Abstract.
We prove lower bounds on the complexity of maintaining fully dynamic k -edge or k -vertex connectivity in plane graphs and in (k-1) -vertex connected graphs. We show an amortized lower bound of \(\Omega\) (log n / {k (log log n} + log b)) per edge insertion, deletion, or query operation in the cell probe model, where b is the word size of the machine and n is the number of vertices in G . We also show an amortized lower bound of \(\Omega\) (log n /(log log n + log b)) per operation for fully dynamic planarity testing in embedded graphs. These are the first lower bounds for fully dynamic connectivity problems.
Similar content being viewed by others
Author information
Authors and Affiliations
Additional information
Received January 1995; revised February 1997.
Rights and permissions
About this article
Cite this article
Henzinger, M., Fredman, M. Lower Bounds for Fully Dynamic Connectivity Problems in Graphs . Algorithmica 22, 351–362 (1998). https://doi.org/10.1007/PL00009228
Issue Date:
DOI: https://doi.org/10.1007/PL00009228