A new class of balanced search trees : half-balanced binary search tress

Olivié, Hendrik

doi:10.1051/ita/1982160100511

Cited by 28 publications

(8 citation statements)

References 6 publications

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“…We generated five tree operation sequences, each performing a total of 2 26 operations on a tree of size n = 2 13 . To isolate the effect of rebalancing, only insertions and deletions were performed; the expected cost of interspersed accesses can be inferred from the average and maximum path lengths of the tree after each operation.…”

Section: Resultsmentioning

confidence: 99%

“…An algorithm for rebalancing after a deletion appeared several years later, in a technical report by a different author [7]; deletion requires O(log n) rotations rather than O (1). For all existing forms of balanced trees, of which there are many [3,4,5,9,10,12,13,16], deletion is at least a little more complicated than insertion, although for some kinds of balanced search trees, notably red-black trees [9] and the recently introduced rank-balanced trees [10], rebalancing after a deletion can be done in O(1) rotations. Many textbooks describe algorithms for insertion but not deletion.…”

Section: Introductionmentioning

confidence: 99%

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Deletion Without Rebalancing in Balanced Binary Trees

Sen¹,

Tarjan²

2010

Proceedings of the Twenty-First Annual ACM-SIAM Symposium on Discrete Algorithms

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We address the vexing issue of deletions in balanced trees. Rebalancing after a deletion is generally more complicated than rebalancing after an insertion. Textbooks neglect deletion rebalancing, and many database systems do not do it. We describe a relaxation of AVL trees in which rebalancing is done after insertions but not after deletions, yet access time remains logarithmic in the number of insertions. For many applications of balanced trees, our structure offers performance competitive with that of classical balanced trees. With the addition of periodic rebuilding, the performance of our structure is theoretically superior to that of many if not all classic balanced tree structures. Our structure needs O(log log m) bits of balance information per node, where m is the number of insertions, or O(log log n) with periodic rebuilding, where n is the number of nodes. An insertion takes up to two rotations and O(1) amortized time. Using an analysis that relies on an exponential potential function, we show that rebalancing steps occur with a frequency that is exponentially small in the height of the affected node.

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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Deletion Without Rebalancing in Balanced Binary Trees

Sen¹,

Tarjan²

2010

Proceedings of the Twenty-First Annual ACM-SIAM Symposium on Discrete Algorithms

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“…(3) Rank-balanced trees, like the half-balanced trees [14,15]. (4) Degree-balanced trees, like the ubiquitous B-tree [2].…”

Section: Definition 3 ( Parametrically Balanced Trees)mentioning

confidence: 99%

Splay trees: a reweighing lemma and a proof of competitiveness vs. dynamic balanced trees

Γεωργακόπουλος

2004

Journal of Algorithms

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“…Also symmetric binary B-trees [5] and half-balanced trees [27] fulfill the requirements, so worst-case logarithmic rebalancing per update is obtained. This is not too surprising since these are similar to red-black trees, in the sense that the shape of the trees arising from these two paradigms can always be colored in such a way that a red-black tree is obtained.…”

Section: Examplesmentioning

confidence: 99%

Relaxed balance for search trees with local rebalancing

Larsen¹,

Ottmann²,

Soininen³

2001

Acta Informatica

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Search trees with relaxed balance were introduced with the aim of facilitating fast updating on shared-memory asynchronous parallel architectures. To obtain this, rebalancing has been uncoupled from the updating, so extensive locking in connection with updates is avoided. Rebalancing is taken care of by background processes, which do only a constant amount of work at a time before they release locks. Thus, the rebalancing and the associated locks are very localized in time as well as in space. In particular, there is no exclusive locking of whole paths. This means that the amount of parallelism possible is not limited by the height of the tree.Search trees with relaxed balance have been obtained by adapting standard sequential search trees to this new paradigm; clearly using similar techniques in each case, but no general result has been obtained. We show how any search tree with local bottom-up rebalancing can be used in a relaxed variant, preserving the complexity of the rebalancing from the sequential case. Additionally, we single out the one high level locking mechanism that a parallel implementation must provide in order to guarantee consistency.

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A new class of balanced search trees : half-balanced binary search tress

Cited by 28 publications

References 6 publications

Deletion Without Rebalancing in Balanced Binary Trees

Deletion Without Rebalancing in Balanced Binary Trees

Splay trees: a reweighing lemma and a proof of competitiveness vs. dynamic balanced trees

Relaxed balance for search trees with local rebalancing

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