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- W3201248676 abstract "The definition of <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink> <tex-math notation=LaTeX>$text {k}^{th}$ </tex-math></inline-formula> -order empirical entropy of strings is extended to node-labelled binary trees: A notion of <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink> <tex-math notation=LaTeX>$text {k}^{th}$ </tex-math></inline-formula> -order empirical entropy for node-labelled binary trees is proposed that is able to capture regularities in both labels and structure of a tree. A suitable binary encoding of tree straight-line programs (that have been used for grammar-based tree compression before) is shown to yield binary tree encodings of size bounded by the <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink> <tex-math notation=LaTeX>$text {k}^{th}$ </tex-math></inline-formula> -order empirical entropy plus some lower order terms. This result is then extended from node-labelled binary trees to node-labelled unranked trees. This generalizes recent results for grammar-based string compression to grammar-based tree compression. Additionally, experimental results with real XML document trees are presented, in which the proposed notion of <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink> <tex-math notation=LaTeX>$text {k}^{th}$ </tex-math></inline-formula> -order empirical tree entropy is computed and compared to the performance of grammar-based tree compressors for those XML document trees." @default.
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- W3201248676 date "2021-11-01" @default.
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- W3201248676 title "Entropy Bounds for Grammar-Based Tree Compressors" @default.
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