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Lower Bounds for Fully Dynamic Connectivity Problems in Graphs

Author
Fredman, Michael; Henzinger, Monika
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.
Date Issued
1995-12Publisher
Cornell University
Subject
computer science; technical report
Previously Published As
http://techreports.library.cornell.edu:8081/Dienst/UI/1.0/Display/cul.cs/TR95-1523
Type
technical report