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Parallel Implementations of Gusfield’s Cut Tree Algorithm

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7016))

Abstract

This paper presents parallel versions of Gusfield’s cut tree algorithm. Cut trees are a compact representation of the edge-connectivity between every pair of vertices of an undirected graph. Cut trees have many applications in combinatorial optimization and in the analysis of networks originated in many applied fields. However, surprisingly few works have been published on the practical performance of cut tree algorithms. This paper describes two parallel versions of Gusfield’s cut tree algorithm and presents extensive experimental results which show a significant speedup on most real and synthetic graphs in our dataset.

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References

  1. Albert, R., Barabási, A.L.: Statistical mechanics of complex networks. Rev. Mod. Phys. 74(1), 47–97 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  2. Backstrom, L., Dwork, C., Kleinberg, J.: Wherefore art thou r3579x?: anonymized social networks, hidden patterns, and structural steganography. In: Proceedings of the 16th int’l conference on World Wide Web. WWW 2007. ACM, NY (2007)

    Google Scholar 

  3. Bader, D.A., Sachdeva, V.: A cache-aware parallel implementation of the push-relabel network flow algorithm and experimental evaluation of the gap relabeling heuristic. In: ISCA PDCS (2005)

    Google Scholar 

  4. Batagelj, V., Mrvar, A.: Pajek datasets (2006), http://vlado.fmf.uni-lj.si/pub/networks/data/

  5. Bollobás, B.: Random Graphs, 2nd edn. Cambridge University Press, Cambridge (2001)

    Book  MATH  Google Scholar 

  6. Chapman, B., Jost, G., Van der Pas, R.: Using OpenMP: portable shared memory parallel programming. MIT Press, Cambridge (2008)

    Google Scholar 

  7. Chekuri, C.S., Goldberg, A.V., Karger, D.R., Levine, M.S., Stein, C.: Experimental study of minimum cut algorithms. In: SODA ’97: Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms. pp. 324–333. Society for Industrial and Applied Mathematics, Philadelphia, PA, USA (1997)

    Google Scholar 

  8. Cherkassky, B.V., Goldberg, A.V.: On Implementing the Push-Relabel Method for the Maximum Flow Problem. Algorithmica 19(4), 390–410 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  9. Flake, G.W., Tarjan, R.E., Tsioutsiouliklis, K.: Graph clustering and minimum cut trees. Internet Mathematics 1(4) (2003)

    Google Scholar 

  10. Goldberg, A.V., Rao, S.: Beyond the flow decomposition barrier. J. ACM 45, 783–797 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  11. Goldberg, A.V., Tarjan, R.E.: A new approach to the maximum-flow problem. J. ACM 35, 921–940 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  12. Goldberg, A.V., Tsioutsiouliklis, K.: Cut tree algorithms. In: SODA 1999: Proceedings of the Tenth Annual ACM-SIAM Symposium on Discrete Algorithms. Society for Industrial and Applied Mathematics, USA (1999)

    Google Scholar 

  13. Gomory, R.E., Hu, T.C.: Multi-terminal network flows. Journal of the Society for Industrial and Applied Mathematics 9(4), 551–570 (1961)

    Article  MathSciNet  MATH  Google Scholar 

  14. Görke, R., Hartmann, T., Wagner, D.: Dynamic Graph Clustering Using Minimum-Cut Trees. In: Dehne, F., Gavrilova, M., Sack, J.R., Tóth, C. (eds.) WADS 2009. LNCS, vol. 5664, pp. 339–350. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  15. Gusfield, D.: Very simple methods for all pairs network flow analysis. SIAM J. Comput. 19, 143–155 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  16. Hong, B., He, Z.: An asynchronous multi-threaded algorithm for the maximum network flow problem with non-blocking global relabeling heuristic. IEEE Transactions on Parallel and Distributed Systems 99 (2010)

    Google Scholar 

  17. Leskovec, J., Kleinberg, J., Faloutsos, C.: Graph evolution: Densification and shrinking diameters. In: ACM Trans. on Knowledge Discovery from Data, ACM TKDD (2007)

    Google Scholar 

  18. Letchford, A., Reinelt, G., Theis, D.: Odd minimum cut-sets and b-matchings revisited. SIAM Journal on Discrete Mathematics 22(4) (2008)

    Google Scholar 

  19. Mitrofanova, A., Farach-Colton, M., Mishra, B.: Efficient and robust prediction algorithms for protein complexes using gomory-hu trees. In: Altman, R.B., Dunker, A.K., Hunter, L., Murray, T., Klein, T.E. (eds.) Pacific Symposium on Biocomputing, pp. 215–226 (2009)

    Google Scholar 

  20. Nagamochi, H., Ibaraki, T.: Algorithmic Aspects of Graph Connectivity. Cambridge University Press, New York (2008)

    Book  MATH  Google Scholar 

  21. Rao, G., Stone, H., Hu, T.: Assignment of tasks in a distributed processor system with limited memory. IEEE Transactions on Computers 28, 291–299 (1979)

    Article  MathSciNet  MATH  Google Scholar 

  22. Saran, H., Vazirani, V.V.: Finding k cuts within twice the optimal. SIAM J. Comput. 24(1), 101–108 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  23. Tuncbag, N., Salman, F.S., Keskin, O., Gursoy, A.: Analysis and network representation of hotspots in protein interfaces using minimum cut trees. Proteins: Structure, Function, and Bioinformatics 78(10), 2283–2294 (2010)

    Article  Google Scholar 

  24. Watts, D.J., Strogatz, S.H.: Collective dynamics of ’small-world’ networks. Nature 393(6684), 440–442 (1998)

    Article  MATH  Google Scholar 

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© 2011 Springer-Verlag Berlin Heidelberg

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Cohen, J., Rodrigues, L.A., Silva, F., Carmo, R., Guedes, A.L.P., Duarte, E.P. (2011). Parallel Implementations of Gusfield’s Cut Tree Algorithm. In: Xiang, Y., Cuzzocrea, A., Hobbs, M., Zhou, W. (eds) Algorithms and Architectures for Parallel Processing. ICA3PP 2011. Lecture Notes in Computer Science, vol 7016. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24650-0_22

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  • DOI: https://doi.org/10.1007/978-3-642-24650-0_22

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-24649-4

  • Online ISBN: 978-3-642-24650-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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