Algorithmics on SLP-compressed strings: A survey

Lohrey, Markus

doi:10.1515/gcc-2012-0016

Cited by 125 publications

(106 citation statements)

References 149 publications

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“…The LCS problem on two GC-strings has been considered by Lifshits and Lohrey [45,46], and proven to be PP-hard (and therefore NP-hard).…”

Section: Compressed String Comparisonmentioning

confidence: 99%

Fast Distance Multiplication of Unit-Monge Matrices

Tiskin

2013

Algorithmica

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Monge matrices play a fundamental role in optimisation theory, graph and string algorithms. Distance multiplication of two Monge matrices of size n can be performed in time O(n 2 ). Motivated by applications to string algorithms, we introduced in previous works a subclass of Monge matrices, that we call simple unit-Monge matrices. We also gave a distance multiplication algorithm for such matrices, running in time O(n 1.5 ). Landau asked whether this problem can be solved in linear time. In the current work, we give an algorithm running in time O(n log n), thus approaching an answer to Landau's question within a logarithmic factor. The new algorithm implies immediate improvements in running time for a number of algorithms on strings and graphs. In particular, we obtain an algorithm for finding a maximum clique in a circle graph in time O(n log 2 n), and a surprisingly efficient algorithm for comparing compressed strings. We also point to potential applications in group theory, by making a connection between unit-Monge matrices and Coxeter monoids. We conclude that unit-Monge matrices are a fascinating object and a powerful tool, that deserve further study from both the mathematical and the algorithmic viewpoints.

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“…The LCS problem on two GC-strings has been considered by Lifshits and Lohrey [45,46], and proven to be PP-hard (and therefore NP-hard).…”

Section: Compressed String Comparisonmentioning

confidence: 99%

Fast Distance Multiplication of Unit-Monge Matrices

Tiskin

2013

Algorithmica

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“…Using Plandowski's result [28], this can be checked in time polynomial in the size of G and hence in time polynomial in the size of the SLT grammar G. Note that more efficient alternatives than Plandowski's algorithm exist, see, e.g. [18] for a survey, but all of them require at least quadratic time in the size of the SL grammar.…”

Section: Subtree Equality Checkmentioning

confidence: 99%

“…Recall that the series B(z) is defined by (18). We follow the same steps as in the proof of Proposition 27.…”

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confidence: 99%

XML Compression via Directed Acyclic Graphs

et al. 2014

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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.

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“…The intrinsic hierarchical definition of a CFG allows string-manipulation algorithms to perform operations directly on their compressed representations without the need for a prior decompression [2] [3] [4] [5]. A potential reduction in the temporary storage space required for data manipulation, and shorter execution times can be expected by decreasing the amount of data to be processed [2].…”

Section: Introductionmentioning

confidence: 99%

“…A potential reduction in the temporary storage space required for data manipulation, and shorter execution times can be expected by decreasing the amount of data to be processed [2]. These features are attractive for improving efficiency in processing large volume of data.…”

Section: Introductionmentioning

confidence: 99%