## Relaxed Multi-Way Trees with Group Updates (2000)

Venue: | In Proceedings of the twentieth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems |

Citations: | 2 - 0 self |

### BibTeX

@INPROCEEDINGS{Larsen00relaxedmulti-way,

author = {Kim S. Larsen},

title = {Relaxed Multi-Way Trees with Group Updates},

booktitle = {In Proceedings of the twentieth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems},

year = {2000},

pages = {93--101},

publisher = {ACM Press}

}

### OpenURL

### Abstract

Data structures with relaxed balance dier from standard structures in that rebalancing can be delayed and interspersed with updates. This gives extra exibility in both sequential and parallel applications. We study the version of multi-way trees called (a; b)-trees (which includes B-trees) with the operations insertion, deletion, and group insertion. The latter has applications in for instance document databases and WWW search engines. We prove that we obtain the optimal asymptotic rebalancing complexities of amortized constant time for insertion and deletion and amortized logarithmic time in the size of the group for group insertion. These results hold even for the relaxed version. Our results also demonstrate that a binary tree scheme with the same complexities can be designed. This is an improvement over the existing results. 1 Introduction We focus on the type of multi-way trees usually referred to as (a; b)-trees [8, 15], and in particular, we adopt the relaxed (a...

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Citation Context ... that updating may be carried out independent of rebalancing which can be carried out later, possibly in small steps. In the context of B-trees [3], this approach was discussedsrst in [16]. The paper =-=[10]-=- contains a fairly complete reference list to the work on relaxed structures in general. The disadvantage of relaxation is that the strict control on search path lengths is loosened (temporarily). The... |

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Citation Context ..., possibly by a background process, for instance when the search frequency drops. For red-black trees [6] and height-valued trees [13] (an AVL-tree [1] variant), relaxed variants have been studied in =-=[7, 14]-=- where an entire tree of new keys to be inserted can be brought into the tree as one update. For both structures, the upper bound derived on the number of rebalancing operations required to balance th... |

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Citation Context ..., possibly by a background process, for instance when the search frequency drops. For red-black trees [6] and height-valued trees [13] (an AVL-tree [1] variant), relaxed variants have been studied in =-=[7, 14]-=- where an entire tree of new keys to be inserted can be brought into the tree as one update. For both structures, the upper bound derived on the number of rebalancing operations required to balance th... |