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The Connected p-Centdian Problem on Block Graphs

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Combinatorial Optimization and Applications

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9486))

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Abstract

In this paper, we consider the problems of locating p-vertex \(X_p\) on block graphs such that the induced subgraph of the selected p vertices is connected. Two problems are proposed: one problem is to minimizes the sum of its weighted distances from all vertices to \(X_p\), another problem is to minimize the maximum distance from each vertex in \(V-X_p\) to \(X_p\) and at the same time to minimize the sum of its distances from all vertices. We prove that the first problem is linearly solvable on block graphs with unit edge length. For the second problem, it is shown that the set of Pareto-optimal solutions of the two criteria has cardinality not greater than n, and can be obtained in \(O(n^2)\) time, where n is the number of vertices of the block graph.

Research was partially supported by the National Nature Science Foundation of China (Nos. 11471210, 11571222).

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References

  1. Averbakh, I., Berman, O.: Algorithms for path medi-centers of a tree. Comput. Oper. Res. 26, 1395–1409 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  2. Becker, R.I., Lari, I., Scozzari, A.: Algorithms for central-median paths with bounded length on trees. Eur. J. Oper. Res. 179, 1208–1220 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  3. Behtoei, A., Jannesari, M., Tseri, B.: A characterization of block graphs. Discrete Appl. Math. 158, 219–221 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  4. Chen, M.L., Francis, R.L., Lawrence, J.F., Lowe, T.J., Tufekci, S.: Block-vertex duality and the one-median problem. Networks 15, 395–412 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  5. Halpern, J.: The location of a cent-dian convex combination on an undirected tree. J. Reg. Sci. 16, 237–245 (1976)

    Article  Google Scholar 

  6. Halpern, J.: Finding minimal center-median combination (Cent-Dian) of a graph. Manage. Sci. 24, 535–544 (1978)

    Article  MATH  Google Scholar 

  7. Handler, G.Y.: Medi-centers of a tree. Transp. Sci. 19, 246–260 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  8. Hansen, P., LabbeH, M., Thisse, J.-F.: From the median to the generalized center. Oper. Res. 25, 73–86 (1991)

    MathSciNet  MATH  Google Scholar 

  9. Tamir, A., Puerto, J., Pérez-Brito, D.: The centdian subtree on tree networks. Discrete Appl. Math. 118, 263–278 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  10. Shan, E., Zhou, J., Kang, L.: The connected \(p\)-center and p-median problems on interval and circular-arc graphs. Acta Mathematicae Applicatae Sinica (Accepted)

    Google Scholar 

  11. Yen, W.C.-K.: The connected \(p\)-center problem on block graphs with forbidden vertices. Theor. Comput. Sci. 426, 13–24 (2012)

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mathematics, Shanghai University, Shanghai, 200444, People’s Republic of China

    Liying Kang, Jianjie Zhou & Erfang Shan

  2. School of Management, Shanghai University, Shanghai, 200444, People’s Republic of China

    Erfang Shan

Authors
  1. Liying Kang
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  2. Jianjie Zhou
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  3. Erfang Shan
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Corresponding author

Correspondence to Erfang Shan .

Editor information

Editors and Affiliations

  1. Dept. of Mathematics and Computer Science, Marywood University, Scranton, Pennsylvania, USA

    Zaixin Lu

  2. North Carolina Central University, Durham, North Carolina, USA

    Donghyun Kim

  3. University of Texas at Dallas, Richardson, Texas, USA

    Weili Wu

  4. Texas Southern University, Houston, Texas, USA

    Wei Li

  5. University of Texas at Dallas, Richardson, Texas, USA

    Ding-Zhu Du

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© 2015 Springer International Publishing Switzerland

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Kang, L., Zhou, J., Shan, E. (2015). The Connected p-Centdian Problem on Block Graphs. In: Lu, Z., Kim, D., Wu, W., Li, W., Du, DZ. (eds) Combinatorial Optimization and Applications. Lecture Notes in Computer Science(), vol 9486. Springer, Cham. https://doi.org/10.1007/978-3-319-26626-8_37

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  • DOI: https://doi.org/10.1007/978-3-319-26626-8_37

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-26625-1

  • Online ISBN: 978-3-319-26626-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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