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Scandinavian Workshop on Algorithm Theory

SWAT 2000: Algorithm Theory - SWAT 2000 pp 1–9Cite as

Dynamic Graph Algorithms with Applications

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1851))

Abstract. p]First we review amortized fully-dynamic polylogarithmic algorithms for connectivity, minimum spanning trees (MST), 2-edge- and biconnectivity. Second we discuss how they yield improved static algorithms: connectivity for constructing a tree from homeomorphic subtrees, 2-edge connectivity for finding unique matchings in graphs, and MST for packing spanning trees in graphs.

The application of MST for spanning tree packing is new and when boot-strapped, it yields a fully-dynamic polylogarithmic algorithm for approximating general edge connectivity within a factor \( \sqrt {2 + o\left( 1 \right)} \) . Finally, on the more practical side, we will discuss how output sensitive algorithms for dynamic shortest paths have been applied successfully to speed up local search algorithms for improving routing on the internet, roughly doubling the capacity.

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References

  1. E. H. L. Aarts and J. K. Lenstra, editors. Local Search in Combinatorial Optimization. Discrete Mathematics and Optimization. Wiley-Interscience, Chichester, England, June 1997.

    MATH  Google Scholar 

  2. A.V. Aho, Y. Sagiv, T.G. Szymanski, and J.D. Ullman. Inferring a tree from lowest common ancestors with an application to the optimization of relational expressions. SIAM J. Computing, 10(3):405–421, 1981.

    Article  MATH  MathSciNet  Google Scholar 

  3. T.C. Biedl, P. Bose, E.D. Demaine, and A. Lubiw. Efficient algorithms for Petersen’s matching theorem. In Proc. 10th ACM-SIAM Symp. on Discrete Algorithms,pages 130–139, 1999.

    Google Scholar 

  4. E. W. Dijkstra. A note on two problems in connection with graphs. Numer. Math., 1:269–271, 1959.

    Article  MATH  MathSciNet  Google Scholar 

  5. D. Eppstein, Z. Galil, G. F. Italiano, and A. Nissenzweig. Sparsification — a technique for speeding up dynamic graph algorithms. J. ACM, 44(5):669–696, 1997. See also FOCS’92.

    Article  MATH  MathSciNet  Google Scholar 

  6. B. Fortz and M. Thorup. Internet traffic engineering by optimizing OSPF weights. In Proc. 19th IEEE INFOCOM-Conf. Computer Communications, pages 519–528, 2000.

    Google Scholar 

  7. D. Frigioni, M. Ioffreda, U. Nanni, and G. Pasqualone. Experimental analysis of dynamic algorithms for the single-source shortest path problem. ACM J. Experimental Algorithmics, 3, article 5, 1998.

    Google Scholar 

  8. H. N. Gabow. A matroid approach to finding edge connectivity and packing arborescences. J. Comp. Syst. Sc., 50:259–273, 1995.

    Article  MATH  MathSciNet  Google Scholar 

  9. H.N. Gabow, H. Kaplan, and R.E. Tarjan. Unique maximum matching algorithms. In Proc. 31st ACM Symp. on Theory of Computing, pages 70–78, 1999.

    Google Scholar 

  10. M.R. Henzinger, V. King, and T. Warnow. Constructing a tree from homeomorphic subtrees, with applications to computational evolutionary biology. Algorithmica, 24(1):1–13, 1999.

    Article  MATH  MathSciNet  Google Scholar 

  11. J. Holm, K. de Lichtenberg, and M. Thorup. Poly-logarithmic deterministic fully-dynamic algorithms for connectivity, minimum spanning tree, 2-edge, and biconnectivity. In Proc. 30th ACM Symp. on Theory of Computing, pages 79–89, 1998.

    Google Scholar 

  12. S. Kannan, T. Warnow, and S. Yooseph. Computing the local consensus of trees. SIAM J. Computing, 27(6):1695–1724, 1998.

    Article  MATH  MathSciNet  Google Scholar 

  13. D. R. Karger. Using randomized sparsification to approximate minimum cuts. In Proc. 5th ACM-SIAM Symp. on Discrete Algorithms, pages 424–432, 1994.

    Google Scholar 

  14. D. R. Karger. Better random sampling algorithms for flows in undirected graphs. In Proc. 9th ACM-SIAM Symp. on Discrete Algorithms, pages 490–499, 1998.

    Google Scholar 

  15. D. R. Karger. Minimum cuts in near-linear time. J. ACM, 47(1), 2000.

    Google Scholar 

  16. V. King. Fully dynamic algorithms for maintaining all-pairs shortest paths and transitive closure in digraphs. In Proc. 40th IEEE Symp. on Foundations of Computer Science, pages 81–89, 1999.

    Google Scholar 

  17. A. Kotzig. On the theory of finite graphs with a linear factor I. Mat.-Fyz. Casopis Slovensk. Akad. Vied, 9:73–91, 1959.

    MATH  Google Scholar 

  18. D. W. Matula. A linear time 2 + ∈ approximation algorithm for edge connectivity. In Proc. 4th ACM-SIAM Symp. on Discrete Algorithms, pages 500–504, 1993.

    Google Scholar 

  19. J. T. Moy. OSPF: Anatomy of an Internet Routing Protocol. Addison-Wesley, 1999.

    Google Scholar 

  20. H. Nagamochi and T. Ibaraki. Linear time algorithms for finding a sparse k-connected spanning subgraph of a k-connected graph. Algorithmica, 7:583–596, 1992.

    Article  MathSciNet  MATH  Google Scholar 

  21. C. St. J. A. Nash-Williams. Edge disjoint spanning trees of finite graphs. J. London Math. Soc., 36:445–450, 1991.

    Article  MathSciNet  Google Scholar 

  22. J. Petersen. Die theorie der regulären graphs. Acta Mathematica, 15:193–220, 1891.

    Article  MathSciNet  Google Scholar 

  23. S. A. Plotkin, D. B. Shmoys, and E. Tardos. Fast approximation algorithms for fractional packing and covering problems. Mathematics of Operations Research, 20:257–301, 1995.

    Article  MATH  MathSciNet  Google Scholar 

  24. G. Ramalingam and T. Reps. An incremental algorithm for a generalization of the shortest-path problem. J. Algorithms, 21(2):267–305, 1996.

    Article  MATH  MathSciNet  Google Scholar 

  25. N. Young. Randomized rounding without solving the linear program. In Proc. 6th ACM-SIAM Symp. on Discrete Algorithms (SODA), pages 170–178, 1995.

    Google Scholar 

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Authors and Affiliations

  1. AT&T Labs-Research, Shannon Laboratory, 180 Park Avenue, Florham Park, NJ, 07932

    Mikkel Thorup

  2. MIT Laboratory for Computer Science, Cambridge, MA, 02138

    David R. Karger

Authors
  1. Mikkel Thorup
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  2. David R. Karger
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© 2000 Springer-Verlag Berlin Heidelberg

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Thorup, M., Karger, D.R. (2000). Dynamic Graph Algorithms with Applications. In: Algorithm Theory - SWAT 2000. SWAT 2000. Lecture Notes in Computer Science, vol 1851. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44985-X_1

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  • DOI: https://doi.org/10.1007/3-540-44985-X_1

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-67690-4

  • Online ISBN: 978-3-540-44985-0

  • eBook Packages: Springer Book Archive

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