Nested Counters in Bit-Parallel String Matching

Fredriksson, Kimmo; Grabowski, Szymon

doi:10.1007/978-3-642-00982-2_29

Cited by 7 publications

(12 citation statements)

References 14 publications

(15 reference statements)

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“…String indexing for patterns with variable length gaps has applications in information retrieval, data mining and computational biology [16,18,29,31,33]. In particular, the PROSITE data base [5,21] uses patterns with variable length gaps to identify and classify protein sequences.…”

Section: Variable Length Gapsmentioning

confidence: 99%

String Indexing for Patterns with Wildcards

et al. 2013

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We consider the problem of indexing a string t of length n to report the occurrences of a query pattern p containing m characters and j wildcards. Let occ be the number of occurrences of p in t, and σ the size of the alphabet. We obtain the following results.• A linear space index with query time O(m + σ j log log n + occ). This significantly improves the previously best known linear space index by Lam et al. [ISAAC 2007], which requires query time Θ(jn) in the worst case.• An index with query time O(m + j + occ) using space O(σ k 2 n log k log n), where k is the maximum number of wildcards allowed in the pattern. This is the first non-trivial bound with this query time.• A time-space trade-off, generalizing the index by Cole et al. [STOC 2004].We also show that these indexes can be generalized to allow variable length gaps in the pattern. Our results are obtained using a novel combination of well-known and new techniques, which could be of independent interest.

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Section: Variable Length Gapsmentioning

confidence: 99%

String Indexing for Patterns with Wildcards

et al. 2013

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“…Variable length gaps are frequently used in computational biology applications [8,9,22,24,25]. For instance, the PROSITE data base [7,13] supports searching for proteins specified by patterns formed by concatenation of characters, character classes, and variable length gaps.…”

Section: Character Class Intervalsmentioning

confidence: 99%

“…This algorithm encodes each variable length gap using a number of bits proportional to the upper bound on the length of the gap. Fredriksson and Grabowski [8,9] improved this for the case when all variable length gaps have lower bound 0 and identical upper bound y. They showed how to encode each such gaps using O(log y) bits [8] and subsequently O(log log y) bits [9], leading to an algorithm using O(m log log y w +1) time per character.…”

Section: Character Class Intervalsmentioning

confidence: 99%

“…We introduce an improved algorithm for maintaining counters in parallel as a key component in Theorem 1.2. Plugging in these counters in the algorithms of Fredriksson and Grabowski [8,9] we obtain an algorithm using O( m y + 1) per character for this problem. With our counters we can even remove the restriction that each variable length gap should have the same upper bound.…”

Section: Character Class Intervalsmentioning

confidence: 99%

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Regular Expression Matching with Multi-Strings and Intervals

Bille¹,

Thorup²

2010

Proceedings of the Twenty-First Annual ACM-SIAM Symposium on Discrete Algorithms

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Regular expression matching is a key task (and often computational bottleneck) in a variety of software tools and applications. For instance, the standard grep and sed utilities, scripting languages such as perl, internet traffic analysis, XML querying, and protein searching. The basic definition of a regular expression is that we combine characters with union, concatenation, and kleene star operators. The length m is proportional to the number of characters. However, often the initial operation is to concatenate characters in fairly long strings, e.g., if we search for certain combinations of words in a firewall. As a result, the number k of strings in the regular expression is significantly smaller than m. Our main result is a new algorithm that essentially replaces m with k in the complexity bounds for regular expression matching. More precisely, after an O(m log k) time and O(m) space preprocessing of the expression, we can match it in a string presented as a stream of characters in O(k log w w + log k) time per character, where w is the number of bits in a memory word. For large w, this corresponds to the previous best bound of O(m log w w + log m). Prior to this work no O(k) bound per character was known. We further extend our solution to efficiently handle character class interval operators C{x, y}. Here, C is a set of characters and C{x, y}, where x and y are integers such that 0 ≤ x ≤ y, represents a string of length between x and y from C. These character class intervals generalize variable length gaps which are frequently used for pattern matching in computational biology applications.

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“…An efficient approach to solve the problem for a single pattern is based on the simulation of nondeterministic finite automata [12,6]. A method to solve the case of one or more patterns is to translate the patterns into a regular expression [13,4].…”

Section: Introductionmentioning

confidence: 99%

Motif Matching Using Gapped Patterns

Giaquinta

Fredriksson

Grabowski

et al. 2013

Lecture Notes in Computer Science

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Abstract. We present new algorithms for the problem of multiple string matching of gapped patterns, where a gapped pattern is a sequence of strings such that there is a gap of fixed length between each two consecutive strings. The problem has applications in the discovery of transcription factor binding sites in DNA sequences when using generalized versions of the Position Weight Matrix model to describe transcription factor specificities. In these models a motif can be matched as a set of gapped patterns with unit-length keywords. The existing algorithms for matching a set of gapped patterns are worst-case efficient but not practical, or vice versa, in this particular case. The novel algorithms that we present are based on dynamic programming and bit-parallelism, and lie in a middle-ground among the existing algorithms. In fact, their time complexity is close to the best existing bound and, yet, they are also practical. We also provide experimental results which show that the presented algorithms are fast in practice, and preferable if all the strings in the patterns have unit-length.

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Nested Counters in Bit-Parallel String Matching

Cited by 7 publications

References 14 publications

String Indexing for Patterns with Wildcards

String Indexing for Patterns with Wildcards

Regular Expression Matching with Multi-Strings and Intervals

Motif Matching Using Gapped Patterns

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