XML Compression via Directed Acyclic Graphs

Bousquet-Mélou, Mireille; Lohrey, Markus; Maneth, Sebastian; Noeth, Eric

doi:10.1007/s00224-014-9544-x

Cited by 27 publications

(27 citation statements)

References 29 publications

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“…Whereas dags only allow to share repeated subtrees, TSLPs can also share repeated internal tree patterns. Several grammar-based tree compressors were developed in [2,8,11,28,37], where the work from [2] is based on another type of tree grammars (elementary ordered tree grammars). The algorithm from [28] achieves an approximation ratio of O(log n) (for a constant set of node labels).…”

Section: Introductionmentioning

confidence: 99%

Constructing small tree grammars and small circuits for formulas

Ganardi

Hucke

Je³

et al. 2017

Journal of Computer and System Sciences

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It is shown that every tree of size n over a fixed set of σ different ranked symbols can be decomposed (in linear time as well as in logspace) into O n log σ n = O n log σ log n many hierarchically defined pieces. Formally, such a hierarchical decomposition has the form of a straight-line linear context-free tree grammar of size O n log σ n , which can be used as a compressed representation of the input tree. This generalizes an analogous result for strings. Previous grammar-based tree compressors were not analyzed for the worst-case size of the computed grammar, except for the top dag of Bille et al. [6], for which only the weaker upper bound of O n log 0.19 σ n (which was very recently improved to O n·log log σ n log σ n [23]) for unranked and unlabelled trees has been derived. The main result is used to show that every arithmetical formula of size n, in which only m ≤ n different variables occur, can be transformed (in linear time as well as in logspace) into an arithmetical circuit of size O n·log m log n and depth O(log n). This refines a classical result of Brent from 1974, according to which an arithmetical formula of size n can be transformed into a logarithmic depth circuit of size O(n). A short version of this paper appeared as [24]. * The fourth and fifth author are supported by the DFG research project QUANT-KOMP (Lo 748/10-1). †

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Section: Introductionmentioning

confidence: 99%

Constructing small tree grammars and small circuits for formulas

Ganardi

Hucke

Je³

et al. 2017

Journal of Computer and System Sciences

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“…It should be noted that (4) holds only if Φ is invariant under permutation of arguments. In addition,…”

Section: A Proof Of Propositionmentioning

confidence: 99%

Approximation of trees by self-nested trees

Azaïs¹,

Durand²,

Godin³

2019

2019 Proceedings of the Twenty-First Workshop on Algorithm Engineering and Experiments (ALENEX)

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The class of self-nested trees presents remarkable compression properties because of the systematic repetition of subtrees in their structure. In this paper, we provide a better combinatorial characterization of this specific family of trees. In particular, we show from both theoretical and practical viewpoints that complex queries can be quickly answered in self-nested trees compared to general trees. We also present an approximation algorithm of a tree by a self-nested one that can be used in fast prediction of edit distance between two trees.

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“…Motivated by applications where large tree structured data occur, like XML processing, grammar-based compression has been extended to trees [9,10,26,33], see [31] for a survey. Unless otherwise specified, a tree in this paper is always a rooted ordered tree over a ranked alphabet, i.e., every node is labelled with a symbol and the rank of this symbol is equal to the number of children of the node.…”

Section: Introductionmentioning

confidence: 99%

Tree Compression Using String Grammars

et al. 2017

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We study the compressed representation of a ranked tree by a (string) straight-line program (SLP) for its preorder traversal, and compare it with the well-studied representation by straight-line context free tree grammars (which are also known as tree straight-line programs or TSLPs). Although SLPs turn out to be exponentially more succinct than TSLPs, we show that many simple tree queries can still be performed efficiently on SLPs, such as computing the height and Horton-Strahler number of a tree, tree navigation, or evaluation of Boolean expressions. Other problems on tree traversals turn out to be intractable, e.g. pattern matching and evaluation of tree automata.

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XML Compression via Directed Acyclic Graphs

Cited by 27 publications

References 29 publications

Constructing small tree grammars and small circuits for formulas

Constructing small tree grammars and small circuits for formulas

Approximation of trees by self-nested trees

Tree Compression Using String Grammars

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