On Approximate Jumbled Pattern Matching in Strings

Burcsi, Péter; Cicalese, Ferdinando; Fici, Gabriele; Lipták, Zsuzsanna

doi:10.1007/s00224-011-9344-5

Cited by 47 publications

(41 citation statements)

References 20 publications

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“…The index provides only a yes/no answer for a query pattern; additional O(log n) time can be used to restore a witness occurrence [12]. The construction time was improved independently by Burcsi et al [6] (see also [7,8]) and Moosa and Rahman [20] to O n 2 log n , and then by Moosa and Rahman [21] to O n 2 (log n) 2 . All these results work in the word-RAM model.…”

Section: The Binary Casementioning

confidence: 99%

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Efficient Indexes for Jumbled Pattern Matching with Constant-Sized Alphabet

2016

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We introduce efficient indexes for a problem in non-standard stringology: jumbled pattern matching. An index is a data structure constructed for a text of length n over an alphabet of size σ that can answer queries asking if the text contains a fragment which is jumbled (Abelian) equivalent to a pattern, specified by its so-called Parikh vector. We denote the length of the pattern by m. Moosa and Rahman (J Discrete Algorithms 10:5-9, 2012) gave an index for the case of binary alphabets with O n 2 (log n) 2 -time construction in the word-RAM model. Several earlier papers stated as an open problem the existence of an efficient solution for larger alphabets. In this paper we develop an index for any constant-sized alphabet. The construction involves a trade-off parameter, which in particular lets us achieve the following complexities: O(n 2−δ ) space and O(m (2σ −1)δ ) query time for any 0 < δ < 1, or O n 2 (log log n) 2 log n space and polylogarithmic, o(log 2σ −1 m), query time. The construction time in both cases is subquadratic: O n 2 (log log n) 2 log n in the word-RAM model (using bit-parallelism). Our construction algorithms are randomized (Las Vegas, running time w.h.p.), which is due to the usage of perfect hashing. On the other hand, all queries are answered deterministically. A preliminary version of this work appeared at ESA 2013 (Kociumaka et al. in Algorithms, ESA 2013. LNCS, vol 8125. Springer, Berlin, pp. 625-636, 2013 time construction of the index with O(n 2−δ ) space and O(m (2σ −1)δ ) query time, which was not present in the preliminary version. We also extend the index so that the position of the leftmost occurrence of the query pattern is provided at no additional cost in the complexity; this required rather nontrivial changes in the construction algorithm.

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Section: The Binary Casementioning

confidence: 99%

“…Several researchers (see, e.g., [8,20,21]) posed an open problem asking for a construction of an o(n 2 ) indexing scheme with o(n) query time for general alphabets. In particular, even for a ternary alphabet none was known, since the basic observation used to obtain a binary index is not applicable to any larger alphabet.…”

Section: Indexes For Larger Alphabetsmentioning

confidence: 99%

Efficient Indexes for Jumbled Pattern Matching with Constant-Sized Alphabet

2016

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“…Jumbled pattern matching problem [9,14] (also known as Abelian pattern matching or permutation matching) is a variation of string matching.…”

Section: Problem Definition and Applicationsmentioning

confidence: 99%

“…In the recent past, numerous variations of this problem have appeared, such as exact string matching, approximate string matching, circular sting matching [63], order preserving matching [2,17,43], jumbled pattern matching [9,14] and many more. The task of exact string matching is to find all occurrences of the pattern P in the text T , i.e.…”

Section: Introductionmentioning

confidence: 99%

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Improved online algorithms for jumbled matching

Ghuman

Tarhio

Chhabra

2020

Discrete Applied Mathematics

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Flexible and Efficient Algorithms for Abelian Matching in Genome Sequence

Faro

Pavone

2019

Bioinformatics and Biomedical Engineering

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The abelian pattern matching problem consists in finding all substrings of a text which are permutations of a given pattern. This problem finds application in many areas and can be solved in linear time by a naïve sliding window approach. In this short communication we present a new class of algorithms based on a new efficient fingerprint computation approach, called Heap-Counting, which turns out to be fast, flexible and easy to be implemented. It can be proved that our solutions have a linear worst case time complexity and, in addition, we present an extensive experimental evaluation which shows that our newly presented algorithms are among the most efficient and flexible solutions in practice for the abelian matching problem in strings. ⋆ This is a short preliminary version of a full paper submitted to an international journal. Most examples, details, lemmas and theorems have been omitted.

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On Approximate Jumbled Pattern Matching in Strings

Cited by 47 publications

References 20 publications

Efficient Indexes for Jumbled Pattern Matching with Constant-Sized Alphabet

Efficient Indexes for Jumbled Pattern Matching with Constant-Sized Alphabet

Improved online algorithms for jumbled matching

Flexible and Efficient Algorithms for Abelian Matching in Genome Sequence

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