Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Efficient Representation of Multidimensional Data over Hierarchical
  Domains   We consider the problem of representing multidimensional data where the
domain of each dimension is organized hierarchically, and the queries require
summary information at a different node in the hierarchy of each dimension.
This is the typical case of OLAP databases. A basic approach is to represent
each hierarchy as a one-dimensional line and recast the queries as
multidimensional range queries. This approach can be implemented compactly by
generalizing to more dimensions the $k^2$-treap, a compact representation of
two-dimensional points that allows for efficient summarization queries along
generic ranges. Instead, we propose a more flexible generalization, which
instead of a generic quadtree-like partition of the space, follows the domain
hierarchies across each dimension to organize the partitioning. The resulting
structure is much more efficient than a generic multidimensional structure,
since queries are resolved by aggregating much fewer nodes of the tree.

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The categories of this paper are: dg-ga
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The categories of this paper are: chem-ph
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The categories of this paper are: funct-an
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The categories of this paper are: physics
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The categories of this paper are: bayes-an
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The categories of this paper are: atom-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: eess
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-ex
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The categories of this paper are: stat
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The categories of this paper are: ao-sci
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The categories of this paper are: solv-int
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The categories of this paper are: math-ph
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The categories of this paper are: econ
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The categories of this paper are: nucl-th