Querying and Embedding Compressed Texts

Lifshits, Yury; Lohrey, Markus

doi:10.1007/11821069_59

Cited by 26 publications

(34 citation statements)

References 24 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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“…The LCS problem on a pair of GC-strings has been considered by Lifshits and Lohrey [80], and proven to be NP-hard.…”

Section: Three-way Semi-local Lcsmentioning

confidence: 99%

“…This running time should be contrasted with standard LCS algorithms on plain strings, running in time O mn log(m+n) [84,34], and with the NP-hardness of the LCS problem on two GC-strings [80].…”

Section: Algorithm 8 (Three-way Semi-local Lcs)mentioning

confidence: 99%

Semi-local String Comparison: Algorithmic Techniques and Applications

Tiskin

2008

Math.comput.sci.

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The longest common subsequence (LCS) problem is a classical problem in computer science. The semi-local LCS problem is a generalisation of the LCS problem, arising naturally in the context of string comparison. In this work, we present a number of algorithmic techniques related to the semi-local LCS problem, and give a number of algorithmic applications of these techniques. Summarising the presented results, we conclude that semilocal string comparison turns out to be a useful algorithmic plug-in, which unifies, and often improves on, a number of previous approaches to various substring-and subsequence-related problems.

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“…Define the word W as in (12). Finally, we describe an alternating HFA A that accepts the word W if and only if (V, E, v ξ , F, β) is a positive AGAP-instance.…”

Section: Compressed Membership Problems For Hierarchical Automatamentioning

confidence: 99%

“…Consider the language (13) and the word W from (12). First, we can replace every occurrence of a * by a {∪, ·}-expression µ for {ε} ∪ ran(code), where ran(code) is the (finite) range of the mapping code.…”

Section: Point (A) Is Easy To See: For the Only If-direction One Showmentioning

confidence: 99%

Querying and Embedding Compressed Texts

Cited by 26 publications

References 24 publications

Fast Distance Multiplication of Unit-Monge Matrices

Fast Distance Multiplication of Unit-Monge Matrices

Semi-local String Comparison: Algorithmic Techniques and Applications

Compressed Membership Problems for Regular Expressions and Hierarchical Automata

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