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The Performance of Concurrent RedBlack Tree Algorithms
 Lecture Notes in Computer Science
, 1998
"... 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 bala ..."
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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 redblack 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 redblack 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 redblack trees, and the relaxed redblack tree. Furthermore, we compare the relaxed balancing algorithms with the standard redblack tree, i.e. the strictly balanced redblack tree combined with the locking scheme of El...
A General Technique for Nonblocking Trees
"... Abstract. We describe a general technique for obtaining provably correct, nonblocking implementations of a large class of tree data structures where pointers are directed from parents to children. Updates are permitted to modify any contiguous portion of the tree atomically. Our nonblocking algo ..."
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Abstract. We describe a general technique for obtaining provably correct, nonblocking implementations of a large class of tree data structures where pointers are directed from parents to children. Updates are permitted to modify any contiguous portion of the tree atomically. Our nonblocking algorithms make use of the LLX, SCX and VLX primitives, which are multiword generalizations of the standard LL, SC and VL primitives and have been implemented from singleword CAS [10]. To illustrate our technique, we describe how it can be used in a fairly straightforward way to obtain a nonblocking implementation of a chromatic tree, which is a relaxed variant of a redblack tree. The height of the tree at any time is O(c + logn), where n is the number of keys and c is the number of updates in progress. We provide an experimental performance analysis which demonstrates that our Java implementation of a chromatic tree rivals, and often significantly outperforms, other leading concurrent dictionaries. 1
Relaxed MultiWay Trees with Group Updates
 In Proceedings of the twentieth ACM SIGMODSIGACTSIGART symposium on Principles of database systems
, 2000
"... 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 multiway trees called (a; b)trees (which includes Btrees) with ..."
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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 multiway trees called (a; b)trees (which includes Btrees) 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 multiway trees usually referred to as (a; b)trees [8, 15], and in particular, we adopt the relaxed (a...
Variants of (a, b)Trees with Relaxed Balance
, 1999
"... New variants of (a, b)trees with relaxed balance are proposed. These variants have better space utilization than the earlier proposals, while the asymptotic complexity of rebalancing is unchanged. The proof of complexity, which is derived, is much simpler than the ones previously published. Through ..."
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New variants of (a, b)trees with relaxed balance are proposed. These variants have better space utilization than the earlier proposals, while the asymptotic complexity of rebalancing is unchanged. The proof of complexity, which is derived, is much simpler than the ones previously published. Through experiments, some of the most interesting applications of this data structure are modeled, and it is demonstrated that the new variants are competitive.
Complexity of Layered Binary Search Trees with Relaxed Balance
, 1999
"... When search trees are made relaxed, balance constraints are weakened such that updates can be made without immediate rebalancing. This can lead to a speedup in some circumstances. However, the weakened balance constraints also make it more challenging to prove complexity results for relaxed str ..."
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When search trees are made relaxed, balance constraints are weakened such that updates can be made without immediate rebalancing. This can lead to a speedup in some circumstances. However, the weakened balance constraints also make it more challenging to prove complexity results for relaxed structures. In our opinion, one of the simplest and most intuitive presentations of balanced search trees has been given via layered trees. We show that relaxed layered trees are among the best of the relaxed structures. More precisely, rebalancing is worstcase logarithmic and amortized constant per update, and restructuring is worstcase constant per update. Introduction Usually, updating in a balanced search tree is carried out as follows: First, a search is carried out in order to determine the location of the update. Second, the update is performed. Third, local balance constraints are reconsidered. Supported in part by the Danish Natural Sciences Research Council (SNF). y Depart...