)
Frederickson, G.N., Jà Jà , J.: Approximation algorithms for several graph augmentation problems. SIAM Journal of Computing 10(2), 270–283 (1981)
Kachalo, S., Zhang, R., Sontag, E., Albert, R., DasGupta, B.: NET-SYNTHESIS: A software for synthesis, inference and simplification of signal transduction networks. Bioinformatics 24(2), 293–295 (2008)
Karp, R.M.: A simple derivation of Edmonds’ algorithm for optimum branching. Networks 1, 265–272 (1972)
Khuller, S., Raghavachari, B., Young, N.: Approximating the minimum equivalent digraph. SIAM Journal of Computing 24(4), 859–872 (1995)
Khuller, S., Raghavachari, B., Young, N.: On strongly connected digraphs with bounded cycle length. Discrete Applied Mathematics 69(3), 281–289 (1996)
Khuller, S., Raghavachari, B., Zhu, A.: A uniform framework for approximating weighted connectivity problems. In: 19th Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 937–938 (1999)
Moyles, D.M., Thompson, G.L.: Finding a minimum equivalent of a digraph. JACM 16(3), 455–460 (1969)
Papadimitriou, C.: Computational Complexity, p. 212. Addison-Wesley, Reading (1994)
Vetta, A.: Approximating the minimum strongly connected subgraph via a matching lower bound. In: 12th ACM-SIAM Symposium on Discrete Algorithms, pp. 417–426 (2001)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
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
Download citation
DOI: https://doi.org/10.1007/978-3-642-03367-4_7
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-03366-7
Online ISBN: 978-3-642-03367-4
eBook Packages: Computer ScienceComputer Science (R0)