Encyclopedia of Algorithms

2008 Edition
| Editors: Ming-Yang Kao

Fully Dynamic Connectivity

2001; Holm, de Lichtenberg, Thorup
  • Valerie King
Reference work entry
DOI: https://doi.org/10.1007/978-0-387-30162-4_152

Keywords and Synonyms

Incremental algorithms for graphs; Fully dynamic graph algorithm for maintaining connectivity

Problem Definition

Design a data structure for an undirected graph with a fixed set of nodes which can process queries of the form “Are nodes i and j connected?” and updates of the form “Insert edge \( { \{i,j\} } \)

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Recommended Reading

  1. 1.
    Eppstein, D., Galil, Z., Italiano, G.F., Nissenzweig, A.:. Sparsification–a technique for speeding up dynamic graph algorithms. J. ACM 44(5), 669–696.1 (1997)MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    Henzinger, M.R., King, V.: Randomized fully dynamic graph algorithms with polylogarithmic time per operation. J. ACM 46(4), 502–536 (1999) (presented at ACM STOC 1995)MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    Henzinger, M.R., Thorup, M.: Sampling to provide or to bound: With applications to fully dynamic graph algorithms. Random Struct. Algorithms 11(4), 369–379 (1997) (presented at ICALP 1996)MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    Holm, J., De Lichtenberg, K., Thorup, M.: Poly-logarithmic Deterministic Fully-Dynamic Algorithms for Connectivity, Minimum Spanning Tree, 2-Edge, and Biconnectivity. J. ACM 48(4), 723–760 (2001) (presented at ACM STOC 1998)MathSciNetzbMATHCrossRefGoogle Scholar
  5. 5.
    Iyer, R., Karger, D., Rahul, H., Thorup, M.: An experimental study of poly-logarithmic fully-dynamic connectivity algorithms. J. Exp. Algorithmics 6(4) (2001) (presented at ALENEX 2000)Google Scholar
  6. 6.
    Pătraşcu, M., Demaine, E.: Logarithmic Lower Bounds in the Cell-Probe Model. SIAM J. Comput. 35(4), 932–963 (2006) (presented at ACM STOC 2004)MathSciNetzbMATHCrossRefGoogle Scholar
  7. 7.
    Thorup, M.: Near-optimal fully-dynamic graph connectivity. In: Proceedings of the 32th ACM Symposium on Theory of Computing pp. 343–350. ACM STOC (2000) Google Scholar
  8. 8.
    Thorup, M.: Dynamic Graph Algorithms with Applications. In: Halldórsson, M.M. (ed) 7th Scandinavian Workshop on Algorithm Theory (SWAT), Norway, 5–7 July 2000, pp. 1–9Google Scholar
  9. 9.
    Zaroliagis, C.D.: Implementations and experimental studies of dynamic graph algorithms. In: Experimental Algorithmics, Dagstuhl seminar, September 2000, Lecture Notes in Computer Science, vol. 2547. Springer (2002), Journal Article: J. Exp. Algorithmics 229–278 (2000)Google Scholar

Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  • Valerie King
    • 1
  1. 1.Department of Computer ScienceUniversity of VictoriaVictoriaCanada