Improved approximate string matching and regular expression matching on Ziv-Lempel compressed texts
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This work significantly improves the space bounds of the Ziv-Lempel adaptive dictionary compression schemes, improving the previously known complexities for both approximate string matching and regular expression matching problems.Abstract:
We study the approximate string matching and regular expression matching problem for the case when the text to be searched is compressed with the Ziv-Lempel adaptive dictionary compression schemes. We present a time-space trade-off that leads to algorithms improving the previously known complexities for both problems. In particular, we significantly improve the space bounds, which in practical applications are likely to be a bottleneck.read more
Citations
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Random Access to Grammar-Compressed Strings and Trees
TL;DR: A novel grammar representation that allows efficient random access to any character or substring without decompressing the string is presented.
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Random access to grammar-compressed strings
TL;DR: In this paper, the authors presented two representations of a string of length n compressed into a context-free grammar S of size n with O(log N) random access time and O(n · αk(n)) construction time and space on the RAM.
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Random Access to Grammar Compressed Strings
TL;DR: Two representations of a string of length n compressed into a context-free grammar of size n achieving random access time and several new techniques and data structures of independent interest are introduced, including a predecessor data structure, two "biased" weighted ancestor data structures, and a compact representation of heavy- paths in grammars.
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Semi-local String Comparison: Algorithmic Techniques and Applications
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Searching and Indexing Genomic Databases via Kernelization
Travis Gagie,Simon J. Puglisi +1 more
TL;DR: The 20-year history of the idea of searching or indexing only one reference genome and the parts of the other genomes where they differ is surveyed and its relation to kernelization in parameterized complexity is discussed.
References
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Journal ArticleDOI
A universal algorithm for sequential data compression
Jacob Ziv,A. Lempel +1 more
TL;DR: The compression ratio achieved by the proposed universal code uniformly approaches the lower bounds on the compression ratios attainable by block-to-variable codes and variable- to-block codes designed to match a completely specified source.
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Compression of individual sequences via variable-rate coding
Jacob Ziv,A. Lempel +1 more
TL;DR: The proposed concept of compressibility is shown to play a role analogous to that of entropy in classical information theory where one deals with probabilistic ensembles of sequences rather than with individual sequences.
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A guided tour to approximate string matching
TL;DR: This work surveys the current techniques to cope with the problem of string matching that allows errors, and focuses on online searching and mostly on edit distance, explaining the problem and its relevance, its statistical behavior, its history and current developments, and the central ideas of the algorithms.
Journal ArticleDOI
A Technique for High-Performance Data Compression
TL;DR: A new compression algorithm is introduced that is based on principles not found in existing commercial methods in that it dynamically adapts to the redundancy characteristics of the data being compressed, and serves to illustrate system problems inherent in using any compression scheme.