  Fully dynamic graph algorithms that achieve polylogarithmic or better time
per operation use either a hierarchical graph decomposition or random-rank
based approach. There are so far two graph properties for which efficient
algorithms for both types of data structures exist, namely fully dynamic (Delta
+ 1) coloring and fully dynamic maximal matching. In this paper we present an
extensive experimental study of these two types of algorithms for these two
problems together with very simple baseline algorithms to determine which of
these algorithms are the fastest. Our results indicate that the data structures
used by the different algorithms dominate their performance.
