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2017 | OriginalPaper | Buchkapitel

Generating All Patterns of Graph Partitions Within a Disparity Bound

verfasst von : Jun Kawahara, Takashi Horiyama, Keisuke Hotta, Shin-ichi Minato

Erschienen in: WALCOM: Algorithms and Computation

Verlag: Springer International Publishing

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Abstract

A balanced graph partition on a vertex-weighted graph is a partition of the vertex set such that the partition has k parts and the disparity, which is defined as the ratio of the maximum total weight of parts to the minimum one, is at most r. In this paper, a novel algorithm is proposed that enumerates all the graph partitions with small disparity. Experimental results show that five millions of partitions with small disparity for some graph with more than 100 edges can be enumerated within ten minutes.

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Literatur
2.
3.
Zurück zum Zitat Hardy, G., Lucet, C., Limnios, N.: K-terminal network reliability measures with binary decision diagrams. IEEE Trans. Reliab. 56(3), 506–515 (2007)CrossRef Hardy, G., Lucet, C., Limnios, N.: K-terminal network reliability measures with binary decision diagrams. IEEE Trans. Reliab. 56(3), 506–515 (2007)CrossRef
4.
Zurück zum Zitat Imai, H., Sekine, K., Imai, K.: Computational investigations of all-terminal network reliability via BDDs. IEICE Trans. Fundam. Electron. Commun. Comput. Sci. E82–A, 714–721 (1999) Imai, H., Sekine, K., Imai, K.: Computational investigations of all-terminal network reliability via BDDs. IEICE Trans. Fundam. Electron. Commun. Comput. Sci. E82–A, 714–721 (1999)
6.
Zurück zum Zitat Inoue, T., Takano, K., Watanabe, T., Kawahara, J., Yoshinaka, R., Kishimoto, A., Tsuda, K., Minato, S., Hayashi, Y.: Distribution loss minimization with guaranteed error bound. IEEE Trans. Smart Grid 5(1), 102–111 (2014)CrossRef Inoue, T., Takano, K., Watanabe, T., Kawahara, J., Yoshinaka, R., Kishimoto, A., Tsuda, K., Minato, S., Hayashi, Y.: Distribution loss minimization with guaranteed error bound. IEEE Trans. Smart Grid 5(1), 102–111 (2014)CrossRef
7.
Zurück zum Zitat Karpinski, M.: Approximability of the minimum bisection problem: an algorithmic challenge. In: Diks, K., Rytter, W. (eds.) MFCS 2002. LNCS, vol. 2420, pp. 59–67. Springer, Heidelberg (2002). doi:10.1007/3-540-45687-2_4 CrossRef Karpinski, M.: Approximability of the minimum bisection problem: an algorithmic challenge. In: Diks, K., Rytter, W. (eds.) MFCS 2002. LNCS, vol. 2420, pp. 59–67. Springer, Heidelberg (2002). doi:10.​1007/​3-540-45687-2_​4 CrossRef
8.
Zurück zum Zitat Kawahara, J., Inoue, T., Iwashita, H., Minato, S.: Frontier-based search for enumerating all constrained subgraphs with compressed representation. Hokkaido University, Division of Computer Science, TCS Technical reports TCS-TR-A-13-76 (2014) Kawahara, J., Inoue, T., Iwashita, H., Minato, S.: Frontier-based search for enumerating all constrained subgraphs with compressed representation. Hokkaido University, Division of Computer Science, TCS Technical reports TCS-TR-A-13-76 (2014)
10.
Zurück zum Zitat Knuth, D.E.: The Art of Computer Programming, Vol. 4A. Combinatorial Algorithms, Part 1, 1st edn. Addison-Wesley Professional, Boston (2011)MATH Knuth, D.E.: The Art of Computer Programming, Vol. 4A. Combinatorial Algorithms, Part 1, 1st edn. Addison-Wesley Professional, Boston (2011)MATH
11.
Zurück zum Zitat Minato, S.: Zero-suppressed BDDs for set manipulation in combinatorial problems. In: Proceedings of the 30th ACM/IEEE Design Automation Conference, pp. 272–277 (1993) Minato, S.: Zero-suppressed BDDs for set manipulation in combinatorial problems. In: Proceedings of the 30th ACM/IEEE Design Automation Conference, pp. 272–277 (1993)
12.
Zurück zum Zitat Nemoto, T., Hotta, K.: On the limits of the reduction in population disparity between single-member election districts in Japan. Jpn. J. Electoral Stud. 20, 136–147 (2005). (in Japanese) Nemoto, T., Hotta, K.: On the limits of the reduction in population disparity between single-member election districts in Japan. Jpn. J. Electoral Stud. 20, 136–147 (2005). (in Japanese)
13.
Zurück zum Zitat Sekine, K., Imai, H., Tani, S.: Computing the Tutte polynomial of a graph of moderate size. In: Staples, J., Eades, P., Katoh, N., Moffat, A. (eds.) ISAAC 1995. LNCS, vol. 1004, pp. 224–233. Springer, Heidelberg (1995). doi:10.1007/BFb0015427 CrossRef Sekine, K., Imai, H., Tani, S.: Computing the Tutte polynomial of a graph of moderate size. In: Staples, J., Eades, P., Katoh, N., Moffat, A. (eds.) ISAAC 1995. LNCS, vol. 1004, pp. 224–233. Springer, Heidelberg (1995). doi:10.​1007/​BFb0015427 CrossRef
14.
Zurück zum Zitat Takizawa, A., Takechi, Y., Ohta, A., Katoh, N., Inoue, T., Horiyama, T., Kawahara, J., Minato, S.: Enumeration of region partitioning for evacuation planning based on ZDD. In: Proceedings of 11th International Symposium on Operations Research and its Applications in Engineering, Technology and Management (ISORA 2013), pp. 1–8 (2013) Takizawa, A., Takechi, Y., Ohta, A., Katoh, N., Inoue, T., Horiyama, T., Kawahara, J., Minato, S.: Enumeration of region partitioning for evacuation planning based on ZDD. In: Proceedings of 11th International Symposium on Operations Research and its Applications in Engineering, Technology and Management (ISORA 2013), pp. 1–8 (2013)
Metadaten
Titel
Generating All Patterns of Graph Partitions Within a Disparity Bound
verfasst von
Jun Kawahara
Takashi Horiyama
Keisuke Hotta
Shin-ichi Minato
Copyright-Jahr
2017
DOI
https://doi.org/10.1007/978-3-319-53925-6_10

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