# Efficient Evaluation of Hyper-Rectangular Blocks of Update Operations Applied to General Data Structures

Abstract : In this paper we present novel solutions for the following problem: We have a general data structure $DS$ and a set of update operations organized into a $D$-dimensional cube of side $N$ (thus, there are $N^D$ update operations). We are interested in efficiently evaluating range queries of the following type: compute the result of applying all the update operations within a hyper-rectangular block $B$ of the $D$-dimensional cube to $DS$ (considering that $DS$ is initially empty). The result of applying the updates consists of computing some aggregate values over the data structure. We consider that the order of applying the updates is irrelevant (i.e. the update operations are commutative) and that the aggregate results corresponding to a block of updates cannot easily be computed by combining the results of a set of sub-blocks whose disjoint union is $B$. However, the results can be efficiently maintained after each update operation, if the operations are performed sequentially in any order.
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Preprints, Working Papers, ...

Cited literature [13 references]

https://hal.archives-ouvertes.fr/hal-01024287
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Submitted on : Thursday, July 17, 2014 - 5:01:24 PM
Last modification on : Saturday, June 12, 2021 - 8:30:03 PM
Long-term archiving on: : Tuesday, October 20, 2015 - 4:33:30 PM

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• HAL Id : hal-01024287, version 1

### Citation

Mugurel Ionut Andreica, Andrei Grigorean, Andrei Parvu, Nicolae Tapus. Efficient Evaluation of Hyper-Rectangular Blocks of Update Operations Applied to General Data Structures. 2013. ⟨hal-01024287⟩

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