Fast Indexes for Gapped Pattern Matching

Cáceres, Manuel; Puglisi, Simon J.; Zhukova, Bella

doi:10.1007/978-3-030-38919-2_40

Cited by 6 publications

(8 citation statements)

References 20 publications

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“…Cáceres et al [7] provided indexes in the context of huge data sets for variable lengthgapped (VLG) patterns. These variable-length gapped patterns include two or more subpatterns.…”

Section: Background Workmentioning

confidence: 99%

An Efficient Algorithm for 2-Dimensional Pattern Matching Problem

2020

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AbstractPattern matching is the area of computer science which deals with security and analysis of data. This work proposes two 2D pattern matching algorithms based on two different input domains. The first algorithm is for the case when the given pattern contains only two symbols, that is, binary symbols 0 and 1. The second algorithm is in the case when the given pattern contains decimal numbers, that is, the collection of symbols between 0 and 9. The algorithms proposed in this manuscript convert the given pattern into an equivalent binary or decimal number, correspondingly find the cofactors of the same dimension and convert these cofactors into numbers if a particular cofactor number matches indicate the matching of the pattern. Furthermore, the algorithm is enhanced for decimal numbers. In the case of decimal numbers, each row of the pattern is changed to its decimal equivalent, and then, modulo with a suitable prime number changes the decimal equivalent into a number less than the prime number. If the number mismatched pattern does not exist, the complexity of the proposed algorithm is very low as compared to other traditional algorithms.

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“…Cáceres et al [7] provided indexes in the context of huge data sets for variable lengthgapped (VLG) patterns. These variable-length gapped patterns include two or more subpatterns.…”

Section: Background Workmentioning

confidence: 99%

An Efficient Algorithm for 2-Dimensional Pattern Matching Problem

2020

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“…Typical queries include existential queries (decide if the pattern occurs in S), reporting queries (return all positions where the pattern occurs), and counting queries (return the number of occurrences of the pattern). An important variant of this problem is the gapped string indexing problem [6,8,10,14,27,28,31]. Here, the goal is to compactly represent the string such that given two patterns P 1 and P 2 and a gap range [α, β] we can quickly find occurrences of P 1 and P 2 with distance in [α, β].…”

Section: Introductionmentioning

confidence: 99%

“…Here, the goal is to compactly represent the string such that given two patterns P 1 and P 2 and a gap range [α, β] we can quickly find occurrences of P 1 and P 2 with distance in [α, β]. Searching and indexing with gaps is frequently used in computational biology applications [6,11,13,14,19,21,22,32,35,38].…”

Section: Introductionmentioning

confidence: 99%

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Gapped Indexing for Consecutive Occurrences

Bille¹,

Gørtz²,

Pedersen³

et al. 2021

Preprint

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The classic string indexing problem is to preprocess a string S into a compact data structure that supports efficient pattern matching queries. Typical queries include existential queries (decide if the pattern occurs in S), reporting queries (return all positions where the pattern occurs), and counting queries (return the number of occurrences of the pattern). In this paper we consider a variant of string indexing, where the goal is to compactly represent the string such that given two patterns P1 and P2 and a gap range [α, β] we can quickly find the consecutive occurrences of P1 and P2 with distance in [α, β], i.e., pairs of occurrences immediately following each other and with distance within the range. We present data structures that use O(n) space and query time O(|P1| + |P2| + n 2/3 ) for existence and counting and O(|P1| + |P2| + n 2/3 occ 1/3 ) for reporting. We complement this with a conditional lower bound based on the set intersection problem showing that any solution using O(n) space must use Ω(|P1| + |P2| + √ n) query time. To obtain our results we develop new techniques and ideas of independent interest including a new suffix tree decomposition and hardness of a variant of the set intersection problem.

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“…The goal is to obtain a compact data structure while supporting fast queries in terms of the length of the pattern P and the number of reported occurrences k. For an example, see Figure 1. 4,7,11,22,24,26,30,39 and 41 in S. The top 5 close consecutive occurrences are (22,24), (24,26), (39, 41), (4,7), and (7,11), with the tie between (7,11) and (26,30) broken arbitrarily.…”

Section: Introductionmentioning

confidence: 99%

String Indexing for Top-$k$ Close Consecutive Occurrences

Bille¹,

Gørtz²,

Pedersen³

et al. 2020

Preprint

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The classic string indexing problem is to preprocess a string S into a compact data structure that supports efficient subsequent pattern matching queries, that is, given a pattern string P , report all occurrences of P within S. In this paper, we study a basic and natural extension of string indexing called the string indexing for top-k close consecutive occurrences problem (Sitcco). Here, a consecutive occurrence is a pair (i, j), i < j, such that P occurs at positions i and j in S and there is no occurrence of P between i and j, and their distance is defined as j − i. Given a pattern P and a parameter k, the goal is to report the top-k consecutive occurrences of P in S of minimal distance. The challenge is to compactly represent S while supporting queries in time close to length of P and k. We give two new time-space trade-offs for the problem. Our first result achieves near-linear space and optimal query time, and our second result achieves linear space and near optimal query time. Along the way, we develop several techniques of independent interest, including a new translation of the problem into a line segment intersection problem and a new recursive clustering technique for trees.

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Fast Indexes for Gapped Pattern Matching

Cited by 6 publications

References 20 publications

An Efficient Algorithm for 2-Dimensional Pattern Matching Problem

An Efficient Algorithm for 2-Dimensional Pattern Matching Problem

Gapped Indexing for Consecutive Occurrences

String Indexing for Top-$k$ Close Consecutive Occurrences

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