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An Efficient Algorithm for Judicious Partition of Hypergraphs

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Combinatorial Optimization and Applications (COCOA 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10628))

Abstract

Judicious partition of hypergraphs \(\mathcal {H}\)=(V, H) is to optimize several quantities simultaneously, and the goal of this paper is to partition the vertex set V into K parts: \(\{V_1,V_2,\dots ,V_K\}\) so as to minimize the \(\max \{L(V_1),L_(V_2),\dots ,L(V_K)\}\), where \(L(V_j)\) is the number of hyperedges incident to the part \(V_j(\mathcal {H})\). The bounds for the objective function are given and the relationship between the maximum hyperdegree and the objective value is analyzed. Before giving an efficient algorithm for the judicious partition of hypergraphs, a sub-problem is obtained, which is proved to be an unweighted set cover problem, apart from a tiny difference. A greedy algorithm is applied to solve the sub-problem. Last but not least, the judicious partition of hypergraphs is successfully divided into a series of sub-problems and an efficient algorithm is developed for the original problem.

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References

  1. Karypis, G., Aggarwal, R., Kumar, V., Shekhar, S.: Multilevel hypergraph partitioning: applications in VLSI domain. IEEE Trans. Very Large Scale Integr. (VLSI) Syst. 7(1), 69–79 (1999)

    Article  Google Scholar 

  2. Zhang, Y., Tang, Y.C., Yan, G.Y.: On judicious partitions of hypergraphs with edges of size at most 3. Eur. J. Comb. 49, 232–239 (2015)

    Article  MATH  MathSciNet  Google Scholar 

  3. Scott, A.D.: Judicious partitions and related problems. Surv. Comb. 327, 95–117 (2005)

    MATH  MathSciNet  Google Scholar 

  4. Bollobás, B., Scott, A.D.: Judicious partitions of hypergraphs. J. Comb. Theory Ser. A 78(1), 15–31 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  5. Bollobás, B., Scott, A.D.: Judicious partitions of 3-uniform hypergraphs. Eur. J. Comb. 21(3), 289–300 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  6. Haslegrave, J.: The bollobás-thomason conjecture for 3-uniform hypergraphs. Combinatorica 32(4), 451–471 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  7. Haslegrave, J.: Judicious partitions of uniform hypergraphs. Combinatorica 34(5), 561–572 (2014)

    Article  MATH  MathSciNet  Google Scholar 

  8. Ma, J., Yen, P.-L., Yu, X.: On several partitioning problems of bollobás and scott. J. Comb. Theory Ser. B 100(6), 631–649 (2010)

    Article  MATH  Google Scholar 

  9. Bollobás, B., Scott, A.D.: Judicious partitions of bounded-degree graphs. J. Graph Theory 46(2), 131–143 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  10. Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms. Cambridge University Press, New York (2011)

    Book  MATH  Google Scholar 

  11. Vazirani, V.V.: Approximation Algorithms. Springer Science & Business Media, New York (2013)

    Google Scholar 

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Acknowledgements

All the authors are supported by the National 973 Plan project under Grant No. 2011CB706900, the National 863 Plan project under Grant No. 2011AA01A102, the NSFC (11331012, 71171189,11571015), the “Strategic Priority Research Program” of CAS (XDA06010302).

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Authors and Affiliations

  1. School of Mathematical Sciences, University of Chinease Academy of Sciences, Beijing, China

    Tunzi Tan, Jihong Gui, Sainan Wang, Suixiang Gao & Wenguo Yang

  2. Key Laboratory of Big Data Mining and Knowledge Management, Chinese Academy of Sciences, Beijing, China

    Tunzi Tan, Jihong Gui, Sainan Wang, Suixiang Gao & Wenguo Yang

Authors
  1. Tunzi Tan
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  2. Jihong Gui
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  3. Sainan Wang
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  4. Suixiang Gao
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  5. Wenguo Yang
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Corresponding author

Correspondence to Tunzi Tan .

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Editors and Affiliations

  1. Shanghai Jiao Tong University, Shanghai, China

    Xiaofeng Gao

  2. Harbin Institute of Technology, Shenzhen, China

    Hongwei Du

  3. Kennesaw State University, Kennesaw, Georgia, USA

    Meng Han

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Tan, T., Gui, J., Wang, S., Gao, S., Yang, W. (2017). An Efficient Algorithm for Judicious Partition of Hypergraphs. In: Gao, X., Du, H., Han, M. (eds) Combinatorial Optimization and Applications. COCOA 2017. Lecture Notes in Computer Science(), vol 10628. Springer, Cham. https://doi.org/10.1007/978-3-319-71147-8_33

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  • DOI: https://doi.org/10.1007/978-3-319-71147-8_33

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-71146-1

  • Online ISBN: 978-3-319-71147-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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