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Integer Programming Formulations for Minimum Spanning Forests and Connected Components in Sparse Graphs

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Combinatorial Optimization and Applications (COCOA 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8881))

Abstract

In this paper, we first review several integer programming formulations for the minimum spanning tree problem, and then adapt these formulations for solving the minimum spanning forest problem in sparse graphs. Some properties for the spanning forest and connected components are studied, and then we present the integer programming formulation for finding the largest connected component, which has been widely used for network vulnerability analysis.

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References

  1. Carlsson, G.: Topology and data. Bull. Am. Math. Soc. 46(2), 255–308 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  2. Cole, R., Klein, P.N., Tarjan, R.E.: Finding minimum spanning forests in logarithmic time and linear work using random sampling. In: SPAA ’96 Proceedings of the Eighth Annual ACM Symposium on Parallel Algorithms and Architectures, pp. 243–250 (1996)

    Google Scholar 

  3. Pettie, S., Ramachandran, V.: A randomized time-work optimal parallel algorithm for finding a minimum spanning forest. SIAM J. Comput. 31(6), 1879–1895 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  4. Pop, P.C.: A survey of different integer programming formulations of the generalized minimum spanning tree problem. Carpathian J. Math. 25(1), 104–118 (2009)

    MATH  MathSciNet  Google Scholar 

  5. Edmonds, J.: Matroids and the greedy algorithm. Math. Program. 1, 127–136 (1971)

    Article  MATH  MathSciNet  Google Scholar 

  6. Conforti, M., Cornuéjols, G., Zambelli, G.: Extended formulations in combinatorial optimization. 4OR 8(1), 1–48 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  7. Myung, Y.S., Lee, C.H., Tcha, D.W.: On the generalized minimum spanning tree problem. Networks 26(4), 231–241 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  8. Feremans, C., Labbe, M., Laporte, G.: A comparative analysis of several formulations for the generalized minimum spanning tree problem. Networks 39(1), 29–34 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  9. Martin, R.K.: Using separation algorithms to generate mixed integer model reformulations. Oper. Res. Lett. 10, 119–128 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  10. Yannakakis, M.: Expressing combinatorial optimization problems by linear programs. J. Comput. Syst. Sci. 43(3), 441–466 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  11. Kaibel, V., Pashkovich, K., Theis, D.O.: Symmetry matters for the sizes of extended formulations. In: Eisenbrand, F., Shepherd, F.B. (eds.) IPCO 2010. LNCS, vol. 6080, pp. 135–148. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  12. Nguyen, D.T., Shen, Y., Thai, M.T.: Detecting critical nodes in interdependent power networks for vulnerability assessment. IEEE Trans. Smart Grid 4(1), 151–159 (2013)

    Article  Google Scholar 

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Authors and Affiliations

  1. Systems and Industrial Engineering Department, University of Arizona, Tucson, 85721, USA

    Neng Fan & Mehdi Golari

Authors
  1. Neng Fan
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  2. Mehdi Golari
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Corresponding author

Correspondence to Neng Fan .

Editor information

Editors and Affiliations

  1. Zhejiang Normal University, Jinhua, Zhejiang, China

    Zhao Zhang

  2. University of Texas, Tyler, Texas, USA

    Lidong Wu

  3. University of Texas, Dallas, Texas, USA

    Wen Xu

  4. University of Texas, Dallas, USA

    Ding-Zhu Du

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© 2014 Springer International Publishing Switzerland

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Fan, N., Golari, M. (2014). Integer Programming Formulations for Minimum Spanning Forests and Connected Components in Sparse Graphs. In: Zhang, Z., Wu, L., Xu, W., Du, DZ. (eds) Combinatorial Optimization and Applications. COCOA 2014. Lecture Notes in Computer Science(), vol 8881. Springer, Cham. https://doi.org/10.1007/978-3-319-12691-3_46

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  • DOI: https://doi.org/10.1007/978-3-319-12691-3_46

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-12690-6

  • Online ISBN: 978-3-319-12691-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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