## Amortized Constant Relaxed Rebalancing Using Standard Rotations (1998)

Venue: | Acta Informatica |

Citations: | 4 - 3 self |

### BibTeX

@ARTICLE{Larsen98amortizedconstant,

author = {Kim S. Larsen},

title = {Amortized Constant Relaxed Rebalancing Using Standard Rotations},

journal = {Acta Informatica},

year = {1998},

volume = {35},

pages = {35--10}

}

### OpenURL

### Abstract

The idea of relaxed balance is to uncouple the rebalancing in search trees from the updating in order to speed up request processing in main-memory 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 main-memory databases. The motivation is two-fold: 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...

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Citation Context ...first relaxed version of B-trees [3] is also from [15] with proofs of complexity matching the sequential ones in [12]. Since [12] really treats (a; b)-trees [9], it also provides proofs for 2-3 trees =-=[8, 2]-=-, as well as for (a; b)- trees with other choices of a and b. A relaxed version of red-black trees [6] was introduced in [16, 17] and complexities matching the sequential case were established in [5] ... |

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Citation Context ...atching the complexity from the sequential case, was obtained in [11]. A different AVL-based version with some especially nice properties was treated in [19, 14]. The first relaxed version of B-trees =-=[3]-=- is also from [15] with proofs of complexity matching the sequential ones in [12]. Since [12] really treats (a; b)-trees [9], it also provides proofs for 2-3 trees [8, 2], as well as for (a; b)- trees... |

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Citation Context ...is challenging to prove the complexity results for them. We give a brief account of the work done in relaxed balancing. The idea of uncoupling the rebalancing from the updating was first mentioned in =-=[6]-=-, and the first partial result, dealing with insertions only, is from [10]. The first relaxed version of AVL-trees [1] was presented in [15] and proofs of complexity for the rebalancing, matching the ... |

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Citation Context ...ce properties was treated in [19, 14]. The first relaxed version of B-trees [3] is also from [15] with proofs of complexity matching the sequential ones in [12]. Since [12] really treats (a; b)-trees =-=[9]-=-, it also provides proofs for 2-3 trees [8, 2], as well as for (a; b)- trees with other choices of a and b. A relaxed version of red-black trees [6] was introduced in [16, 17] and complexities matchin... |

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Citation Context ...ing the rebalancing from the updating was first mentioned in [6], and the first partial result, dealing with insertions only, is from [10]. The first relaxed version of AVL-trees [1] was presented in =-=[15]-=- and proofs of complexity for the rebalancing, matching the complexity from the sequential case, was obtained in [11]. A different AVL-based version with some especially nice properties was treated in... |

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Citation Context ...ns only, is from [10]. The first relaxed version of AVL-trees [1] was presented in [15] and proofs of complexity for the rebalancing, matching the complexity from the sequential case, was obtained in =-=[11]-=-. A different AVL-based version with some especially nice properties was treated in [19, 14]. The first relaxed version of B-trees [3] is also from [15] with proofs of complexity matching the sequenti... |

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Citation Context ...2] really treats (a; b)-trees [9], it also provides proofs for 2-3 trees [8, 2], as well as for (a; b)- trees with other choices of a and b. A relaxed version of red-black trees [6] was introduced in =-=[16, 17]-=- and complexities matching the sequential case were established in [5] and [4] for variants of the original proposal. In [19], some of these early results are surveyed. In [18, 13], it is shown how a ... |

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Citation Context ...potential change is at most \Gamma5 + 3 + 1 = \Gamma1. For weight-temp, it is \Gamma1, and for weight-push, it is \Gamma3 + 2 = \Gamma1.sThe operations from [4] are basicaly the same as the ones from =-=[5]-=-, and in the latter it was shown that for any k, starting with a red-black tree (not necessarily empty), k updates gives rise to at most O(k log(n + i)) rebalancing operations, where n is the number o... |

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Citation Context ...of the original proposal. In [19], some of these early results are surveyed. In [18, 13], it is shown how a large class of standard search trees can automatically be equipped with relaxed balance. In =-=[7]-=-, a version of red-black trees based on the same ideas as [18, 13] is presented, and rebalancing is proven to be logarithmic in the number of updates. Now we turn to the subject of this paper. In [4],... |

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Citation Context .... The idea of uncoupling the rebalancing from the updating was first mentioned in [6], and the first partial result, dealing with insertions only, is from [10]. The first relaxed version of AVL-trees =-=[1]-=- was presented in [15] and proofs of complexity for the rebalancing, matching the complexity from the sequential case, was obtained in [11]. A different AVL-based version with some especially nice pro... |

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Citation Context ...and proofs of complexity for the rebalancing, matching the complexity from the sequential case, was obtained in [11]. A different AVL-based version with some especially nice properties was treated in =-=[19, 14]-=-. The first relaxed version of B-trees [3] is also from [15] with proofs of complexity matching the sequential ones in [12]. Since [12] really treats (a; b)-trees [9], it also provides proofs for 2-3 ... |

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Citation Context ...and proofs of complexity for the rebalancing, matching the complexity from the sequential case, was obtained in [11]. A different AVL-based version with some especially nice properties was treated in =-=[19, 14]-=-. The first relaxed version of B-trees [3] is also from [15] with proofs of complexity matching the sequential ones in [12]. Since [12] really treats (a; b)-trees [9], it also provides proofs for 2-3 ... |

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Citation Context ...nt AVL-based version with some especially nice properties was treated in [19, 14]. The first relaxed version of B-trees [3] is also from [15] with proofs of complexity matching the sequential ones in =-=[12]-=-. Since [12] really treats (a; b)-trees [9], it also provides proofs for 2-3 trees [8, 2], as well as for (a; b)- trees with other choices of a and b. A relaxed version of red-black trees [6] was intr... |

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Citation Context ... well as for (a; b)- trees with other choices of a and b. A relaxed version of red-black trees [6] was introduced in [16, 17] and complexities matching the sequential case were established in [5] and =-=[4]-=- for variants of the original proposal. In [19], some of these early results are surveyed. In [18, 13], it is shown how a large class of standard search trees can automatically be equipped with relaxe... |

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Citation Context ...] was introduced in [16, 17] and complexities matching the sequential case were established in [5] and [4] for variants of the original proposal. In [19], some of these early results are surveyed. In =-=[18, 13]-=-, it is shown how a large class of standard search trees can automatically be equipped with relaxed balance. In [7], a version of red-black trees based on the same ideas as [18, 13] is presented, and ... |

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Citation Context ...2] really treats (a; b)-trees [9], it also provides proofs for 2-3 trees [8, 2], as well as for (a; b)- trees with other choices of a and b. A relaxed version of red-black trees [6] was introduced in =-=[16, 17]-=- and complexities matching the sequential case were established in [5] and [4] for variants of the original proposal. In [19], some of these early results are surveyed. In [18, 13], it is shown how a ... |

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Citation Context ...first relaxed version of B-trees [3] is also from [15] with proofs of complexity matching the sequential ones in [12]. Since [12] really treats (a; b)-trees [9], it also provides proofs for 2-3 trees =-=[8, 2]-=-, as well as for (a; b)- trees with other choices of a and b. A relaxed version of red-black trees [6] was introduced in [16, 17] and complexities matching the sequential case were established in [5] ... |