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Robustness of Minimum Cost Arborescences

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Book cover Algorithms and Computation (ISAAC 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7074))

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Abstract

In this paper, we study the minimum cost arborescence problem in a directed graph from the viewpoint of robustness of the optimal objective value. More precisely, we characterize an input graph in which the optimal objective value does not change even if we remove several arcs. Our characterizations lead to efficient algorithms for checking robustness of an input graph.

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References

  1. Li, Y., Thai, M.T., Wang, F., Du, D.Z.: On the construction of a strongly connected broadcast arborescence with bounded transmission delay. IEEE Transactions on Mobile Computing 5(10), 1460–1470 (2006)

    Article  Google Scholar 

  2. Kamiyama, N., Katoh, N., Takizawa, A.: An efficient algorithm for the evacuation problem in a certain class of networks with uniform path-lengths. Discrete Applied Mathematics 157(17), 3665–3677 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  3. Chu, Y., Liu, T.: On the shortest arborescence of a directed graph. Scientia Sinica 14, 1396–1400 (1965)

    MathSciNet  MATH  Google Scholar 

  4. Edmonds, J.: Optimum branchings. J. Res. Nat. Bur. Standards Sect. B 71B, 233–240 (1967)

    Article  MathSciNet  MATH  Google Scholar 

  5. Bock, F.: An algorithm to construct a minimum directed spanning tree in a directed network. In: Developments in Operations Research, pp. 29–44. Gordon and Breach (1971)

    Google Scholar 

  6. Fulkerson, D.R.: Packing rooted directed cuts in a weighted directed graph. Mathematical Programming 6, 1–13 (1974)

    Article  MathSciNet  MATH  Google Scholar 

  7. Gabow, H.N., Galil, Z., Spencer, T., Tarjan, R.E.: Efficient algorithms for finding minimum spanning trees in undirected and directed graphs. Combinatorica 6, 109–122 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  8. Gravin, N., Chen, N.: A note on k-shortest paths problem. Journal of Graph Theory 67(1), 34–37 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  9. Schrijver, A.: Combinatorial Optimization: Polyhedra and Efficiency. Springer, Heidelberg (2003)

    MATH  Google Scholar 

  10. Edmonds, J.: Edge-disjoint branchings. In: Combinatorial Algorithms, pp. 91–96. Academic Press (1973)

    Google Scholar 

  11. Bang-Jensen, J., Gutin, G.Z.: Digraphs: Theory, Algorithms and Applications, 2nd edn. Springer, Heidelberg (2008)

    MATH  Google Scholar 

  12. Edmonds, J.: Submodular functions, matroids, and certain polyhedra. In: Guy, R., Hanani, H., Sauer, N., Schönheim, J. (eds.) Combinatorial Structures and their Applications, pp. 69–87. Gordon and Breach, New York (1970)

    Google Scholar 

  13. Frank, A.: A weighted matroid intersection algorithm. J. Algorithms 2(4), 328–336 (1981)

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Information and System Engineering, Chuo University, Japan

    Naoyuki Kamiyama

Authors
  1. Naoyuki Kamiyama
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Editor information

Editors and Affiliations

  1. Chuo University, Kasuga, Bunkyo-ku, 112-8551, Tokyo, Japan

    Takao Asano

  2. Gunma University, 1-5-1 Tenjin-Cho, 376-8515, Kiryu-Shi, Japan

    Shin-ichi Nakano

  3. Japan Advanced Institute of Science and Technology, 1-1 Asahidai, 923-1292, Nomi, Ishikawa, Japan

    Yoshio Okamoto

  4. Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, 152-8552, Tokyo, Japan

    Osamu Watanabe

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© 2011 Springer-Verlag Berlin Heidelberg

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Kamiyama, N. (2011). Robustness of Minimum Cost Arborescences. In: Asano, T., Nakano, Si., Okamoto, Y., Watanabe, O. (eds) Algorithms and Computation. ISAAC 2011. Lecture Notes in Computer Science, vol 7074. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25591-5_15

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  • DOI: https://doi.org/10.1007/978-3-642-25591-5_15

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-25590-8

  • Online ISBN: 978-3-642-25591-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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