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Relaxed balanced redblack trees
 In Proc. 3rd Italian Conference on Algorithms and Complexity
, 1997
"... Abstract. Relaxed balancing means that, in a dictionary stored as a balanced tree, the necessary rebalancing after updates may be delayed. This is in contrast to strict balancing meaning that rebalancing is performed immediately after the update. Relaxed balancing is important for efficiency in high ..."
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Abstract. Relaxed balancing means that, in a dictionary stored as a balanced tree, the necessary rebalancing after updates may be delayed. This is in contrast to strict balancing meaning that rebalancing is performed immediately after the update. Relaxed balancing is important for efficiency in highly dynamic applications where updates can occur in bursts. The rebalancing tasks can be performed gradually after all urgent updates, allowing the concurrent use of the dictionary even though the underlying tree structure is not completely in balance. In this paper we propose a new scheme of how to make known rebalancing techniques relaxed in an efficient way. The idea is applied to the redblack trees, but can be applied to any class of balanced trees. The key idea is to accumulate insertions and deletions such that they can be settled in arbitrary order using the same rebalancing operations as for standard balanced search trees. As a result it can be shown that the number of needed rebalancing operations known from the strict balancing scheme carry over to relaxed balancing. 1
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...
HyperChromatic trees: a finegrained approach to distributed algorithms on RedBlack trees
, 1998
"... . We introduce a relaxed version of RedBlack trees. As concurrent algorithms on balanced search trees are nowadays based on local rules, we propose a set of finegrained local rules that take more advantage of concurrency than previous approaches. Based on them we design a rebalancing concurrent alg ..."
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. We introduce a relaxed version of RedBlack trees. As concurrent algorithms on balanced search trees are nowadays based on local rules, we propose a set of finegrained local rules that take more advantage of concurrency than previous approaches. Based on them we design a rebalancing concurrent algorithm and prove its correctness. Finally we sketch how to complete this algorithm to include concurrent insertions and deletions. Keywords: Concurrent algorithms, RedBlack trees, Concurrent rebalancing, Safety and liveness proofs, Local rules. 1 Motivation RedBlack trees are balanced search trees that have been recognized as an important data structure to deal with Dictionaries and Data Bases [CLR90]. Our aim is to deal with RedBlack trees in a concurrent environment. In this section we survey the previous approaches to this problem and outline our contributions. In a concurrent approach, algorithms are designed for a sharedmemory asynchronous parallel architecture. The first ones were d...
Amortized Constant Relaxed Rebalancing Using Standard Rotations
 Acta Informatica
, 1998
"... The idea of relaxed balance is to uncouple the rebalancing in search trees from the updating in order to speed up request processing in mainmemory databases during bursts of updates. This paper contains the first proof that amortized constant time rebalancing can be obtained in a relaxed binary sea ..."
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The idea of relaxed balance is to uncouple the rebalancing in search trees from the updating in order to speed up request processing in mainmemory databases during bursts of updates. This paper contains the first proof that amortized constant time rebalancing can be obtained in a relaxed binary search tree using only standard single and double rotations. 1 Introduction The idea of relaxed balance is to uncouple the rebalancing in search trees from the updating in order to speed up request processing in mainmemory databases. The motivation is twofold: If search and update requests for a search tree come in bursts (possibly from several external sources), the search tree may occasionally not be able to process the requests as fast as it might be desirable. For this reason, it would be convenient to be able to "turn off" rebalancing for a short period of time in order to speed up the request processing. However, when the burst is over, the tree should be rebalanced again, while search...
Chromatic Search Trees Revisited
, 1997
"... Relaxed balancing of search trees was introduced with the aim of speeding up the updates and allowing a high degree of concurrency. In a relaxed version of a search tree the rebalancing operations are uncoupled from the updates and may be delayed. Using local transformations the rebalancing can be p ..."
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Relaxed balancing of search trees was introduced with the aim of speeding up the updates and allowing a high degree of concurrency. In a relaxed version of a search tree the rebalancing operations are uncoupled from the updates and may be delayed. Using local transformations the rebalancing can be performed concurrently with updates and search operations. In this paper we revisit the rebalancing of chromatic trees, a relaxed version of redblack trees. During the rebalancing of a chromatic tree it can occur that the rebalancing operations change the search structure of the tree in order to settle rebalancing requests from the history although the tree is already a balanced redblack tree. We propose how to perform the rebalancing task in such a way that each performed structural change indeed correspond to a real imbalance situation in the tree. The number of rebalancing operations needed to restore the redblack tree balance condition is still O(i+d) pointer changes and ...
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...