Efficient Rebalancing of Chromatic Search Trees.
Joan F. Boyar and Kim S. Larsen.
Journal of Computer and System Sciences, 49(3): 667-682, 1994.
Chromatic trees were defined by Nurmi and Soisalon-Soininen, as a new type of binary search tree for databases. 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 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 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.

Link to the publication at the publisher's site - subscription may be required.
Text required by the publisher (if any): The publication is available from ScienceDirect.

open access (153 KB)
The same as the publisher's version, when the publisher permits. Otherwise, the author's last version before the publisher's copyright; this is often exactly the same, but sometimes fonts, page numbers, figure numbers, etc. are different. It may also be a full version. However, it is safe to read this version, and at the same time cite the official version, as long as references to concrete locations, numbered theorems, etc. inside the article are avoided.

other publications
Other publications by the author.