Skip to main content
SpringerLink
Log in

Parameterized Minimum Cost Partition of a Tree with Supply and Demand

  • Conference paper
  • First Online:
Frontiers in Algorithmics (FAW 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9130))

Included in the following conference series:

  • 749 Accesses

Abstract

In this paper, we study the minimum cost partition problem of a tree with supply and demand. For the kernelizaton of the problem, several reduction rules are given, which result in a kernel of size \(O(k^2)\) for the problem. Based on the branching technique, a parameterized algorithm of running time \(O^{*}(2.828^{k})\) is presented.

This work is supported by the National Natural Science Foundation of China under Grants (61232001, 61472449, 61420106009, 61402054), and the Hengyang Foundation for Development of Science and Technology under Grant(2014KJ21).

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Arefifar, S.A., Mohamed, Y.A.I., El-Fouly, T.H.: Supply-adequacy-based optimal construction of microgrids in smart distribution systems. IEEE Trans. Smart Grid 3(3), 1491–1502 (2012)

    Article  Google Scholar 

  2. Berkhin, P.: A survey of clustering data mining techniques. In: Kogan, J., Nicholas, C., Teboulle, M. (eds.) Grouping Multidimensional Data, pp. 25–71. Springer, Heidelberg (2006)

    Google Scholar 

  3. Boulaxis, N.G., Papadopoulos, M.P.: Optimal feeder routing in distribution system planning using dynamic programming technique and gis facilities. IEEE Trans. Power Delivery 17(1), 242–247 (2002)

    Article  Google Scholar 

  4. Hendrickson, B., Kolda, T.G.: Graph partitioning models for parallel computing. Parallel Comput. 26(12), 1519–1534 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  5. Ito, T., Zhou, X., Nishizeki, T.: Partitioning Trees of Supply and Demand. Int. J. Found. Comput. Sci. 16(04), 803–827 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  6. Ito, T., Demaine, E.D., Zhou, X., Nishizeki, T.: Approximability of partitioning graphs with supply and demand. J. Discrete Algorithms 6(4), 627–650 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  7. Ito, T., Zhou, X., Nishizeki, T.: Partitioning graphs of supply and demand. Discrete appl. Math. 157(12), 2620–2633 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  8. Ito, T., Hara, T., Zhou, X., Nishizeki, T.: Minimum cost partitions of trees with supply and demand. Algorithmica 64(3), 400–415 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  9. Jovanovic, R., Bousselham, A.: A greedy method for optimizing the self-adequacy of microgrids presented as partitioning of graphs with supply and demand. In: Proceedings of the 2nd International Renewable and Sustainable Energy Conference(IRSEC 2014), pp. 17–19, Ouarzazate, October 2014

    Google Scholar 

  10. Jovanovic, R., Bousselham, A., Voss, S.: A Heuristic Method for Solving the Problem of Partitioning Graphs with Supply and Demand. arXiv preprint arXiv:1411.1080 (2014)

  11. Kawabata, M., Nishizeki, T.: Partitioning trees with supply, demand and edge-capacity. IEICE Trans. Fundam. Electron. Commun. Comput. Sci. 96(6), 1036–1043 (2013)

    Article  Google Scholar 

  12. Lienig, J., Markov, I.L., Hu, J.: VLSI Physical Design: From Graph Partitioning to Timing Closure. Springer, The Netherlands (2011)

    Google Scholar 

  13. Morishita, S., Nishizeki, T.: Parametric power supply networks. J. Comb. Optim. 29(1), 1–15 (2015)

    Article  MathSciNet  Google Scholar 

  14. Morton, A.B., Mareels, I.M.: An efficient brute-force solution to the network reconfiguration problem. IEEE Trans. Power Delivery 15(3), 996–1000 (2000)

    Article  Google Scholar 

  15. Narayanaswamy, N.S., Ramakrishna, G.: Tree t-spanners in Outerplanar Graphs via Supply Demand Partition. arXiv preprint arXiv:1210.7919 (2012)

  16. Popa, A.: Modelling the power supply network – hardness and approximation. In: Chan, T.-H.H., Lau, L.C., Trevisan, L. (eds.) TAMC 2013. LNCS, vol. 7876, pp. 62–71. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  17. Taoka, S., Watanabe, K., Watanabe, T.: Experimental evaluation of maximum-supply partitioning algorithms for demand-supply graphs. IEICE Trans. Fundum. Electron. Commun. Comput. Sci. 89(4), 1049–1057 (2006)

    Article  Google Scholar 

  18. Teng, J.H., Lu, C.N.: Feeder-switch relocation for customer interruption cost minimization. IEEE Trans. Power Delivery 17(1), 254–259 (2002)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Information Science and Engineering, Central South University, Changsha, China

    Mugang Lin, Wenjun Li & Qilong Feng

  2. Department of Computer Science, Hengyang Normal University, Hengyang, China

    Mugang Lin

Authors
  1. Mugang Lin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Wenjun Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Qilong Feng
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mugang Lin .

Editor information

Editors and Affiliations

  1. Central South University, Changsha, China

    Jianxin Wang

  2. Courant Institute, New York University, New York, New York, USA

    Chee Yap

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this paper

Cite this paper

Lin, M., Li, W., Feng, Q. (2015). Parameterized Minimum Cost Partition of a Tree with Supply and Demand. In: Wang, J., Yap, C. (eds) Frontiers in Algorithmics. FAW 2015. Lecture Notes in Computer Science(), vol 9130. Springer, Cham. https://doi.org/10.1007/978-3-319-19647-3_17

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-19647-3_17

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-19646-6

  • Online ISBN: 978-3-319-19647-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation