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Tree structure compression with RePair
, 2010
"... Larsson and Moffat’s RePair algorithm is generalized from strings to trees. The new algorithm (TreeRePair) produces straightline linear contextfree tree (SLT) grammars which are smaller than those produced by previous grammarbased compressors such as BPLEX. Experiments show that a Huffmanbased ..."
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Cited by 10 (4 self)
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Larsson and Moffat’s RePair algorithm is generalized from strings to trees. The new algorithm (TreeRePair) produces straightline linear contextfree tree (SLT) grammars which are smaller than those produced by previous grammarbased compressors such as BPLEX. Experiments show that a Huffmanbased coding of the resulting grammars gives compression ratios comparable to the best known XML file compressors. Moreover, SLT grammars can be used as efficient memory representation of trees. Our investigations show that tree traversals over TreeRePair grammars are 14 times slower than over pointer structures and 5 times slower than over succinct trees, while memory consumption is only 1/43 and 1/6, respectively. 1
Fast and tiny structural selfindexes for XML
 CoRR
"... XML document markup is highly repetitive and therefore well compressible using dictionarybased methods such as DAGs or grammars. In the context of selectivity estimation, grammarcompressed trees were used before as synopsis for structural XPath queries. Here a fullyfledged index over such gramm ..."
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Cited by 5 (5 self)
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XML document markup is highly repetitive and therefore well compressible using dictionarybased methods such as DAGs or grammars. In the context of selectivity estimation, grammarcompressed trees were used before as synopsis for structural XPath queries. Here a fullyfledged index over such grammars is presented. The index allows to execute arbitrary tree algorithms with a slowdown 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 preorder numbers of result nodes, and show its competitiveness. 1.
Onecontext Unification with STGCompressed Terms is in NP
, 2012
"... Onecontext unification is an extension of firstorder term unification in which a variable of arity one standing for a context may occur in the input terms. This problem arises in areas like program analysis, term rewriting and XML processing and is known to be solvable in nondeterministic polynomi ..."
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Onecontext unification is an extension of firstorder term unification in which a variable of arity one standing for a context may occur in the input terms. This problem arises in areas like program analysis, term rewriting and XML processing and is known to be solvable in nondeterministic polynomial time. We prove that this problem can be solved in nondeterministic polynomial time also when the input is compressed using Singleton Tree Grammars (STG’s). STG’s are a grammarbased compression method for terms that generalizes the directed acyclic graph representation. They have been recently considered as an efficient inmemory representation for large terms, since several operations on terms can be performed efficiently on their STG representation without a prior decompression.
Pattern Matching of Compressed Terms and Contexts and Polynomial Rewriting
, 2011
"... A generalization of the compressed string pattern match that applies to terms with variables is investigated: Given terms s and t compressed by singleton tree grammars, the task is to find an instance of s that occurs as a subterm in t. We show that this problem is in NP and that the task can be pe ..."
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Cited by 3 (1 self)
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A generalization of the compressed string pattern match that applies to terms with variables is investigated: Given terms s and t compressed by singleton tree grammars, the task is to find an instance of s that occurs as a subterm in t. We show that this problem is in NP and that the task can be performed in time O(n cVar(s) ), including the construction of the compressed substitution, and a representation of all occurrences. We show that the special case where s is uncompressed can be performed in polynomial time. As a nice application we show that for an equational deduction of t to t ′ by an equality axiom l = r (a rewrite) a single step can be performed in polynomial time in the size of compression of t and l, r if the number of variables is fixed in l. We also show that n rewriting steps can be performed in polynomial time, if the equational axioms are compressed and assumed to be constant for the rewriting sequence. Another potential application are querying mechanisms on compressed XMLdata bases.
FirstOrder Unification on Compressed Terms
, 2011
"... Singleton Tree Grammars (STGs) have recently drawn considerable attention. They generalize the sharing of subtrees known from DAGs to sharing of connected subgraphs. This allows to obtain smaller inmemory representations of trees than with DAGs. In the past years some important tree algorithms were ..."
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Cited by 2 (1 self)
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Singleton Tree Grammars (STGs) have recently drawn considerable attention. They generalize the sharing of subtrees known from DAGs to sharing of connected subgraphs. This allows to obtain smaller inmemory representations of trees than with DAGs. In the past years some important tree algorithms were proved to perform efficiently (without decompression) over STGs; e.g., type checking, equivalence checking, and unification. We present a tool that implements an extension of the unification algorithm for STGs. This algorithm makes extensive use of equivalence checking. For the latter we implemented two variants, the classical exact one and a recent randomized one. Our experiments show that the randomized algorithm performs better. The running times are also compared to those of unification over uncompressed trees.
Congruence Closure of Compressed Terms in Polynomial Time
, 2011
"... The wordproblem for a finite set of equational axioms between ground terms is the question whether for terms s, t the equation s = t is a consequence. We consider this problem under grammar based compression of terms, in particular compression with singleton tree grammars (STGs) and with directed ..."
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The wordproblem for a finite set of equational axioms between ground terms is the question whether for terms s, t the equation s = t is a consequence. We consider this problem under grammar based compression of terms, in particular compression with singleton tree grammars (STGs) and with directed acyclic graphs (DAGs) as a special case. We show that given a DAGcompressed ground and reduced term rewriting system T, the Tnormal form of an STGcompressed term s can be computed in polynomial time, and hence the Tword problem can be solved in polynomial time. This implies that the word problem of STGcompressed terms w.r.t. a set of DAGcompressed ground equations can be decided in polynomial time. If the ground term rewriting system (gTRS) T is STGcompressed, we show NPhardness of Tnormalform computation. For compressed, reduced gTRSs we show a PSPACE upper bound on the complexity of the normal form computation of STGcompressed terms. Also special cases are considered and a prototypical implementation is presented.
Autor: Betreuer:
"... Front page line art drawing by Pearson Scott Foresman. While every precaution has been taken in the preparation of this work, the author assumes no responsibility for errors or omissions, or for damages resulting from the use of the information contained herein. ..."
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Front page line art drawing by Pearson Scott Foresman. While every precaution has been taken in the preparation of this work, the author assumes no responsibility for errors or omissions, or for damages resulting from the use of the information contained herein.
Tree structure compression with RePair
"... Abstract. In this work we introduce a new linear time compression algorithm, called ”Repair for Trees”, which compresses ranked ordered trees using linear straightline contextfree tree grammars. Such grammars generalize straightline contextfree string grammars and allow basic tree operations, ..."
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Abstract. In this work we introduce a new linear time compression algorithm, called ”Repair for Trees”, which compresses ranked ordered trees using linear straightline contextfree tree grammars. Such grammars generalize straightline contextfree 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 ”Repair ” algorithm developed by N. Jesper Larsson and Alistair Moffat in 2000. The latter algorithm is a dictionarybased compression algorithm for strings. We also introduce a succinct coding which is specialized in further compressing the grammars generated by our algorithm. This is 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 Repair 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.