New Advances in Reoptimizing the Minimum Steiner Tree Problem

  • Davide Bilò
  • Anna Zych
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7464)


In this paper we improve the results in the literature concerning the problem of computing the minimum Steiner tree given the minimum Steiner tree for a similar problem instance. Using a σ-approximation algorithm computing the minimum Steiner tree from scratch, we provide a \(\left(\frac{3 \sigma-1}{2 \sigma-1}+\epsilon\right)\) and a \(\left(\frac{2 \sigma-1}{\sigma}+\epsilon\right)\) -approximation algorithm for altering the instance by removing a vertex from the terminal set and by increasing the cost of an edge, respectively. If we use the best up to date σ = ln 4 + ε, our ratios equal 1.218 and 1.279 respectively.


Problem Instance Approximation Ratio Steiner Tree Recursive Call Steiner Tree Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Archetti, C., Bertazzi, L., Speranza, M.G.: Reoptimizing the traveling salesman problem. Networks 42(3), 154–159 (2003)MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    Archetti, C., Luca, B., Speranza, M.G.: Reoptimizing the 0-1 knapsack problem. Technical Report 267, University of Brescia (2006)Google Scholar
  3. 3.
    Ausiello, G., Escoffier, B., Monnot, J., Paschos, V.T.: Reoptimization of Minimum and Maximum Traveling Salesman’s Tours. In: Arge, L., Freivalds, R. (eds.) SWAT 2006. LNCS, vol. 4059, pp. 196–207. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  4. 4.
    Bern, M.W., Plassmann, P.E.: The Steiner problem with edge lengths 1 and 2. Inf. Process. Lett. 32(4), 171–176 (1989)MathSciNetzbMATHCrossRefGoogle Scholar
  5. 5.
    Bilò, D., Böckenhauer, H.-J., Hromkovič, J., Královič, R., Mömke, T., Widmayer, P., Zych, A.: Reoptimization of Steiner Trees. In: Gudmundsson, J. (ed.) SWAT 2008. LNCS, vol. 5124, pp. 258–269. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  6. 6.
    Bilò, D., Böckenhauer, H.-J., Komm, D., Králović, R., Mömke, T., Seibert, S., Zych, A.: Reoptimization of the shortest common superstring problem. Algorithmica 61(2), 227–251 (2011)MathSciNetzbMATHCrossRefGoogle Scholar
  7. 7.
    Bilò, D., Widmayer, P., Zych, A.: Reoptimization of Weighted Graph and Covering Problems. In: Bampis, E., Skutella, M. (eds.) WAOA 2008. LNCS, vol. 5426, pp. 201–213. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  8. 8.
    Böckenhauer, H.-J., Forlizzi, L., Hromkovič, J., Kneis, J., Kupke, J., Proietti, G., Widmayer, P.: Reusing Optimal TSP Solutions for Locally Modified Input Instances (Extended Abstract). In: Navarro, G., Bertossi, L., Kohayakawa, Y. (eds.) TCS 2006. IFIP, vol. 209, pp. 251–270. Springer, Boston (2006)Google Scholar
  9. 9.
    Böckenhauer, H.-J., Hromković, J., Králović, R., Mömke, T., Rossmanith, P.: Reoptimization of Steiner trees: Changing the terminal set, vol. 410, pp. 3428–3435. Elsevier Science Publishers Ltd. (August 2009)Google Scholar
  10. 10.
    Böckenhauer, H.-J., Hromkovič, J., Mömke, T., Widmayer, P.: On the Hardness of Reoptimization. In: Geffert, V., Karhumäki, J., Bertoni, A., Preneel, B., Návrat, P., Bieliková, M. (eds.) SOFSEM 2008. LNCS, vol. 4910, pp. 50–65. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  11. 11.
    Böckenhauer, H.-J., Komm, D.: Reoptimization of the Metric Deadline TSP. In: Ochmański, E., Tyszkiewicz, J. (eds.) MFCS 2008. LNCS, vol. 5162, pp. 156–167. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  12. 12.
    Byrka, J., Grandoni, F., Rothvoß, T., Sanità, L.: An Improved LP-based Approximation for Steiner Tree. In: STOC 2010, Best Paper Award (2010)Google Scholar
  13. 13.
    Escoffier, B., Milanic, M., Paschos, V.T.: Simple and fast reoptimizations for the Steiner tree problem. Technical Report 2007-01, DIMACS (2007)Google Scholar
  14. 14.
    Escoffier, B., Milanič, M., Paschos, V.T.: Simple and fast reoptimizations for the Steiner tree problem 4(2), 86–94 (2009)Google Scholar
  15. 15.
    Escoffier, B., Ausiello, G., Bonifaci, V.: Complexity and Approximation in Reoptimization. In: Computability in Context: Computation and Logic in the Real World. Imperial College Press (2011)Google Scholar
  16. 16.
    Böckenhauer, H.-J., Freiermuth, K., Hromkovič, J., Mömke, T., Sprock, A., Steffen, B.: The Steiner Tree Reoptimization Problem with Sharpened Triangle Inequality. In: Calamoneri, T., Diaz, J. (eds.) CIAC 2010. LNCS, vol. 6078, pp. 180–191. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  17. 17.
    Mikhailyuk, V.A.: Reoptimization of set covering problems. Cybernetics and Sys. Anal. 46, 879–883 (2010)CrossRefGoogle Scholar
  18. 18.
    Prömel, H.J., Steger, A.: The Steiner Tree Problem. Advanced Lectures in Mathematics. Friedr. Vieweg & Sohn, Braunschweig (2002)zbMATHCrossRefGoogle Scholar
  19. 19.
    Robins, G., Zelikovsky, A.: Improved Steiner tree approximation in graphs. In: ACM-SIAM Symposium on Discrete Algorithms, pp. 770–779. ACM (2000)Google Scholar
  20. 20.
    Schäffter, M.W.: Scheduling with forbidden sets. Discrete Applied Mathematics 72(1-2), 155–166 (1997)MathSciNetzbMATHCrossRefGoogle Scholar
  21. 21.
    Zych, A.: Reoptimization of NP-hard problems. Ph.D. thesis, ETH ZürichGoogle Scholar
  22. 22.
    Zych, A., Bilò, D.: New reoptimization techniques applied to Steiner tree problem. Electronic Notes in Discrete Mathematics 37, 387–392 (2011); LAGOS 2011 - VI Latin-American Algorithms, Graphs and Optimization SymposiumGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Davide Bilò
    • 1
  • Anna Zych
    • 2
  1. di Teorie e Ricerche dei Sistemi CulturaliUniversity of SassariItaly
  2. 2.Uniwersytet WarszawskiPoland

Personalised recommendations