XML Compression via Directed Acyclic Graphs

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

Research output: Contribution to journalArticlepeer-review


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.
Original languageEnglish
Pages (from-to)1322-1371
Number of pages50
JournalTheory of Computing Systems
Issue number4
Early online date25 May 2014
Publication statusPublished - 30 Nov 2015


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