 Efficient Rebalancing of Chromatic Search Trees.
 Joan F. Boyar and Kim S. Larsen.
In 3rd Scandinavian Workshop on Algorithm Theory (SWAT), volume 621 of Lecture Notes in Computer Science, pages 151164. Springer, 1992.
In PODS'91, Nurmi and SoisalonSoininen presented a new type of binary
search tree for databases,
which they call a
chromatic tree. The aim is to improve
runtime performance by allowing a greater degree of concurrency, which, in
turn, is obtained by uncoupling updating from rebalancing. This also allows
rebalancing to be postponed completely or partially until after peak working
hours.
The advantages of the proposal of Nurmi and SoisalonSoininen are quite
significant, but there are definite problems with it.
First, they give no explicit upper bound on
the complexity of their algorithm. Second, some of their rebalancing
operations can be applied many more times than necessary. Third, some of their
operations, when removing one problem, create another.
We define a
new set of rebalancing operations which we prove give rise to at most
floor(log_2(N+1))1 rebalancing operations per insertion
and at most floor(log_2(N+1))2 rebalancing operations per deletion,
where N is the maximum size the tree
could ever have, given its initial size and the number of insertions
performed.
Most of these rebalancing operations, in fact, do no restructuring; they simply
move weights around. The number of operations which actually change the
structure of the tree is at most one per update.

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