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Efficient Rebalancing of Chromatic Search Trees
 Journal of Computer and System Sciences
, 1993
"... In PODS'91, Nurmi and SoisalonSoininen presented a new type of binary search tree for databases, which they call a chromatic tree. The aim is to improve runtime performance by allowing a greater degree of concurrency, which, in turn, is obtained by uncoupling updating from rebalancing. This also al ..."
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Cited by 21 (7 self)
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In PODS'91, Nurmi and SoisalonSoininen presented a new type of binary search tree for databases, which they call a chromatic tree. The aim is to improve runtime performance by allowing a greater degree of concurrency, which, in turn, is obtained by uncoupling updating from rebalancing. This also allows rebalancing to be postponed completely or partially until after peak working hours. The advantages of the proposal...
BTrees with Relaxed Balance
 In Proceedings of the 9th International Parallel Processing Symposium
, 1993
"... Btrees with relaxed balance have been defined to facilitate fast updating on sharedmemory asynchronous parallel architectures. To obtain this, rebalancing has been uncoupled from the updating such that extensive locking can be avoided in connection with updates. We analyze Btrees with relaxed bal ..."
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Cited by 13 (6 self)
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Btrees with relaxed balance have been defined to facilitate fast updating on sharedmemory asynchronous parallel architectures. To obtain this, rebalancing has been uncoupled from the updating such that extensive locking can be avoided in connection with updates. We analyze Btrees with relaxed balance, and prove that each update gives rise to at most blog a (N=2)c + 1 rebalancing operations, where a is the degree of the Btree, and N is the bound on its maximal size since it was last in balance. Assuming that the size of nodes are at least twice the degree, we prove that rebalancing can be performed in amortized constant time. So, in the long run, rebalancing is constant time on average, even if any particular update could give rise to logarithmic time rebalancing. We also prove that the amount of rebalancing done at any particular level decreases exponentially going from the leaves towards the root. This is important since the higher up in the tree a lock due to a rebalancing operat...
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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Cited by 13 (0 self)
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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...
Relaxed Balance through Standard Rotations
 In Fifth International Workshop on Algorithms and Data Structures
, 1997
"... We consider binary search trees, where rebalancing transformations need not be connected with updates but may be delayed. For standard AVL tree rebalancing, we prove that even though the rebalancing operations are uncoupled from updates, their total number is bounded by O(M log(M+N)), where M is the ..."
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Cited by 12 (4 self)
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We consider binary search trees, where rebalancing transformations need not be connected with updates but may be delayed. For standard AVL tree rebalancing, we prove that even though the rebalancing operations are uncoupled from updates, their total number is bounded by O(M log(M+N)), where M is the number of updates to an AVL tree of initial size N. Hence, relaxed balancing of AVL trees comes at no extra cost asymptotically. Furthermore, our scheme differs from most other relaxed balancing schemes in an important aspect: No rebalancing transformation can be done in the wrong direction, i.e., no performed rotation can make the tree less balanced. Moreover, each performed rotation indeed corresponds to a real imbalance situation in the tree. Our results are important in designing efficient concurrency control strategies for mainmemory databases. Mainmemory search structures have gained new applications in large embedded systems, such as switching systems for mobile telephones.
Pattern Discovery from Biosequences
, 2002
"... In this thesis we have developed novel methods for analyzing biological data, the primary sequences of the DNA and proteins, the microarray based gene expression data, and other functional genomics data. The main contribution is the development of the pattern discovery algorithm SPEXS, accompanied b ..."
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Cited by 9 (1 self)
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In this thesis we have developed novel methods for analyzing biological data, the primary sequences of the DNA and proteins, the microarray based gene expression data, and other functional genomics data. The main contribution is the development of the pattern discovery algorithm SPEXS, accompanied by several practical applications for analyzing real biological problems. For performing these biological studies that integrate different types of biological data we have developed a comprehensive webbased biological data analysis environment Expression Profiler (http://ep.ebi.ac.uk/)...
Amortization Results for Chromatic Search Trees, with an Application to Priority Queues
, 1997
"... this paper, we prove that only an amortized constant amount of rebalancing is necessary after an update in a chromatic search tree. We also prove that the amount of rebalancing done at any particular level decreases exponentially, going from the leaves toward the root. These results imply that, in p ..."
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Cited by 7 (0 self)
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this paper, we prove that only an amortized constant amount of rebalancing is necessary after an update in a chromatic search tree. We also prove that the amount of rebalancing done at any particular level decreases exponentially, going from the leaves toward the root. These results imply that, in principle, a linear number of processes can access the tree simultaneously. We have included one interesting application of chromatic trees. Based on these trees, a priority queue with possibilities for a greater degree of parallelism than previous proposals can be implemented. ] 1997 Academic Press 1.
Relaxed Balancing Made Simple
, 1995
"... 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 dyn ..."
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Cited by 6 (0 self)
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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. The contribution of the present paper is that we introduce a new scheme for relaxed balancing, which is obtained by a simple generalization of strict balancing. Our approach implies a simple proof of the fact that the number of the needed rebalancing operations (to put the tree in balance) for relaxed balancing is the same as for strict balancing. 1 Introduction A dictionary is a scheme for storing a set of data such that the operations sea...
Chromatic Priority Queues
, 1994
"... We investigate the problem of implementing a priority queue to be used in a parallel environment, where asynchronous processes have access to a shared memory. Chromatic trees are a generalization of redblack trees appropriate for applications in such an environment, and it turns out that an appropr ..."
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Cited by 5 (2 self)
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We investigate the problem of implementing a priority queue to be used in a parallel environment, where asynchronous processes have access to a shared memory. Chromatic trees are a generalization of redblack trees appropriate for applications in such an environment, and it turns out that an appropriate priority queue can be obtained via minor modifications of chromatic trees. As opposed to earlier proposals, our deletemin operation is worstcase constant time, and insert is carried out as a fast search and constant time update, followed by an amortized constant number of rebalancing operations, which can be performed later by other processes, one at a time. If a general delete is desired, it can be implemented as a fast search and constant time update, followed by an amortized constant number of rebalancing operations, which again can be performed later by other processes, one at time. The amortization results here extend the results previously obtained for chromatic search trees. Sin...
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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Cited by 4 (3 self)
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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...
A SpeculationFriendly Binary Search Tree
"... We introduce the first binary search tree algorithm designed for speculative executions. Prior to this work, tree structures were mainly designed for their pessimistic (nonspeculative) accesses to have a bounded complexity. Researchers tried to evaluate transactional memory using such tree structur ..."
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Cited by 4 (1 self)
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We introduce the first binary search tree algorithm designed for speculative executions. Prior to this work, tree structures were mainly designed for their pessimistic (nonspeculative) accesses to have a bounded complexity. Researchers tried to evaluate transactional memory using such tree structures whose prominent example is the redblack tree library developed by Oracle Labs that is part of multiple benchmark distributions. Although wellengineered, such structures remain badly suited for speculative accesses, whose step complexity might raise dramatically with contention. We show that our speculationfriendly tree outperforms the existing transactionbased version of the AVL and the redblack trees. Its key novelty stems from the decoupling of update operations: they are split into one transaction that modifies the abstraction state and multiple ones that restructure its tree implementation in the background. In particular, the speculationfriendly tree is shown correct, reusable and it speeds up a transactionbased travel reservation application by up to 3.5×.