A dichromatic framework for balanced trees

Guibas, Leo J.; Sedgewick, Robert

doi:10.1109/sfcs.1978.3

Cited by 448 publications

(249 citation statements)

References 7 publications

Supporting

Mentioning

241

Contrasting

Unclassified

Order By: Relevance

“…The analysis of the behavior of a relaxed version of AVL trees [1] introduced in [22] was given in [17]. The structure chromatic search tree of interest in this paper is a relaxed version of red black trees [3,9]. As already mentioned, this structure was introduced in [21] and analyzed in [8].…”

Section: Introductionmentioning

confidence: 99%

Amortization results for chromatic search trees, with an application to priority queues

Boyar¹,

Fagerberg²,

Larsen³

1995

Lecture Notes in Computer Science

View full text Add to dashboard Cite

The intention in designing data structures with relaxed balance, such as chromatic search trees, is to facilitate fast updating on shared-memory asynchronous parallel architectures. To obtain this, the updating and rebalancing have been uncoupled, so extensive locking in connection with updates is avoided. In 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

show abstract

Section: Introductionmentioning

confidence: 99%

Amortization results for chromatic search trees, with an application to priority queues

Boyar¹,

Fagerberg²,

Larsen³

1995

Lecture Notes in Computer Science

View full text Add to dashboard Cite

show abstract

“…One standard implementation of a dictionary is as a red-black tree [GS78], which is a type of balanced binary search tree. However, often when a data structure is accessed and updated by different processes in a concurrent environment, parts of the structure have to be locked while data items are changed or deleted.…”

Section: Introductionmentioning

confidence: 99%

“…However, often when a data structure is accessed and updated by different processes in a concurrent environment, parts of the structure have to be locked while data items are changed or deleted. In the case of red-black trees of size n, an update requires locking O(log 2 (n)) nodes, though not necessarily simultaneously [GS78], in order to rebalance the tree. No other users can access the subtree below a node which is locked.…”

Section: Introductionmentioning

confidence: 99%

Efficient Rebalancing of Chromatic Search Trees

Boyar

Larsen²

1992

DPB

View full text Add to dashboard Cite

In PODS'91, Nurmi and Soisalon-Soininen 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 of Nurmi and Soisalon-Soininen are quite significant, but there are definite problems with it. First, they give no explicit upper bound on the complexity of their algorithm. Second, some of their rebalancing operations can be applied many more times than necessary. Third, some of their operations, when removing one problem, create another.We define a new set of rebalancing operations which we prove give rise to at most log 2 (N + 1) − 1 rebalancing operations per insertion and at most log 2 (N + 1) − 2 rebalancing operations per deletion, where N is the maximum size the tree could ever have, given its initial size and the number of insertions performed. Most of these rebalancing operations, in fact, do no restructuring; they simply move weights around. The number of operations which actually change the structure of the tree is at most one per update.

show abstract

“…), an external implementation is necessary. The choice was to use the GLIBC tsearch built-in function family [4], that provides a very efficient implementation of balanced binary trees (more precisely, of Red-Black-Trees [5]). …”

Section: Implementation Detailsmentioning

confidence: 99%

Solving Multilocal Optimization Problems with a Recursive Parallel Search of the Feasible Region

Pereira

Rufino

2014

Computational Science and Its Applications – ICCSA 2014

View full text Add to dashboard Cite

Abstract. Stretched Simulated Annealing (SSA) combines simulated annealing with a stretching function technique, in order to solve multilocal programming problems. This work explores an approach to the parallelization of SSA, named PSSA-HeD, based on a recursive heterogeneous decomposition of the feasible region and the dynamic distribution of the resulting subdomains by the processors involved. Three PSSAHeD variants were implemented and evaluated, with distinct limits on the recursive search depth, offering different levels of numerical and computational efficiency. Numerical results are presented and discussed.

show abstract

A dichromatic framework for balanced trees

Cited by 448 publications

References 7 publications

Amortization results for chromatic search trees, with an application to priority queues

Amortization results for chromatic search trees, with an application to priority queues

Efficient Rebalancing of Chromatic Search Trees

Solving Multilocal Optimization Problems with a Recursive Parallel Search of the Feasible Region

Contact Info

Product

Resources

About