Efficient Cycle Search for the Minimum Routing Cost Spanning Tree Problem

  • Steffen Wolf
  • Peter Merz
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6022)


The Minimum Routing Cost Spanning Tree problem is an optimization problem that strongly benefits from local search. Well-established approaches are the Ahuja-Murty local search and a weaker subtree search used in an evolutionary framework. We present a new and efficient cycle search that has a lower time complexity but achieves the same results as the strong but slow Ahuja-Murty local search. Moreover, we show that an evolutionary framework using this cycle search outperforms previous approaches regarding both quality and time. Our approach is able to find (near-)optimal solutions in all runs for all tested instances.


Local Search Communication Cost Memetic Algorithm Iterate Local Search Desktop Grid 
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.


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  1. 1.
    Hu, T.C.: Optimum Communication Spanning Trees. SIAM Journal of Computing 3(3), 188–195 (1974)zbMATHCrossRefGoogle Scholar
  2. 2.
    Johnson, D.S., Lenstra, J.K., Rinnooy Kan, A.H.G.: The Complexity of the Network Design Problem. Networks 8, 279–285 (1978)zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Garey, M.R., Johnson, D.S.: Computers and Intractibility: A guide to the theory of NP-completeness. W. H. Freeman and Co., San Francisco (1979)zbMATHGoogle Scholar
  4. 4.
    Merz, P., Wolf, S.: Evolutionary Local Search for Designing Peer-to-Peer Overlay Topologies based on Minimum Routing Cost Spanning Trees. In: Runarsson, T.P., Beyer, H.-G., Burke, E.K., Merelo-Guervós, J.J., Whitley, L.D., Yao, X. (eds.) PPSN 2006. LNCS, vol. 4193, pp. 272–281. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  5. 5.
    Ahuja, R.K., Murty, V.V.S.: Exact and Heuristic Algorithms for the Optimum Communication Spanning Tree Problem. Transportation Science 21(3), 163–170 (1987)zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Wu, B.Y., Chao, K.M.: Spanning Trees and Optimization Problems. In: Discrete Mathematics and its Applications. Chapman & Hall/CRC, Boca Raton (2004)Google Scholar
  7. 7.
    Wu, B.Y., Lancia, G., Bafna, V., Chao, K.M., Ravi, R., Tang, C.Y.: A Polynomial-Time Approximation Scheme for Minimum Routing Cost Spanning Trees. SIAM Journal of Computing 29(3), 761–778 (1999)CrossRefMathSciNetGoogle Scholar
  8. 8.
    Singh, A.: A New Heuristic for the Minimum Routing Cost Spanning Tree Problem. In: International Conference on Information Technology (ICIT 2008), pp. 9–13. IEEE Computer Society, Los Alamitos (2008)Google Scholar
  9. 9.
    Lourenço, H.R., Martin, O., Stützle, T.: Iterated Local Search. In: Glover, F.W., Kochenberger, G.A. (eds.) Handbook of Metaheuristics. International Series in Operations Research & Management Science, vol. 57, pp. 321–353. Springer, Heidelberg (2002)Google Scholar
  10. 10.
    Moscato, P.: On Evolution, Search, Optimization, Genetic Algorithms and Martial Arts: Towards Memetic Algorithms. Caltech Concurrent Computation Program, C3P Report 826, California Institute of Technology, Pasadena, USA (1989)Google Scholar
  11. 11.
    Chun, B., Culler, D., Roscoe, T., Bavier, A., Peterson, L., Wawrzoniak, M., Bowman, M.: PlanetLab: An Overlay Testbed for Broad-Coverage Services. ACM SIGCOMM Computer Communication Review 33(3), 3–12 (2003)CrossRefGoogle Scholar
  12. 12.
    Banerjee, S., Griffin, T.G., Pias, M.: The Interdomain Connectivity of PlanetLab Nodes. In: Barakat, C., Pratt, I. (eds.) PAM 2004. LNCS, vol. 3015, pp. 73–82. Springer, Heidelberg (2004)Google Scholar
  13. 13.
    Stribling, J.: PlanetLab All-Pairs-Pings (2003–2005),

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Steffen Wolf
    • 1
  • Peter Merz
    • 2
  1. 1.University of KaiserslauternKaiserslauternGermany
  2. 2.University of Applied Sciences and Arts, HannoverHannoverGermany

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