Relaxed balance for search trees with local rebalancing

Abstract

Search trees with relaxed balance were introduced with the aim of facilitating fast updating on shared-memory asynchronous parallel architectures. To obtain this, rebalancing has been uncoupled from the updating, so extensive locking in connection with updates is avoided. Rebalancing is taken care of by background processes, which do only a constant amount of work at a time before they release locks. Thus, the rebalancing and the associated locks are very localized in time as well as in space. In particular, there is no exclusive locking of whole paths. This means that the amount of parallelism possible is not limited by the height of the tree.Search trees with relaxed balance have been obtained by adapting standard sequential search trees to this new paradigm; clearly using similar techniques in each case, but no general result has been obtained. We show how any search tree with local bottom-up rebalancing can be used in a relaxed variant, preserving the complexity of the rebalancing from the sequential case. Additionally, we single out the one high level locking mechanism that a parallel implementation must provide in order to guarantee consistency.

AVL Trees with Relaxed Balance

“…Some of the earlier results are surveyed in [28]. In [18,27], it is shown how a large class of standard search trees can automatically be equipped with relaxed balance, and a version of red black trees based on these general ideas is described in [10]. Finally, a description and an analysis of group updates in relaxed trees can be found in [21], and experimental results which indicate that relaxed trees improve the performance in multiprocessor environments are reported in [9].…”

A general technique for non-blocking trees

“…For example, a chromatic tree is a relaxed-balance version of a red-black tree (RBT) which splits up the insertion or deletion of a key and any subsequent rotations into a sequence of localized updates. There is a rich literature of relaxed-balance versions of sequential data structures [22], and several papers (e.g., [24]) have described general techniques that can be used to easily produce them from large classes of existing sequential data structures. The small number of nodes involved in each update makes relaxed-balance data structures perfect candidates for efficient implementation using our technique.…”