Robustness of Minimum Cost Arborescences

  • Naoyuki Kamiyama
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7074)


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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  1. 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)CrossRefGoogle Scholar
  2. 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)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Chu, Y., Liu, T.: On the shortest arborescence of a directed graph. Scientia Sinica 14, 1396–1400 (1965)MathSciNetzbMATHGoogle Scholar
  4. 4.
    Edmonds, J.: Optimum branchings. J. Res. Nat. Bur. Standards Sect. B 71B, 233–240 (1967)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 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. 6.
    Fulkerson, D.R.: Packing rooted directed cuts in a weighted directed graph. Mathematical Programming 6, 1–13 (1974)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 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)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Gravin, N., Chen, N.: A note on k-shortest paths problem. Journal of Graph Theory 67(1), 34–37 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Schrijver, A.: Combinatorial Optimization: Polyhedra and Efficiency. Springer, Heidelberg (2003)zbMATHGoogle Scholar
  10. 10.
    Edmonds, J.: Edge-disjoint branchings. In: Combinatorial Algorithms, pp. 91–96. Academic Press (1973)Google Scholar
  11. 11.
    Bang-Jensen, J., Gutin, G.Z.: Digraphs: Theory, Algorithms and Applications, 2nd edn. Springer, Heidelberg (2008)zbMATHGoogle Scholar
  12. 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. 13.
    Frank, A.: A weighted matroid intersection algorithm. J. Algorithms 2(4), 328–336 (1981)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Naoyuki Kamiyama
    • 1
  1. 1.Department of Information and System EngineeringChuo UniversityJapan

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