Algorithmica

, Volume 33, Issue 2, pp 168–182

Quasi-Fully Dynamic Algorithms for Two-Connectivity and Cycle Equivalence

Authors

  • M. R. Korupolu
    • Department of Computer Sciences, University of Texas at Austin, Austin, TX 78712-1188, USA. {madhukar, vlr}@cs.utexas.edu.
  • V. Ramachandran
    • Department of Computer Sciences, University of Texas at Austin, Austin, TX 78712-1188, USA. {madhukar, vlr}@cs.utexas.edu.
Article

DOI: 10.1007/s00453-001-0108-5

Cite this article as:
Korupolu, M. & Ramachandran, V. Algorithmica (2002) 33: 168. doi:10.1007/s00453-001-0108-5
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Abstract

We introduce a new class of dynamic graph algorithms called quasi-fully dynamic algorithms , which are much more general than backtracking algorithms and are much simpler than fully dynamic algorithms. These algorithms are especially suitable for applications in which a certain core connected portion of the graph remains fixed, and fully dynamic updates occur on the remaining edges in the graph. We present very simple quasi-fully dynamic algorithms with O(log  n) worst-case time per operation for 2-edge connectivity and O(log  n) amortized time per operation for cycle equivalence. The former is deterministic while the latter is Monte-Carlo-type randomized. For 2-vertex connectivity, we give a deterministic quasi-fully dynamic algorithm with O(log 3 n) amortized time per operation. The quasi-fully dynamic algorithm we present for cycle equivalence (which has several applications in optimizing compilers) is of special interest since the algorithm is quite simple, and no special-purpose incremental or backtracking algorithm is known for this problem.

Key words. Dynamic algorithms, Graph algorithms, Cycle equivalence, Connected graphs, Edge and vertex connectivity, Randomized algorithms, Compiler optimization.

Copyright information

© Springer-Verlag New York 2002