XML Compression via Directed Acyclic Graphs

Unranked node-labeled trees can be represented using their minimal dag (directed acyclic graph). For XML this achieves high compression ratios due to their repetitive mark up. Unranked trees are often represented through first child/next sibling (fcns) encoded binary trees. We study the difference i...

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Bibliographic Details
Published in:Theory of computing systems 2015-11, Vol.57 (4), p.1322-1371
Main Authors: Bousquet-Mélou, Mireille, Lohrey, Markus, Maneth, Sebastian, Noeth, Eric
Format: Article
Language:English
Subjects:
Analysis
Asymptotic methods
Asymptotic properties
Compressing
Computer Science
Data Structures and Algorithms
Encoding
Extensible Markup Language
Graph theory
Graphs
Mathematical analysis
Studies
Theory of Computation
Trees
XML
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Summary:Unranked node-labeled trees can be represented using their minimal dag (directed acyclic graph). For XML this achieves high compression ratios due to their repetitive mark up. Unranked trees are often represented through first child/next sibling (fcns) encoded binary trees. We study the difference in size (= number of edges) of minimal dag versus minimal dag of the fcns encoded binary tree. One main finding is that the size of the dag of the binary tree can never be smaller than the square root of the size of the minimal dag, and that there are examples that match this bound. We introduce a new combined structure, the hybrid dag , which is guaranteed to be smaller than (or equal in size to) both dags. Interestingly, we find through experiments that last child/previous sibling encodings are much better for XML compression via dags, than fcns encodings. We determine the average sizes of unranked and binary dags over a given set of labels (under uniform distribution) in terms of their exact generating functions, and in terms of their asymptotical behavior.
ISSN:1432-4350
1433-0490
DOI:10.1007/s00224-014-9544-x