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Cutting Graphs Using Competing Ant Colonies and an Edge Clustering Heuristic

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Evolutionary Computation in Combinatorial Optimization (EvoCOP 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6622))

Abstract

We investigate the usage of Ant Colony Optimization to detect balanced graph cuts. In order to do so we develop an algorithm based on competing ant colonies. We use a heuristic from social network analysis called the edge clustering coefficient, which greatly helps our colonies in local search. The algorithm is able to detect cuts that correspond very well to known cuts on small real-world networks. Also, with the correct parameter balance, our algorithm often outperforms the traditional Kernighan-Lin algorithm for graph partitioning with equal running time complexity. On larger networks, our algorithm is able to obtain low cut sizes, but at the cost of a balanced partition.

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References

  1. Flake, G.W., Tarjan, R.E., Tsioutsiouliklis, K.: Graph clustering and minimum cut trees. Internet Mathematics 1, 385–408 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  2. Chung, F.R.K.: Spectral Graph Theory. CBMS Regional Conference Series in Mathematics, vol. 92. American Mathematical Society, Providence (February 1997)

    MATH  Google Scholar 

  3. Síma, J., Schaeffer, S.E.: On the NP-Completeness of Some Graph Cluster Measures. CoRR, abs/cs/0506100 (2005)

    Google Scholar 

  4. Dorigo, M., Maniezzo, V., Colorni, A.: The Ant System: Optimization by a colony of cooperating agents. IEEE Transactions on Systems, Man, and Cybernetics-Part B 26, 29–41 (1996)

    Article  Google Scholar 

  5. Hao, J., Orlin, J.B.: A faster algorithm for finding the minimum cut in a directed graph. J. Algorithms 17(3), 424–446 (1994)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  7. Brandes, U., Gaertler, M., Wagner, D.: Experiments on graph clustering algorithms. In: Di Battista, G., Zwick, U. (eds.) ESA 2003. LNCS, vol. 2832, pp. 568–579. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  8. Kernighan, B.W., Lin, S.: An efficient heuristic procedure for partitioning graphs. The Bell System Technical Journal 49(1), 291–307 (1970)

    Article  MATH  Google Scholar 

  9. Korošec, P., Šilc, J.: Multilevel optimization of graph bisection with pheromonoes. In: Filipič, B., Šilc, J. (eds.) Proceedings of the International Conference on Bioinspired Optimization Methods and their Applications (BIOMA 2004), Ljubljana, Slovenia, October 11-12, pp. 73–80. Jožef Stefan Institute (2004)

    Google Scholar 

  10. Langham, A.E., Grant, P.W.: Using Competing Ant Colonies to Solve k-way Partitioning Problems with Foraging and raiding strategies. In: Floreano, D., Nicoud, J.D., Mondana, F. (eds.) ECAL 1999. LNCS, vol. 1674, pp. 621–625. Springer, Heidelberg (1999)

    Chapter  Google Scholar 

  11. Leng, M., Yu, S.: An effective multi-level algorithm based on ant colony optimization for bisecting graph. In: Zhou, Z.-H., Li, H., Yang, Q. (eds.) PAKDD 2007. LNCS (LNAI), vol. 4426, pp. 138–149. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  12. Cheng, D., Kannan, R., Vempala, S., Wang, G.: A divide-and-merge methodology for clustering. ACM Trans. Database Syst. 31(4), 1499–1525 (2006)

    Article  Google Scholar 

  13. Blum, C.: Ant colony optimization: Introduction and recent trends. Physics of Life Reviews 2(4), 353–373 (2005)

    Article  Google Scholar 

  14. Papadopoulos, S., Skusa, A., Vakali, A., Kompatsiaris, Y., Wagner, N.: Bridge bounding: A local approach for efficient community discovery in complex networks. Technical report, Informatics & Telematics Institute (CERTH) (2009)

    Google Scholar 

  15. Gutjahr, W.J.: First steps to the runtime complexity analysis of ant colony optimization. Comput. Oper. Res. 35(9), 2711–2727 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  16. Zachary, W.W.: An information flow model for conflict and fission in small groups. Journal of Anthropological Research 33, 452–473 (1977)

    Article  Google Scholar 

  17. Newman, M.E.J.: Fast algorithm for detecting community structure in networks (September 2003)

    Google Scholar 

  18. Krebs, V.: Political polarization during the 2008 us presidential campaign (2008)

    Google Scholar 

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

    Article  MATH  Google Scholar 

  20. Ravikumar, C.P.: Parallel Methods for VLSI Layout Design. Greenwood Publishing Group Inc., Westport (1995)

    Google Scholar 

  21. Lusseau, D., Schneider, K., Boisseau, O.J., Haase, P., Slooten, E., Dawson, S.M.: The bottlenose dolphin community of doubtful sound features a large proportion of long-lasting associations. can geographic isolation explain this unique trait? Behavioral Ecology and Sociobiology 54(4), 396–405 (2003)

    Article  Google Scholar 

  22. Girvan, M., Newman, M.E.J.: Community structure in social and biological networks. PNAS 99(12), 7821–7826 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  23. Knuth, D.E.: The stanford graphbase: A platform for combinatorial computing. Addison-Wesley, Reading (1993)

    MATH  Google Scholar 

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Hinne, M., Marchiori, E. (2011). Cutting Graphs Using Competing Ant Colonies and an Edge Clustering Heuristic. In: Merz, P., Hao, JK. (eds) Evolutionary Computation in Combinatorial Optimization. EvoCOP 2011. Lecture Notes in Computer Science, vol 6622. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20364-0_6

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  • DOI: https://doi.org/10.1007/978-3-642-20364-0_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-20363-3

  • Online ISBN: 978-3-642-20364-0

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