Skip to main content

Efficient Cycle Search for the Minimum Routing Cost Spanning Tree Problem

  • Conference paper
Book cover Evolutionary Computation in Combinatorial Optimization (EvoCOP 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6022))

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Hu, T.C.: Optimum Communication Spanning Trees. SIAM Journal of Computing 3(3), 188–195 (1974)

    Article  MATH  Google Scholar 

  2. Johnson, D.S., Lenstra, J.K., Rinnooy Kan, A.H.G.: The Complexity of the Network Design Problem. Networks 8, 279–285 (1978)

    Article  MATH  MathSciNet  Google Scholar 

  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)

    MATH  Google Scholar 

  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)

    Chapter  Google Scholar 

  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)

    Article  MATH  MathSciNet  Google Scholar 

  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. 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)

    Article  MathSciNet  Google Scholar 

  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. 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. 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. 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)

    Article  Google Scholar 

  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. Stribling, J.: PlanetLab All-Pairs-Pings (2003–2005), http://pdos.csail.mit.edu/~strib/pl_app/

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Wolf, S., Merz, P. (2010). Efficient Cycle Search for the Minimum Routing Cost Spanning Tree Problem. In: Cowling, P., Merz, P. (eds) Evolutionary Computation in Combinatorial Optimization. EvoCOP 2010. Lecture Notes in Computer Science, vol 6022. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-12139-5_24

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-12139-5_24

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-12138-8

  • Online ISBN: 978-3-642-12139-5

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics