Skip to main content
Springer Nature Link
Log in

Approximating Transitive Reductions for Directed Networks

  • Conference paper
Algorithms and Data Structures (WADS 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5664))

Included in the following conference series:

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

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Aho, A., Garey, M.R., Ullman, J.D.: The transitive reduction of a directed graph. SIAM Journal of Computing 1(2), 131–137 (1972)

    Article  MathSciNet  MATH  Google Scholar 

  2. 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)

    Article  MathSciNet  MATH  Google Scholar 

  3. 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)

    Article  MathSciNet  Google Scholar 

  4. 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

  5. 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)

    Google Scholar 

  6. 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)

    Google Scholar 

  7. Frederickson, G.N., JàJà, J.: Approximation algorithms for several graph augmentation problems. SIAM Journal of Computing 10(2), 270–283 (1981)

    Article  MathSciNet  MATH  Google Scholar 

  8. 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)

    Article  Google Scholar 

  9. Karp, R.M.: A simple derivation of Edmonds’ algorithm for optimum branching. Networks 1, 265–272 (1972)

    Article  MathSciNet  MATH  Google Scholar 

  10. Khuller, S., Raghavachari, B., Young, N.: Approximating the minimum equivalent digraph. SIAM Journal of Computing 24(4), 859–872 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  11. Khuller, S., Raghavachari, B., Young, N.: On strongly connected digraphs with bounded cycle length. Discrete Applied Mathematics 69(3), 281–289 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  12. 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)

    Google Scholar 

  13. Moyles, D.M., Thompson, G.L.: Finding a minimum equivalent of a digraph. JACM 16(3), 455–460 (1969)

    Article  MATH  Google Scholar 

  14. Papadimitriou, C.: Computational Complexity, p. 212. Addison-Wesley, Reading (1994)

    MATH  Google Scholar 

  15. 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)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Research partially done while visiting Dept. of Computer Science, University of Bonn and supported by DFG grant Bo 56/174-1, Pennsylvania State University, University Park, PA, 16802, USA

    Piotr Berman

  2. Supported by NSF grants DBI-0543365, IIS-0612044 and IIS-0346973, University of Illinois at Chicago, Chicago, IL, 60607-7053, USA

    Bhaskar DasGupta

  3. Supported in part by DFG grants, Procope grant 31022, and Hausdorff Center research grant EXC59-1, University of Bonn, 53117, Bonn, Germany

    Marek Karpinski

Authors
  1. Piotr Berman
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Bhaskar DasGupta
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Marek Karpinski
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Carleton University, Ottawa, Canada

    Frank Dehne

  2. Department of Computer Science, University of Calgary, 2500 University Drive N.W., T2N 1N4, Calgary, AB, Canada

    Marina Gavrilova

  3. School of Computer Science, Carleton University, 1125 Colonel By Drive, Ottawa, P.O. Box, K1S 5B6, Ontario, Canada

    Jörg-Rüdiger Sack

  4. University of Calgary, Calgary, AB, Canada

    Csaba D. Tóth

Rights and permissions

Reprints 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)

Publish with us

Policies and ethics

Search

Navigation