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Improved Approximation for Orienting Mixed Graphs

  • Iftah Gamzu
  • Moti Medina
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7355)

Abstract

An instance of the maximum mixed graph orientation problem consists of a mixed graph and a collection of source-target vertex pairs. The objective is to orient the undirected edges of the graph so as to maximize the number of pairs that admit a directed source-target path. This problem has recently arisen in the study of biological networks, and it also has applications in communication networks.

In this paper, we identify an interesting local-to-global orientation property. This property enables us to modify the best known algorithms for maximum mixed graph orientation and some of its special structured instances, due to Elberfeld et al. (CPM ’11), and obtain improved approximation ratios. We further proceed by developing an algorithm that achieves an even better approximation guarantee for the general setting of the problem. Finally, we study several well-motivated variants of this orientation problem.

Keywords

Short Path Local Neighborhood Improve Approximation Underlying Graph Undirected Edge 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Afek, Y., Bremler-Barr, A.: Self-stabilizing unidirectional network algorithms by power supply. Chicago J. Theor. Comput. Sci. (1998)Google Scholar
  2. 2.
    Afek, Y., Gafni, E.: Distributed algorithms for unidirectional networks. SIAM J. Comput. 23(6), 1152–1178 (1994)MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    Arkin, E.M., Hassin, R.: A note on orientations of mixed graphs. Discrete Applied Mathematics 116(3), 271–278 (2002)MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    Dorn, B., Hüffner, F., Krüger, D., Niedermeier, R., Uhlmann, J.: Exploiting Bounded Signal Flow for Graph Orientation Based on Cause–Effect Pairs. In: Marchetti-Spaccamela, A., Segal, M. (eds.) TAPAS 2011. LNCS, vol. 6595, pp. 104–115. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  5. 5.
    Elberfeld, M., Bafna, V., Gamzu, I., Medvedovsky, A., Segev, D., Silverbush, D., Zwick, U., Sharan, R.: On the approximability of reachability-preserving network orientations. Internet Mathematics 7, 209–232 (2011)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Elberfeld, M., Segev, D., Davidson, C.R., Silverbush, D., Sharan, R.: Approximation Algorithms for Orienting Mixed Graphs. In: Giancarlo, R., Manzini, G. (eds.) CPM 2011. LNCS, vol. 6661, pp. 416–428. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  7. 7.
    Feige, U., Goemans, M.X.: Aproximating the value of two prover proof systems, with applications to MAX 2SAT and MAX DICUT. In: 3rd ISTCS, pp. 182–189 (1995)Google Scholar
  8. 8.
    Fields, S.: High-throughput two-hybrid analysis: The promise and the peril. The FEBS Journal 272(21), 5391–5399 (2005)CrossRefGoogle Scholar
  9. 9.
    Gamzu, I., Segev, D.: A Sublogarithmic Approximation for Highway and Tollbooth Pricing. In: Abramsky, S., Gavoille, C., Kirchner, C., Meyer auf der Heide, F., Spirakis, P.G. (eds.) ICALP 2010. LNCS, vol. 6198, pp. 582–593. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  10. 10.
    Gamzu, I., Segev, D., Sharan, R.: Improved Orientations of Physical Networks. In: Moulton, V., Singh, M. (eds.) WABI 2010. LNCS, vol. 6293, pp. 215–225. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  11. 11.
    Gavin, A.C., Bosche, M., Krause, R., Grandi, P., Marzioch, M., Bauer, A., Schultz, J., Rick, J.M., Michon, A.M., Cruciat, C.M., Remor, M., Hofert, C., Schelder, M., Brajenovic, M., Ruffner, H., Merino, A., Klein, K., Hudak, M., Dickson, D., Rudi, T., Gnau, V., Bauch, A., Bastuck, S., Huhse, B., Leutwein, C., Heurtier, M.A., Copley, R.R., Edelmann, A., Querfurth, E., Rybin, V., Drewes, G., Raida, M., Bouwmeester, T., Bork, P., Seraphin, B., Kuster, B., Neubauer, G., Superti-Furga, G.: Functional organization of the yeast proteome by systematic analysis of protein complexes. Nature 415, 141–147 (2002)CrossRefGoogle Scholar
  12. 12.
    Louis Hakimi, S., Schmeichel, E.F., Young, N.E.: Orienting graphs to optimize reachability. IPL 63(5), 229–235 (1997)CrossRefGoogle Scholar
  13. 13.
    Lewin, M., Livnat, D., Zwick, U.: Improved Rounding Techniques for the MAX 2-SAT and MAX DI-CUT Problems. In: Cook, W.J., Schulz, A.S. (eds.) IPCO 2002. LNCS, vol. 2337, pp. 67–82. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  14. 14.
    Marina, M.K., Das, S.R.: Routing performance in the presence of unidirectional links in multihop wireless networks. In: 3rd MobiHoc, pp. 12–23 (2002)Google Scholar
  15. 15.
    Medvedovsky, A., Bafna, V., Zwick, U., Sharan, R.: An Algorithm for Orienting Graphs Based on Cause-Effect Pairs and Its Applications to Orienting Protein Networks. In: Crandall, K.A., Lagergren, J. (eds.) WABI 2008. LNCS (LNBI), vol. 5251, pp. 222–232. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  16. 16.
    Silverbush, D., Elberfeld, M., Sharan, R.: Optimally Orienting Physical Networks. In: Bafna, V., Sahinalp, S.C. (eds.) RECOMB 2011. LNCS, vol. 6577, pp. 424–436. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  17. 17.
    Yeang, C.H., Ideker, T., Jaakkola, T.: Physical network models. Journal of Computational Biology 11(2/3), 243–262 (2004)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Iftah Gamzu
    • 1
    • 2
  • Moti Medina
    • 3
  1. 1.Computer Science DivisionThe Open Univ.Israel
  2. 2.Blavatnik School of Computer ScienceTel-Aviv Univ.Israel
  3. 3.School of Electrical EngineeringTel-Aviv Univ.Israel

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