Abstract
An important application of graph partitioning is data clustering using a graph model — the pairwise similarities between all data objects form a weighted graph adjacency matrix that contains all necessary information for clustering. The min-cut bipartitioning problem is a fundamental graph partitioning problem and is NP-Complete. In this paper, we present a new multi-level algorithm based on particle swarm optimization (PSO) for bisecting graph. The success of our algorithm relies on exploiting both the PSO method and the concept of the graph core. Our experimental evaluations on 18 different graphs show that our algorithm produces encouraging solutions compared with those produced by MeTiS that is a state-of-the-art partitioner in the literature.
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References
Alpert, C.J., Kahng, A.B.: Recent directions in netlist partitioning. Integration, the VLSI Journal 19, 1–81 (1995)
Khannat, G., Vydyanathant, N.: A hypergraph partitioning based approach for scheduling of tasks with batch-shared I/O. In: IEEE International Symposium on Cluster Computing and the Grid, pp. 792–799 (2005)
Hsu, W.H., Anvil, L.S.: Self-organizing systems for knowledge discovery in large databases. In: International Joint Conference on Neural Networks, pp. 2480–2485 (1999)
Ding, C., He, X., Zha, H., Gu, M., Simon, H.: A Min-Max cut algorithm for graph partitioning and data clustering. In: Proc. IEEE Conf Data Mining, pp. 107–114 (2001)
Hendrickson, B., Leland, R.: An improved spectral graph partitioning algorithm for mapping parallel computations. SIAM Journal on Scientific Computing 16, 452–469 (1995)
Garey, M.R., Johnson, D.S.: Computers and intractability: A guide to the theory of NP-completeness. WH Freeman, New York (1979)
Bui, T., Leland, C.: Finding good approximate vertex and edge partitions is NP-hard. Information Processing Letters 42, 153–159 (1992)
Kernighan, B.W., Lin, S.: An efficient heuristic procedure for partitioning graphs. Bell System Technical Journal 49, 291–307 (1970)
Fiduccia, C., Mattheyses, R.: A linear-time heuristics for improving network partitions. In: Proc. 19th Design Automation Conf. pp. 175–181 (1982)
Leng, M., Yu, S.: An effective multi-level algorithm for bisecting graph. In: Li, X., Zaïane, O.R., Li, Z. (eds.) ADMA 2006. LNCS (LNAI), vol. 4093, pp. 493–500. Springer, Heidelberg (2006)
Żola, J., Wyrzykowski, R.: Application of genetic algorithm for mesh partitioning. In: Proc. Workshop on Parallel Numerics, pp. 209–217 (2000)
Bahreininejad, A., Topping, B.H.V., Khan, A.I.: Finite element mesh partitioning using neural networks. Advances in Engineering Software, 103–115 (1996)
Leng, M., Yu, S.: An effective multi-level algorithm based on ant colony optimization for bisecting graph. In: Ng, W.-K., Kitsuregawa, M., Li, J., Chang, K. (eds.) PAKDD 2006. LNCS (LNAI), vol. 3918, pp. 138–149. Springer, Heidelberg (2006)
Karypis, G., Kumar, V.: MeTiS 4.0: Unstructured graphs partitioning and sparse matrix ordering system. Technical Report, Department of Computer Science, University of Minnesota (1998), available on the WWW at URL http://www.cs.umn.edu/~metis
Amine, A.B., Karypis, G.: Multi-level algorithms for partitioning power-law graphs. Technical Report, Department of Computer Science, University of Minnesota (2005), available on the WWW at URL http://www.cs.umn.edu/~metis
Karypis, G., Aggarwal, R., Kumar, V., Shekhar, S.: Multilevel hypergraph partitioning: Application in VLSI domain. In: Proc. Design Automation Conf., pp. 526–529 (1997)
Kennedy, J., Eberhart, R.C.: A discrete binary version of the particle swarm algorithm. In: IEEE International Conference on Systems, Man, and Cybernetics, pp. 4104–4108 (1997)
Alpert, C.J.: The ISPD 1998 circuit benchmark suite. In: Proc. Intel Symposium of Physical Design, pp. 80–85 (1998)
Kennedy, J., Eberhart, R.: Particle swarm optimization. Proc. IEEE Conf. Neural Networks IV, pp. 1942–1948 (1995)
Seidman, S.B.: Network structure and minimum degree. Social Networks, 269–287 (1983)
Batagelj, V., Zavers̃snik, M.: An O(m) Algorithm for cores decomposition of networks. Journal of the ACM, 799–804 (2001)
Batagelj, V., Zavers̃nik, M.: Generalized cores. Journal of the ACM, 1–8 (2002)
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Sun, L., Leng, M., Yu, S. (2007). A New Multi-level Algorithm Based on Particle Swarm Optimization for Bisecting Graph. In: Alhajj, R., Gao, H., Li, J., Li, X., Zaïane, O.R. (eds) Advanced Data Mining and Applications. ADMA 2007. Lecture Notes in Computer Science(), vol 4632. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73871-8_8
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DOI: https://doi.org/10.1007/978-3-540-73871-8_8
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-73870-1
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