Skip to main content
SpringerLink
Log in

The connected p-median problem on block graphs

  • Original Paper
  • Published:
Optimization Letters Aims and scope Submit manuscript

Abstract

In this paper, we study a variant of the p-median problem on block graphs G in which the p-median is asked to be connected, and this problem is called the connected p-median problem. We first show that the connected p-median problem is NP-hard on block graphs with multiple edge weights. Then, we propose an O(n)-time algorithm for solving the problem on unit-edge-weighted block graphs, where n is the number of vertices in G.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2

Similar content being viewed by others

References

  1. Blum, M., Floyd, R.W., Pratt, V.R., Rivest, R.L., Tarjan, R.E.: Time bounds for selection. J. Comput. Syst. Sci. 7, 448–461 (1972)

    Article  MathSciNet  MATH  Google Scholar 

  2. Burkard, R.E., Fathali, J.: A polynomial method for the pos/neg weighted 3-median problem on a tree. Math. Method Oper. Res. 65, 229–238 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  3. Burkard, R.E., Hatzl, J.: Median problems with positive and negative weights on cycles and cacti. J. Comb. Optim. 20, 27–46 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  4. Burkard, R.E., Krarup, J.: A linear algorithm for the pos/neg-weighted 1-median problem on a cactus. Computing 60, 193–215 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  5. Benkoczi, R., Bhattacharya, B.: A new template for solving \(p\)-median problems for trees in sub-quadratic time. LNCS 3669, 271–282 (2005)

    MathSciNet  MATH  Google Scholar 

  6. Chang, S.C., Yen, C.K., Wang, Y.L., Liu, J.J.: The NP-hardness of the connected \(p\)-median problem on bipartite graphs and split graphs. Chiang Mai J. Sci. 40, 83–88 (2013)

    MathSciNet  MATH  Google Scholar 

  7. Chen, G.T., Ding, W., Li, S.W.: Connected \(p\)-median problems in tree networks. J. Hangzhou Dianzi Univ. 29, 89–91 (2009)

    Google Scholar 

  8. Chen, G.T., Xin, S., Cui, S.H.: The connected \(p\)-median problem on the 3-cactus graph. J. Hangzhou Dianzi Univ. 30, 77–80 (2010)

    Google Scholar 

  9. Cheng, Y.K., Kang, L.Y., Lu, C.H.: The pos/neg-weighted \(1\)-median problem on tree graphs with subtree-shaped customers. Theor. Comput. Sci. 411, 1038–1044 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  10. Daskin, M.S.: Networks and Discrete Location, Models, Algorithms, and Applications. Wiley, New York (1995)

    Book  MATH  Google Scholar 

  11. Drezner, Z., Hamacher, H.: Facility Location: Applications and Theory. Springer, Heidelberg (2002)

    Book  MATH  Google Scholar 

  12. Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. W. H. Freeman & Co., New York (1978)

    MATH  Google Scholar 

  13. Gavsih, B., Sridhar, S.: Computing the 2-median on tree networks in \(O(n\log n)\) time. Networks 26, 305–317 (1995)

    Article  MathSciNet  Google Scholar 

  14. Goldman, A.J.: Optimal center location in simple networks. Transport. Sci. 5, 212–221 (1971)

    Article  MathSciNet  Google Scholar 

  15. Hatzl, J.: Median problem on wheels and cactus graphs. Computing 80, 377–393 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  16. Kariv, O., Hakimi, S.L.: An algorithmic approach to network location problems, part II: \(p\)-medians. SIAM J. Appl. Math. 27, 539–560 (1979)

    Article  MathSciNet  MATH  Google Scholar 

  17. Lan, Y.F., Wang, Y.L.: An optimal algorithm for solving the 1-median problem on weighted 4-cactus graphs. Eur. J. Oper. Res. 122, 602–610 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  18. Reese, J.: Solution methods for the \(p\)-median problem: an annotated bibliography. Networks 48, 125–142 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  19. Tamir, A.: An \(O(pn^2)\) algorithm for the \(p\)-median and related problems on tree graphs. Oper. Res. Lett. 19, 59–64 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  20. Vieira, C.E.C.: Heuristics for the Connected \(p\)-Median Problem, Ph.D. Thesis, Pontifícia Universidade Católica do Rio de Janeiro (2006)

  21. West, D.B.: Introduction to Graph Theory, 2nd edn. Prentice-Hall, Upper Saddle River (2001)

    Google Scholar 

  22. Yang, B.H., Fang, Z.G., Zhao, J.S., Ye, S.Y.: The location problem in emergency management considering uncertain information. In: Proceedings of 2009 IEEE International Conference on Grey Systems and Intelligent Services, pp. 10–12 (2009)

  23. Zhang, X.Q., Kang, L.Y., Cheng, Y.K.: The pos/neg-weighted median problem on block graphs with subgraph-shaped customers. Computing 88, 97–110 (2010)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgments

This work was supported in part by the National Science Council of Republic of China under contracts NSC 98-2221-E-128-004-, NSC 100-2221-E-011-067-MY3, and NSC 100-2221-E-128-003-.

Author information

Authors and Affiliations

  1. Department of Information Management, National Taiwan University of Science and Technology, Taipei, Taiwan

    Shun-Chieh Chang & Yue-Li Wang

  2. Department of Information Management, Shih Hsin University, Taipei, Taiwan

    William Chung-Kung Yen & Jia-Jie Liu

Authors
  1. Shun-Chieh Chang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. William Chung-Kung Yen
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yue-Li Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Jia-Jie Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yue-Li Wang.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Chang, SC., Yen, W.CK., Wang, YL. et al. The connected p-median problem on block graphs. Optim Lett 10, 1191–1201 (2016). https://doi.org/10.1007/s11590-015-0912-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11590-015-0912-5

Keywords

Search

Navigation