Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Generation Matrix: An Embeddable Matrix Representation for Hierarchical
  Trees   Starting from the local structures to study hierarchical trees is a common
research method. However, the cumbersome analysis and description make the
naive method challenging to adapt to the increasingly complex hierarchical tree
problems. To improve the efficiency of hierarchical tree research, we propose
an embeddable matrix representation for hierarchical trees, called Generation
Matrix. It can transform the abstract hierarchical tree into a concrete matrix
representation and then take the hierarchical tree as a whole to study, which
dramatically reduces the complexity of research. Mathematical analysis shows
that Generation Matrix can simulate various recursive algorithms without
accessing local structures and provides a variety of interpretable matrix
operations to support the research of hierarchical trees. Applying Generation
Matrix to differential privacy hierarchical tree release, we propose a
Generation Matrix-based optimally consistent release algorithm (GMC). It
provides an exceptionally concise process description so that we can describe
its core steps as a simple matrix expression rather than multiple complicated
recursive processes like existing algorithms. Our experiments show that GMC
takes only a few seconds to complete a release for large-scale datasets with
more than 10 million nodes. The calculation efficiency is increased by up to
100 times compared with the state-of-the-art schemes.

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The categories of this paper are: hep-th
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The categories of this paper are: q-bio
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The categories of this paper are: nucl-ex
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The categories of this paper are: funct-an
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The categories of this paper are: acc-phys
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The categories of this paper are: solv-int
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The categories of this paper are: adap-org
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The categories of this paper are: econ
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The categories of this paper are: q-fin
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The categories of this paper are: chao-dyn
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The categories of this paper are: chem-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: alg-geom
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The categories of this paper are: plasm-ph