Tree Compression with Top Trees Revisited

We revisit tree compression with top trees (Bille et al, ICALP'13) and present several improvements to the compressor and its analysis. By significantly reducing the amount of information stored and guiding the compression step using a RePair-inspired heuristic, we obtain a fast compressor achieving good compression ratios, addressing an open problem posed by Bille et al. We show how, with relatively small overhead, the compressed file can be converted into an in-memory representation that supports basic navigation operations in worst-case logarithmic time without decompression. We also show a much improved worst-case bound on the size of the output of top-tree compression (answering an open question posed in a talk on this algorithm by Weimann in 2012).Comment: SEA 201

XML Compression via DAGs

Unranked 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.Comment: A short version of this paper appeared in the Proceedings of ICDT 201

Fast and Tiny Structural Self-Indexes for XML

XML document markup is highly repetitive and therefore well compressible using dictionary-based methods such as DAGs or grammars. In the context of selectivity estimation, grammar-compressed trees were used before as synopsis for structural XPath queries. Here a fully-fledged index over such grammars is presented. The index allows to execute arbitrary tree algorithms with a slow-down that is comparable to the space improvement. More interestingly, certain algorithms execute much faster over the index (because no decompression occurs). E.g., for structural XPath count queries, evaluating over the index is faster than previous XPath implementations, often by two orders of magnitude. The index also allows to serialize XML results (including texts) faster than previous systems, by a factor of ca. 2-3. This is due to efficient copy handling of grammar repetitions, and because materialization is totally avoided. In order to compare with twig join implementations, we implemented a materializer which writes out pre-order numbers of result nodes, and show its competitiveness.Comment: 13 page

A comparison of parsing technologies for the biomedical domain

This paper reports on a number of experiments which are designed to investigate the extent to which current nlp resources are able to syntactically and semantically analyse biomedical text. We address two tasks: parsing a real corpus with a hand-built widecoverage grammar, producing both syntactic analyses and logical forms; and automatically computing the interpretation of compound nouns where the head is a nominalisation (e.g., hospital arrival means an arrival at hospital, while patient arrival means an arrival of a patient). For the former task we demonstrate that exible and yet constrained `preprocessing ' techniques are crucial to success: these enable us to use part-of-speech tags to overcome inadequate lexical coverage, and to `package up' complex technical expressions prior to parsing so that they are blocked from creating misleading amounts of syntactic complexity. We argue that the xml-processing paradigm is ideally suited for automatically preparing the corpus for parsing. For the latter task, we compute interpretations of the compounds by exploiting surface cues and meaning paraphrases, which in turn are extracted from the parsed corpus. This provides an empirical setting in which we can compare the utility of a comparatively deep parser vs. a shallow one, exploring the trade-o between resolving attachment ambiguities on the one hand and generating errors in the parses on the other. We demonstrate that a model of the meaning of compound nominalisations is achievable with the aid of current broad-coverage parsers

Re-pair for Trees

We introduce a new linear time compression algorithm, called 'Repair for Trees', which compresses ordered trees over a ranked alphabet using linear straight-line context-free tree grammars. Such grammars generalize straight-line context-free string grammars and allow basic tree operations, like traversal along edges, to be executed without prior decompression. Our algorithm can be considered as a generalization of the 'Re-pair' algorithm developed by N. Jesper Larsson and Alistair Moffat in 2000. The latter algorithm is a dictionary-based compression algorithm for strings. We also introduce a succinct coding which is specialized in further compressing the grammars generated by our algorithm. Thisis accomplished without loosing the ability do directly execute queries on this compressed representation of the input tree. Finally, we compare the grammars and output files generated by a prototype of the Re-pair for Trees algorithm with those of similar compression algorithms. The obtained results show that that our algorithm outperforms its competitors in terms of compression ratio, runtime and memory usage

Grammar compressed sequences with rank/select support

An early partial version of this paper appeared in Proc. SPIRE 2014: G. Navarro, A. Ordóñez Grammar compressed sequences with rank/select support, Proc. 21st International Symposium on String Processing and Information Retrieval, LNCS, SPIRE, vol. 8799 (2014), pp. 31–44The final publication is available at Springer via http://dx.doi.org/10.1016/j.jda.2016.10.001[Abstract] Sequence representations supporting not only direct access to their symbols, but also rank/select operations, are a fundamental building block in many compressed data structures. Several recent applications need to represent highly repetitive sequences, and classical statistical compression proves ineffective. We introduce, instead, grammar-based representations for repetitive sequences, which use up to 6% of the space needed by statistically compressed representations, and support direct access and rank/select operations within tens of microseconds. We demonstrate the impact of our structures in text indexing applications.Chile. Fondo Nacional de Desarrollo Científico y Tecnológico; 140796Ministerio de Economía, Industria y Competitividad; 00645663/ITC-20133062Ministerio de Economía, Industria y Competitividad; TIN2009-14560-C03-02Ministerio de Economía, Industria y Competitividad; TIN2010-21246-C02-01Ministerio de Economía, Industria y Competitividad; TIN2013-46238-C4-3-RMinisterio de Economía, Industria y Competitividad; TIN2013-47090-C3-3-PMinisterio de Economía, Industria y Competitividad; AP2010-6038Xunta de Galicia; GRC2013/05