- 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 151-164. Springer, 1992.
In PODS'91, Nurmi and Soisalon-Soininen 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
The advantages of the proposal of Nurmi and Soisalon-Soininen 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
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.
- Link to the publication at the publisher's site - subscription may be required.
Text required by the publisher (if any):
The final publication is available at link.springer.com.
Link to the journal version containing all the material and proofs, some of which are usually omitted in the conference version due to space constraints.
Other publications by the author.