AVL Trees With Relaxed Balance

Abstract

AVL trees with relaxed balance were introduced with the aim of improving runtime performance by allowing a greater degree of concurrency. This is obtained by uncoupling updating from rebalancing. An additional benefit is that rebalancing can be controlled separately. In particular, it can be postponed completely or partially until after peak working hours.We define a new collection of rebalancing operations which allows for a significantly greater degree of concurrency than the original proposal. Additionally, in contrast to the original proposal, we prove the complexity of our algorithm.If N is the maximum size of the tree, we prove that each insertion gives rise to at most log φ (N +

A general technique for non-blocking trees

“…Given a copy of [23], and this paper, a first year undergraduate student produced our Java implementation of a relaxed-balance AVL tree in less than a week. Its performance was slightly lower than that of Chromatic.…”

“…Moreover, an amortized constant number of rebalancing steps per Insert or Delete is sufficient to restore balance for any sequence of operations. We have also used our template to implement a non-blocking version of Larsen's leaf-oriented relaxed AVL tree [23]. In such a tree, an amortized logarithmic number of rebalancing steps per Insert or Delete is sufficient to restore balance.…”

Parallelizing DSW Trees

“…A later approach by Larsen [7] attempts to address this requirement by relaxing the balance requirement of the AVL tree. In this approach rather than rebalance immediately, a node will be tagged when it is out of balance.…”

Parallelize DSW Algorithm

“…A plethora of literature investigates this attribute from 1978, when L. J. Guibas first mentioned this in their paper [14]. Then this technique spread over the tree family, including AVL trees [3], [15], B trees [16], [17], (a,b) trees [18], 2-3 trees [19], and red-black trees [14], [20], [21]. As most literature points out, how often should trees be rebalanced depends heavily on applications, therefore we just leave this part alone but focus on the parallelization of the DSW algorithm.…”