Pražský stringologický klub (PSC)

# Publikace

### On-line Searching in IUPAC nucleotide sequences

Autoři
Rok
2019
Publikováno
Proceedings of 12th International Joint Conference on Biomedical Engineering Systems and Technologies (BIOSTEC 2019). Lisboa: SCITEPRESS – Science and Technology Publications, Lda, 2019. p. 66-77. vol. 3. ISSN 2184-4305. ISBN 978-989-758-353-7.
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We propose a novel pattern matching algorithm for consensus nucleotide sequences over IUPAC alphabet, called BADPM (Byte-Aligned Degenerate Pattern Matching). The consensus nucleotide sequences represent a consensus obtained by sequencing a population of the same species and they are considered as so-called degenerate strings. BADPM works at the level of single bytes and it achieves sublinear search time on average. The algorithm is based on tabulating all possible factors of the searched pattern. It needs O (m + mα2 log m)-space data structure and O(mα2 ) time for preprocessing where m is a length of the pattern and α represents a maximum number of variants implied from a 4-gram over IUPAC alphabet. The worst-case locate time is bounded by O (nm2α4 ) for BADPM where n is the length of the input text. However, the experiments performed on real genomic data proved the sublinear search time. BADPM can easily cooperate with the block q-gram inverted index and so achieve still better locate time. We implemented two other pattern matching algorithms for IUPAC nucleotide sequences as a baseline: Boyer-Moore-Horspool (BMH) and Parallel Naive Search (PNS). Especially PNS proves its efficiency insensitive to the length of the searched pattern m. BADPM proved its strong superiority for searching middle and long patterns.

### SOPanG: online text searching over a pan-genome

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Holub, J.; Cislak, A.; Grabowski, S.
Rok
2018
Publikováno
Bioinformatics. 2018, 34(24), 4290-4292. ISSN 1367-4803.
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Motivation: The many thousands of high-quality genomes available now-a-days imply a shift from single genome to pan-genomic analyses. A basic algorithmic building brick for such a scenario is online search over a collection of similar texts, a problem with surprisingly few solutions presented so far.

### Filtering Invalid Off-Targets in CRISPR/Cas9 Design Tools

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Holub, J.; Cvacho, O.
Rok
2018
Publikováno
Proceedings of Data Compression Conference 2018. New York: IEEE Computer Society Press, 2018. p. 403. ISSN 2375-0359. ISBN 978-1-5386-4883-4.
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The paper deals with an approximate string matching in CRISPR/Cas9 design tools. The approximate string matching is transformed into sequence of exact string matching tasks processed by fast succinct (compressed) self-index. The number of the tasks is rapidly decreased by filtering technique based on de Bruijn graph.

### Reconstructing a String from its Lyndon Arrays

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Holub, J.; Daykin, J.W.; Franek, F; Sohidull Islam, A.S.M.; Smyth, W.F.
Rok
2018
Publikováno
Theoretical Computer Science. 2018, 710 44-51. ISSN 0304-3975.
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Given a string x = x[1.. n] on an ordered alphabet of size σ , the Lyndon array λ = λx [1..n] of x is an array of positive integers such that λ[i], 1 ≤ i ≤ n, is the length of the maximal Lyndon word over the ordering of that begins at position i in x. The Lyndon array has recently attracted considerable attention due to its pivotal role in establishing the long-standing conjecture that ρ (n ) < n, where ρ ( n) is the maximum number of maximal periodicities (runs) in any string of length n. Here we first describe two linear-time algorithms that, given a valid Lyndon array λ, compute a corresponding string — one for an alphabet of size n, the other for a smaller alphabet. We go on to describe another linear-time algorithm that determines whether or not a given integer array is a Lyndon array of some string. Finally we show how σ Lyndon arrays λ = {λ1 = λ, λ2 , . . . , λσ } corresponding to σ “rotations” of the alphabet can be used to determine uniquely the string x on such that λx = λ.

### Towards Efficient Positional Inverted Index

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Rok
2017
Publikováno
Algorithms. 2017, 10(1), ISSN 1999-4893.
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We address the problem of positional indexing in the natural language domain. The positional inverted index contains the information of the word positions. Thus, it is able to recover the original text file, which implies that it is not necessary to store the original file. Our Positional Inverted Self-Index (PISI) stores the word position gaps encoded by variable byte code. Inverted lists of single terms are combined into one inverted list that represents the backbone of the text file since it stores the sequence of the indexed words of the original file. The inverted list is synchronized with a presentation layer that stores separators, stop words, as well as variants of the indexed words. The Huffman coding is used to encode the presentation layer. The space complexity of the PISI inverted list is O((N−n)⌈log2bN⌉+(⌊N−nα⌋+n)×(⌈log2bn⌉+1)) where N is a number of stems, n is a number of unique stems, α is a step/period of the back pointers in the inverted list and b is the size of the word of computer memory given in bits. The space complexity of the presentation layer is O(−∑Ni=1⌈log2pn(i)i⌉−∑N′j=1⌈log2p′j⌉+N) with respect to pn(i)i as a probability of a stem variant at position i, p′j as the probability of separator or stop word at position j and N′ as the number of separators and stop words

### Byte-Aligned Pattern Matching in Encoded Genomic Sequences

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Rok
2017
Publikováno
Proceedings of 17th International Workshop on Algorithms in Bioinformatics (WABI 2017). Saarbrücken: Dagstuhl Publishing,, 2017. p. 20:1-20:13. ISSN 1868-8969. ISBN 978-3-95977-050-7.
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Anotace
In this article, we propose a novel pattern matching algorithm, called BAPM, that performs searching in the encoded genomic sequences. The algorithm works at the level of single bytes and it achieves sublinear performance on average. The preprocessing phase of the algorithm is linear with respect to the size of the searched pattern $m$. A simple $\mathcal{O}(m)$-space data structure is used to store all factors (with a defined length) of the searched pattern. These factors are later searched during the searching phase which ensures sublinear time on average. Our algorithm significantly overcomes the state-of-the-art pattern matching algorithms in the locate time on middle and long patterns. Furthermore, it is able to cooperate very easily with the block $q$-gram inverted index. The block $q$-gram inverted index together with our pattern matching algorithm achieve superior results in terms of locate time to the current index data structures for less frequent patterns. We present experimental results using real genomic data. These results prove efficiency of our algorithm.

### Technology Beats Algorithms (in Exact String Matching)

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Holub, J.; Tarhio, J; Giaquinta, E
Rok
2017
Publikováno
Software - Practice and Experience. 2017, 47(12), 1877-1885. ISSN 0038-0644.
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More than 120 algorithms have been developed for exact string matching within the last 40 years. We show by experiments that the \naive{} algorithm exploiting SIMD instructions of modern CPUs (with symbols compared in a special order) is the fastest one for patterns of length up to about 50 symbols and extremely good for longer patterns and small alphabets. The algorithm compares 16 or 32 characters in parallel by applying SSE2 or AVX2 instructions, respectively. Moreover, it uses loop peeling to further speed up the searching phase. We tried several orders for comparisons of pattern symbols and the increasing order of their probabilities in the text was the best.

### Computing All Approximate Enhanced Covers with the Hamming Distance

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Rok
2016
Publikováno
Proceedings of the Prague Stringology Conference 2016. Praha: Czech Technical University in Prague, 2016. p. 146-157. ISBN 978-80-01-05996-8.
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A border p of a string x is an enhanced cover of x if the number of positions of x that lie within some occurrence of p is the maximum among all borders of x. In this paper, more general notion based on the enhanced cover is introduced: a k-approximate enhanced cover, where fixed maximum number of errors k in the Hamming distance is considered. The k-approximate enhanced cover of x is its border and its k-approximate occurrences are also considered in the covered number of positions of x. An O(n^2)-time and a O(n)-space algorithm that computes all k-approximate enhanced covers of a string of length n is presented.

### Approximate String Matching for Self-Indexes

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Holub, J.; Hrbek, L.
Rok
2016
Publikováno
Proceedings of Data Compression Conference 2016. New York: IEEE Computer Society Press, 2016. pp. 604. ISSN 1068-0314. ISBN 978-1-5090-1853-6.
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Stať ve sborníku
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Anotace
Self-index is a data structure that allows to find all exact occurrences of given pattern of length $m$ in $m$ steps. The paper presents an approach how to use self-index for approximate string matching with no more than $k$~differences (given by Hamming or Levenshtein distance). Our approach solution uses filtering based on the pigeonhole principle. For implementation we have selected FM-index. Our program is faster than BLAST for large texts (hundreds of MB) and more space efficient for shorter texts.

### Positional Inverted Self-index

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Rok
2016
Publikováno
Proceedings of Data Compression Conference 2016. New York: IEEE Computer Society Press, 2016. pp. 627. ISSN 1068-0314. ISBN 978-1-5090-1853-6.
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Stať ve sborníku
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Anotace
We address the problem of positional indexing in natural language domain. The positional inverted index contains the information of the word positions. Thus, it is able to recover the original text file, which implies that it is not necessary to store the original file. Our Positional Inverted Self-Index (PISI) stores the word position gaps encoded by variable byte code. The inverted lists of single terms are combined into one inverted list that represents a backbone of the text file since it stores the sequence of the indexed words of the original file. The inverted list is synchronized with presentation layer that stores separators, stopwords, as well as variants of the indexed words. The Huffman coding is used to encode the presentation layer. The trade-off between compression effectiveness and the decompression speed can be tuned by different parameters of the index algorithm. ⌉ ×

### Incremental Locality & Clustering-Based Compression

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Rok
2015
Publikováno
Proceedings of Data Compression Conference 2015. Los Alamitos: IEEE Computer Society Press, 2015. pp. 203-212. ISSN 1068-0314. ISBN 978-1-4799-8430-5.
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Anotace
Current compression solutions either use a limited size locality-based context or the entire input, to which the compressors adapt. This results in suboptimal compression effectiveness due to missing similarities further apart in the former case, or due to too generic adaptation. There are many deduplication and near deduplication systems that search for similarity across the entire input. Although most of these systems excel with their simplicity and speed, none of those goes deeper in terms of full-scale redundancy removal. We propose a novel compression and archival system called ICBCS. Our system goes beyond standard measures for similarity detection, using extended similarity hash and incremental clustering techniques to determine groups of sufficiently similar chunks designated for compression. ICBCS outperforms conventional file compression solutions on datasets consisting of at least mildly redundant files. It also shows that selective application of weak compressor results in better compression ratio and speed than conventional application of a strong compressor.

### Compression of a Set of Files with Natural Language Content

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Rok
2015
Publikováno
Computer Journal. 2015, 58(5), 1169-1185. ISSN 0010-4620.
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Anotace
An algorithm for very efficient compression of a set of natural language text files is presented. Not only a very good compression ratio is reached, the used compression method allows fast pattern matching in compressed text, which is an attractive property especially for search engines. Much information is stored in the form of a large collection of text files. The web search engines can store the web pages in the raw text form to build so-called snippets or to perform so-called positional ranking functions on them. Furthermore, there exist many other similar contexts such as the storage of emails, application logs or the databases of text files (literary works or technical reports). In this paper, we address the problem of the compression of a large collection of text files distributed in cluster of computers, where the single files need to be randomly accessed in very short time. The compression algorithm is based on a word-based approach and the idea of combination of two statistical models: global model (common for all the files of the set) and local model. The latter is built as a set of changes that transform the global model to the proper model of the single compressed file.

### Compressing Similar Biological Sequences using FM-index

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Rok
2014
Publikováno
Proceedings of Data Compression Conference 2014. Los Alamitos: IEEE Computer Society, 2014. pp. 312-321. ISSN 1068-0314. ISBN 978-1-4799-3882-7.
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Anotace
Nowadays, decreasing cost and better accessibility of sequencing methods have enabled studies of genetic variation between individuals of the same species and also between two related species. This has led to a rapid increase in biological data consisting of sequences that are very similar to each other, these sequences usually being stored together in one database. We propose a compression method based on Wavelet Tree FM-index optimized for compression of a set of similar biological sequences. The compression method is based on tracking single changes (together with their context) between every single sequence and the chosen reference sequence. We call our compression method BIO-FMI. It gives very promising results in compression ratio and in locate time when performed on an extremely repetitive data set (less than 0.5 % mutations) and when the searched patterns are of smaller lengths (less than 20 bases). BIO-FMI is competitive in extraction speed and it seems to be superior in time needed to build the index, especially in the case when the alignments of single sequences are given in advance.

### Suffix Tree of Alignment: An Efficient Index for Similar Data

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Holub, J.; Na, J. C.; Park, H.; Crochemore, M.; Iliopoulos, C. S.; Mouchard, L.; Park, K.
Rok
2013
Publikováno
Proceedings of the 24th Workshop on Combinatorial Algorithms (IWOCA 2013). Berlin: Springer, 2013. pp. 337-348. ISSN 0302-9743. ISBN 978-3-642-45277-2.
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We consider an index data structure for similar strings. The generalized suffix tree can be a solution for this. The generalized suffix tree of two strings A and B is a compacted trie representing all suffixes in A and B. It has |A|+|B| leaves and can be constructed in O(|A|+|B|) time. However, if the two strings are similar, the generalized suffix tree is not efficient because it does not exploit the similarity which is usually represented as an alignment of A and B. In this paper we propose a space/time-efficient suffix tree of alignment which wisely exploits the similarity in an alignment. Our suffix tree for an alignment of A and B has |A|+ld +l1 leaves where ld is the sum of the lengths of all parts of B different from A and l1 is the sum of the lengths of some common parts of A and B. We did not compromise the pattern search to reduce the space. Our suffix tree can be searched for a pattern P in O(|P | + occ) time where occ is the number of occurrences of P in A and B. We also present an efficient algorithm to construct the suffix tree of alignment. When the suffix tree is constructed from scratch, the algorithm requires O(|A| + ld + l1 + l2 ) time where l2 is the sum of the lengths of other common substrings of A and B. When the suffix tree of A is already given, it requires O(ld + l1 + l2 ) time.

### Natural Language Compression Optimized for Large Set of Files

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Rok
2013
Publikováno
Proceedings of Data Compression Conference 2013. Los Alamitos, CA: IEEE Computer Soc., 2013. pp. 514. ISSN 1068-0314. ISBN 978-0-7695-4965-1.
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The paper describes one of the typical scenarios of data compression for large collections of files. We address the problem of the compression of a large collection of text files distributed in cluster of computers, where the single files need to be randomly accessed in very short time.

### ODC: Frame for definition of Dense codes

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Rok
2013
Publikováno
European Journal of Combinatorics. 2013, 2013(1), 52-68. ISSN 0195-6698.
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Anotace
The natural language compression made a great progress in last two decades. The main step in this evolution was the introduction of word-based compression by Moffat. Another improvement came with so called Dense codes which proved to be very fast in compression and decompression while keeping good compression ratio and direct search capability. Many variants of the Dense codes were described, each of them using its own definition. In this paper we present generalized concept of dense coding called Open Dense Code (ODC) which aims to be a frame for definition of many other dense code schemas. ODC underlines common features of the dense code schemas but at the same time allows to express the divergences of each of them. Using the frame of ODC we present two new word-based statistical compression algorithms based on dense coding idea: Two Byte Dense Code (TBDC) and Self-Tuning Dense Code (STDC). Our algorithms improve the compression ratio and are considerate to smaller files which are very often omitted.

### On left and right seeds of a string

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Guth, O.; Christou, M.; Crochemore, M.; Iliopoulos, C.S.; Pissis, S.P.
Rok
2012
Publikováno
Journal of Discrete Algorithms. 2012, 17 31-44. ISSN 1570-8667.
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We consider the problem of finding the repetitive structure of a given string y of length n. A factor u of y is a cover of y, if every letter of y lies within some occurrence of u in y. A string v is a seed of y, if it is a cover of a superstring of y. A left seed of y is a prefix of y, that is a cover of a superstring of y. Similarly, a right seed of y is a suffix of y, that is a cover of a superstring of y. An integer array LS is the minimal left-seed (resp. maximal left-seed) array of y, if LS[i] is the minimal (resp. maximal) length of left seeds of y[0..i]. The minimal right-seed (resp. maximal right-seed) arrayRS of y is defined in a similar fashion. In this article, we present linear-time algorithms for computing all left and right seeds of y, a linear-time algorithm for computing the minimal left-seed array of y, a linear-time solution for computing the maximal left-seed array of y, an O(n log n)-time algorithm for computing the minimal right-seed array of y, and a linear-time solution for computing the maximal right-seed array of y. All algorithms use linear auxiliary space.

### The Finite Automata Approaches in Stringology

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Rok
2012
Publikováno
Kybernetika. 2012, 48(3), 386-401. ISSN 0023-5954.
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Anotace
We present an overview of four approaches of the finite automata use in stringology: deterministic finite automaton, deterministic simulation of nondeterministic finite automaton, finite automaton as a model of computation, and compositions of finite automata solutions. We also show how the finite automata can process strings build over more complex alphabet than just single symbols (degenerate symbols, strings, variables).

### Tree-Based 2D Indexing

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Rok
2011
Publikováno
International Journal of Foundations of Computer Science. 2011, 22(8), 1893-1907. ISSN 0129-0541.
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A new approach to the 2D pattern matching and specifically to 2D text indexing is proposed. A transformation of a 2D text into the form of a tree is presented. It preserves the context of each element of the 2D text. The tree can be linearised using the prefix notation into the form of a string (a linear text) and the pattern matching is performed in this text. Pushdown automata indexing the 2D text are constructed over the tree representation. They allow to search for 2D prefixes, 2D suffixes, and 2D factors of the 2D text in time proportional to the size of the representation of a 2D pattern. This result achieves the properties analogous to the results obtained in tree pattern matching and string indexing.

### Finite Automata for Generalized Approach to Backward Pattern Matching

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Melichar, B.; Antoš, A.J.
Rok
2011
Publikováno
Proceedings of the 15th International Conference on Implementation and Application of Automata. Heidelberg: Springer, 2011. pp. 49-58. Lecture Notes in Computer Science. ISSN 0302-9743. ISBN 978-3-642-18097-2.
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We generalized the DAWG backward pattern matching approach to be able to solve a broad range of pattern matching problems. We use a definition of a class of problems. We describe a finite automaton for the basic pattern matching problem of finding an exact occurrence of one string in a text. We propose a mechanism to use simple operations over finite automata in a systematic approach to derive automata for solving problems from a defined class, such as approximate matching, regular expression matching, sequence matching, matching of set of patterns, etc. and their combinations. The benefit of this approach is the ability to quickly derive solutions for newly formulated pattern matching problems.

### On the Right-Seed Array of a String

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Guth, O.; Christou, M.; Crochemore, M.; Iliopoulos, CS; Pissis, SP
Rok
2011
Publikováno
Lecture Notes in Computer Science. 2011, 6842 492-502. ISSN 0302-9743.
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Anotace
We consider the problem of finding the repetitive structure of a given fixed string y. A factor u of y is a cover of y, if every letter of y falls within some occurrence of u in y. A factor v of y is a seed of y, if it is a cover of a superstring of y. There exist linear-time algorithms for solving the minimal cover problem. The minimal seed problem is of much higher algorithmic difficulty, and no linear-time algorithm is known. In this article, we solve one of its variants - computing the minimal and maximal right-seed array of a given string. A right seed of y is the shortest suffix of y that it is a cover of a superstring of y. An integer array RS is the minimal right-seed (resp. maximal right-seed) array of y, if RS [i] is the minimal (resp. maximal) length of right seeds of y[0..i]. We present an O(n log n) time algorithm that computes the minimal right-seed array of a given string, and a linear-time solution to compute the maximal right-seed array.

### Finite Automata in Pattern Matching

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Rok
2011
Publikováno
Algorithms in Computational Molecular Biology: Techniques, Approaches and Applications. New York: J. Willey, 2011. p. 51-71. ISBN 978-0-470-50519-9.
Typ
Kapitola v knize
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Anotace
Stringology is a part of Computer Science dealing with processing strings and sequences. It finds many important applications in various fields used by Information Society. Biological sequences processing is one of the most important fields. On the other hand the finite automata theory is a well developed formal system used for a long time in the area of compiler construction. The chapter aims to show various approaches of the finite automata use in Stringology. The approaches are demonstrated on practical examples. Of course it is impossible to describe all the approaches as it would be out of scope of the chapter. However, we would like to present basic approaches that the reader can modify and combine to a given task.

### Lossless Data Compression Testbed: ExCom and Prague Corpus

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Holub, J.; Řezníček, Jakub
Rok
2011
Publikováno
Proceedings Data Compression Conference. Los Alamitos, CA: IEEE Computer Soc., 2011. pp. 457. ISSN 1068-0314. ISBN 978-0-7695-4352-9.
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Authors developing new algorithms have to compare their implementations with the implementations of the other algorithms. They can do a testing on standard corpora and compare the achieved compression ratio with published compression ratios made on the same corpus. The corpora are static collections of files so they are getting older and do not contain new file types that appear. Moreover one can compare only the compression ratio. The times of compression and decompression are very important as well. In order to compare the times one have to run the implementation on the same platform and the same hardware. So one have to ask the authors for the source codes and incorporate them into his system. Then the tests could be run on the same machine.

### Block-oriented Dense Compressor

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Rok
2011
Publikováno
Proceedings Data Compression Conference. Los Alamitos, CA: IEEE Computer Soc., 2011. pp. 372. ISSN 1068-0314. ISBN 978-0-7695-4352-9.
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We address the problem of block-oriented natural language compression. The block-oriented compression is semi-adaptive in terms of one block but it is adaptive in terms of whole input. Our block-oriented compression method is based on Dense Code idea. It achieves very good compression ratio around 32 % on natural language text. We show that our compression method has some interesting properties which could be applied in digital libraries and other textual databases. The compression method allows direct searching on compressed text. Moreover the vocabulary can be used as a block index which makes some kinds of searching very fast. Another property is that the compressor can send single blocks with corresponding vocabulary which is considerate to limited bandwidth. In addition the compressed file can be continuously extended without need of previous decompression.

### Natural Language Compression per Blocks

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Rok
2011
Publikováno
First International Conference on Data Compression, Communications and Processing. Los Alamitos: IEEE Computer Society, 2011. pp. 67-75. ISBN 978-0-7695-4528-8.
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We present a new natural language compression method: Semi-adaptive Two Byte Dense Code (STBDC). STBDC performs compression per blocks. It means that the input is divided into the several blocks and each of the blocks is compressed separately according to its own statistical model. To avoid the redundancy the final vocabulary file is composed is the sequence of the changes in the model of the two consecutive blocks. STBDC belongs to the family of Dense codes and keeps all their attractive properties including very high compression and decompression speed and acceptable compression ratio around 32 % on natural language text. Moreover STBDC provides other properties applicable in digital libraries and other textual databases. The compression method allows direct searching on the compressed text, whereas the vocabulary can be used as a block index. STBDC is very easy on limited bandwidth in the client/server architecture.

### An algorithm for mapping short reads to a dynamically changing genomic sequence

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Holub, J.; Flouri, T.; Iliopoulos, C.S.I.; Pissis, S.P.P.
Rok
2010
Publikováno
2010 IEEE International Conference on Bioinformatics and Biomedicine. Los Alamitos: IEEE Computer Society, 2010. p. 133-136. ISBN 978-1-4244-8305-1.
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The constant advances in sequencing technology have redefined the way genome sequencing is performed. They are able to produce tens of millions of short sequences (reads), during a single experiment, and with a much lower cost than previously possible. Due to this massive amount of data, efficient algorithms for mapping these reads to reference sequences are in great demand, and recently, there has been ample work for publishing such algorithms. In this paper, we study a different version of this problem: mapping these reads to a dynamically changing genomic sequence. We propose a new practical algorithm, which employs a suitable data structure that takes into account potential dynamic effects (replacements, insertions, deletions) on the genomic sequence. The presented experimental results demonstrate that the proposed approach can be applied to address the problem of mapping millions of reads to multiple genomic sequences.

### Improving Practical Exact String Matching

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Holub, J.; Ďurian, B.; Peltola, H.; Tarhio, J.
Rok
2010
Publikováno
Information Processing Letters. 2010, 110(4), 148-152. ISSN 0020-0190.
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Anotace
We present improved variations of the BNDM algorithm for exact string matching. At each alignment the algorithms read a $q$-gram before testing the state variable. In addition we apply reading a 2-gram in one instruction.

### Using Finite Automata Approach for Searching Approximate Seeds of Strings

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Rok
2010
Publikováno
Intelligent Automation and Computer Engineering. New York: Springer, 2010. p. 347-360. ISSN 1876-1100. ISBN 978-90-481-3516-5.
Typ
Kapitola v knize
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Anotace
Seed is a type of a regularity of strings. A restricted approximate seed w of string T is a factor of T such that w covers a superstring of T under some distance rule. In this paper, the problem of searching of all restricted seeds with the smallest Hamming distance is studied and a polynomial time and space algorithm for solving the problem is presented. It searches for all restricted approximate seeds of a string with given limited approximation using Hamming distance and it computes the smallest distance for each found seed. The solution is based on a finite (suffix) automata approach that provides a straightforward way to design algorithms to many problems in stringology. Therefore, it is shown that the set of problems solvable using finite automata includes the one studied in this paper.

### A Note on a Tree-based 2D Indexing

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Rok
2010
Publikováno
Pre-proceedings of Conference on Implementation and Application of Automata 2010. Manitoba: University of Manitoba, 2010. pp. 269-277.
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Anotace
A transformation of 2D structures into the form of a tree, their linearisation and constructions of pushdown automata indexing this representation of a 2D text are presented.

### A Different Proof of the Crochemore-Ilie Lemma Concerning Microruns

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Holub, J.; Franek, F.
Rok
2009
Publikováno
London Algorithmics 2008: Theory and Practice. London: College Publications, 2009. pp. 1-9. ISBN 978-1-904987-97-0.
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Pracoviště
Anotace
In a resent paper, Crochemore and Ilie improved the upper bound of the maxrun function ro(n)=max{r(x) : |x| = n}, where r(x) denotes the number of runs in a string x, to 1.6n (computational results on Ilie's web page claim the improvement to 1.048n.) Their proof is essentially in two major steps: first step shows that there is at most 1center of a d-run on average in each interval of length d, in the second step they showed that ro9(n) <= n, where ro9(n) is the count limited to runs of size <= 9. The proof of ro9(n) <= n they presented relies on computation. We present an alternative simpler proof, also computational, to provide an independent verification of Crochemore-Ilie's result. The method used is completely different and has a potential to be verified without an aid of computer.

### On Parallel Implementations of Deterministic Finite Automata

Autoři
Holub, J.; Štekr, S.
Rok
2009
Publikováno
Implementation and Application of Automata. Heidelberg: Springer, 2009. p. 54-64. ISSN 0302-9743. ISBN 978-3-642-02978-3.
Typ
Stať ve sborníku
Pracoviště
Anotace
We present implementations of parallel DFA run methods and find whether and under what conditions is worthy to use the parallel methods of simulation of run of finite automata. First, we introduce the parallel DFA run methods for general DFA, which are universal, but due to the dependency of simulation time on the number of states vertical bar Q vertical bar of automaton being run, they are suitable only for run of automata with the smaller number of states. Then we show that if we apply some restrictions to properties of automata being run, we can reach the linear speedup compared to the sequential simulation method. We designed methods benefiting from k-locality that allows optimum parallel run of exact and approximate pattern matching automata. Finally, we show the results of experiments conducted on two types of parallel computers (Cluster of workstations and Symmetric shared-memory multiprocessors).

### New Word-based Adaptive Dense Compressors

Autoři
Rok
2009
Publikováno
Combinatorial Algorithms. Berlin: Springer, 2009. pp. 420-431. Lecture Notes in Computer Science. ISSN 0302-9743. ISBN 978-3-642-10216-5.
Typ
Stať ve sborníku
Pracoviště
Anotace
In the last two decades the natural language compression made a great progress. The main step in this evolution was the introduction of word-based compression by Mofiat. The word-based statistical compression algorithms are able to achieve 35% improvement in the compression ratio in comparison with character-based ones. We present two new word-based statistical compression algorithms based on dense coding idea: Two Byte Dense Code (TBDC) and Self-Tuning Dense Code (SCDC). TBDC uses the codewords with maximal size 2 bytes and must be implemented with some pruning technique. STDC is able to tune its code space during the compression process and so achieve better compression. Our algorithms improve the compression ratio and are considerate to smaller ffles which are very often omitted. We present also a generalized concept of dense coding called Open Dense Code (ODC) which provides a frame for deffnition of these two and many other dense code schemas.

Za obsah stránky zodpovídá: doc. Ing. Štěpán Starosta, Ph.D.