Relaxed balancing has become a commonly used concept in the design of concurrent search tree algorithms. The idea of relaxed balancing is to uncouple the rebalancing from the updating in order to speed up the update operations and to allow a high degree of concurrency. Many different relaxed balancing algorithms have been proposed, especially for red-black trees and AVL trees, but their performance in concurrent environments is not yet well understood. This paper presents an experimental comparison of three relaxed balancing algorithms for red-black trees. Using the simulation of a multi processor environment we study the performance of chromatic trees, the algorithm that is got by applying the general method of how to make strict balancing schemes relaxed to red-black trees, and the relaxed redblack tree. Furthermore, we compare the relaxed balancing algorithms with the standard red-black tree, i.e. the strictly balanced red-black tree combined with the locking scheme of El...

Data structures with relaxed balance dier from standard structures in that rebalancing can be delayed and interspersed with updates. This gives extra exibility in both sequential and parallel applications. We study the version of multi-way trees called (a; b)-trees (which includes B-trees) with the operations insertion, deletion, and group insertion. The latter has applications in for instance document databases and WWW search engines. We prove that we obtain the optimal asymptotic rebalancing complexities of amortized constant time for insertion and deletion and amortized logarithmic time in the size of the group for group insertion. These results hold even for the relaxed version. Our results also demonstrate that a binary tree scheme with the same complexities can be designed. This is an improvement over the existing results. 1 Introduction We focus on the type of multi-way trees usually referred to as (a; b)-trees [8, 15], and in particular, we adopt the relaxed (a...