Skip to main content

Experimental Analysis of Algorithms for Updating Minimum Spanning Trees on Graphs Subject to Changes on Edge Weights

  • Conference paper
Experimental Algorithms (WEA 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4525))

Included in the following conference series:

Abstract

We consider the problem of maintaining a minimum spanning tree of a dynamically changing graph, subject to changes on edge weights. We propose an on-line fully-dynamic algorithm that runs in time O(|E|) when the easy-to-implement DRD-trees data structure for dynamic trees is used. Numerical experiments illustrate the efficiency of the approach.

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.

Similar content being viewed by others

References

  1. Amato, G., Cattaneo, G., Italiano, G.F.: Experimental analysis of dynamic minimum spanning tree algorithms (extended abstract). In: Proceedings of the 8th Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 314–323. New Orleans (1997)

    Google Scholar 

  2. Buriol, L.S., Resende, M.G.C., Ribeiro, C.C., Thorup, M.: A memetic algorithm for OSPF routing. In: Proceedings of the 6th INFORMS Telecom, pp. 187–188. Boca Raton (2002)

    Google Scholar 

  3. Buriol, L.S., Resende, M.G.C., Ribeiro, C.C., Thorup, M.: A hybrid genetic algorithm for the weight setting problem in OSPF/IS-IS routing. Networks 46, 36–56 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  4. Buriol, L.S., Resende, M.G.C., Thorup, M.: Speeding up shortest path algorithms. Technical Report TD-5RJ8B, AT&T Labs Research (September 2003)

    Google Scholar 

  5. Cattaneo, G., Faruolo, P., Ferraro-Petrillo, U., Italiano, G.F.: Maintaining dynamic minimum spanning trees: An experimental study. In: Mount, D.M., Stein, C. (eds.) ALENEX 2002. LNCS, vol. 2409, pp. 111–125. Springer, Heidelberg (2002)

    Google Scholar 

  6. Demetrescu, C., Goldberg, A., Johnson, D.: Ninth DIMACS implementation challenge – shortest paths (2006), On-line reference at http://www.dis.uniroma1.it/c̃hallenge9/ , last visited in June 23

  7. Eppstein, D., Galil, Z., Italiano, G.F., Nissemzweig, A.: Sparsification – A technique for speeding up dynamic graph algorithms. Journal of the ACM 44, 669–696 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  8. Frederickson, G.N.: Data structures for on-line updating of minimum spanning trees, with applications. SIAM Journal on Computing 14, 781–798 (1985)

    Article  MATH  MathSciNet  Google Scholar 

  9. Frederickson, G.N.: Ambivalent data structures for dynamic 2-edge-connectivity and k smallest spanning trees. In: Proceedings of the 32nd Annual Symposium on Foundations of Computer Science, pp. 632–641. San Juan (1991)

    Google Scholar 

  10. Henzinger, M.H., King, V.: Maintaining minimum spanning trees in dynamic graphs. In: Degano, P., Gorrieri, R., Marchetti-Spaccamela, A. (eds.) ICALP 1997. LNCS, vol. 1256, pp. 594–604. Springer, Heidelberg (1997)

    Google Scholar 

  11. Holm, J., de Lichtenberg, K., Thorup, M.: Poly-logarithmic deterministic fully-dynamic algorithms for connectivity, minimum spanning tree, 2-edge, and biconnectivity. In: Proceedings of the 30th ACM Symposium on Theory of Computing, pp. 79–89. ACM Press, New York (1998)

    Google Scholar 

  12. Kruskal, J.B.: On the shortest spanning subtree of a graph and the traveling salesman problem. Proc. of the American Mathematical Society 7, 48–50 (1956)

    Article  MathSciNet  Google Scholar 

  13. Prim, R.C.: Shortest connection networks and some generalizations. Bell Systems Technical Journal 36, 1389–1401 (1957)

    Google Scholar 

  14. Pugh, W.: Skip lists: a probabilistic alternative to balanced trees. Communications of the ACM 33, 668–676 (1990)

    Article  Google Scholar 

  15. Sleator, D.D., Tarjan, R.E.: A data structure for dynamic trees. Journal of Computer and System Sciences 26, 362–391 (1983)

    Article  MATH  MathSciNet  Google Scholar 

  16. Spira, P.M., Pan, A.: On finding and updating spanning trees and shortest paths. SIAM Journal on Computing 4, 375–380 (1975)

    Article  MATH  MathSciNet  Google Scholar 

  17. Werneck, R.F., Tarjan, R.E.: Self-adjusting top trees. In: Proc. of the 16th Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 813–822. Vancouver (2005)

    Google Scholar 

  18. Zaroliagis, C.D.: Implementations and experimental studies of dynamic graph algorithms. In: Fleischer, R., Moret, B.M.E., Schmidt, E.M. (eds.) Experimental Algorithmics. LNCS, vol. 2547, pp. 229–278. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Camil Demetrescu

Rights and permissions

Reprints and permissions

Copyright information

© 2007 Springer Berlin Heidelberg

About this paper

Cite this paper

Ribeiro, C.C., Toso, R.F. (2007). Experimental Analysis of Algorithms for Updating Minimum Spanning Trees on Graphs Subject to Changes on Edge Weights. In: Demetrescu, C. (eds) Experimental Algorithms. WEA 2007. Lecture Notes in Computer Science, vol 4525. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72845-0_30

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-72845-0_30

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-72844-3

  • Online ISBN: 978-3-540-72845-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics