Abstract
We present initial results from the first empirical evaluation of a graph partitioning algorithm inspired by the Arora-Rao-Vazirani algorithm of [5], which combines spectral and flow methods in a novel way. We have studied the parameter space of this new algorithm, e.g., examining the extent to which different parameter settings interpolate between a more spectral and a more flow-based approach, and we have compared results of this algorithm to results from previously known and optimized algorithms such as Metis.
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References
Alon, N., Milman, V.: λ 1, isoperimetric inequalities for graphs and superconcentrators. J. Combin. Theory B 38, 73–88 (1985)
Andersen, R., Lang, K.: An algorithm for improving graph partitions. In: SODA 2008: Proceedings of the 19th ACM-SIAM Symposium on Discrete Algorithms, pp. 651–660 (2008)
Arora, S., Hazan, E., Kale, S.: \({O}(\sqrt {\log n)}\) approximation to sparsest cut in \(\tilde{O}(n^2)\) time. In: FOCS 2004: Proceedings of the 45th Annual Symposium on Foundations of Computer Science, pp. 238–247 (2004)
Arora, S., Kale, S.: A combinatorial, primal-dual approach to semidefinite programs. In: STOC 2007: Proceedings of the 39th Annual ACM Symposium on Theory of Computing, pp. 227–236 (2007)
Arora, S., Rao, S., Vazirani, U.: Expander flows, geometric embeddings and graph partitioning. In: STOC 2004: Proceedings of the 36th Annual ACM Symposium on Theory of Computing, pp. 222–231 (2004)
Arora, S., Rao, S., Vazirani, U.: Geometry, flows, and graph-partitioning algorithms. Communications of the ACM 51(10), 96–105 (2008)
Cherkassky, B., Goldberg, A., Martin, P., Setubal, J., Stolfi, J.: Augment or push: a computational study of bipartite matching and unit-capacity flow algorithms. Journal of Experimental Algorithmics 3, Article 8 (1998)
Cherkassky, B., Goldberg, A.V.: On implementing push-relabel method for the maximum flow problem. Algorithmica 19, 390–410 (1997)
Chung, F.: Spectral graph theory. CBMS Regional Conference Series in Mathematics, vol. 92. American Mathematical Society, Providence (1997)
Goldberg, A., Rao, S.: Beyond the flow decomposition barrier. Journal of the ACM 45, 783–797 (1998)
Guattery, S., Miller, G.: On the quality of spectral separators. SIAM Journal on Matrix Analysis and Applications 19, 701–719 (1998)
Karypis, G., Kumar, V.: A fast and high quality multilevel scheme for partitioning irregular graphs. SIAM Journal on Scientific Computing 20, 359–392 (1998)
Khandekar, R., Rao, S., Vazirani, U.: Graph partitioning using single commodity flows. In: STOC 2006: Proceedings of the 38th Annual ACM Symposium on Theory of Computing, pp. 385–390 (2006)
Lang, K., Rao, S.: Finding near-optimal cuts: an empirical evaluation. In: SODA 1993: Proceedings of the 4th Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 212–221 (1993)
Leighton, T., Rao, S.: Multicommodity max-flow min-cut theorems and their use in designing approximation algorithms. Journal of the ACM 46(6), 787–832 (1999)
Orecchia, L., Schulman, L., Vazirani, U., Vishnoi, N.: On partitioning graphs via single commodity flows. In: STOC 2008: Proceedings of the 40th Annual ACM Symposium on Theory of Computing, pp. 461–470 (2008)
Walshaw, C., Cross, M.: Mesh partitioning: a multilevel balancing and refinement algorithm. SIAM Journal on Scientific Computing 22(1), 63–80 (2000)
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Lang, K.J., Mahoney, M.W., Orecchia, L. (2009). Empirical Evaluation of Graph Partitioning Using Spectral Embeddings and Flow. In: Vahrenhold, J. (eds) Experimental Algorithms. SEA 2009. Lecture Notes in Computer Science, vol 5526. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02011-7_19
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DOI: https://doi.org/10.1007/978-3-642-02011-7_19
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-02010-0
Online ISBN: 978-3-642-02011-7
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