Range LCP

Amir, Amihood; Apostolico, Alberto; Landau, Gad M.; Levy, Avivit; Lewenstein, Moshe; Porat, Ely

doi:10.1016/j.jcss.2014.02.010

Cited by 16 publications

(32 citation statements)

References 6 publications

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“…Recall that in order to define sample k we use identifiers ID k [j] = π k (DBF k [j]), where π k is a permutation of S m k . RandomizedDBF is a modification of CompactDBF, which instead of DBF k [i] operates on ID k [i] = π k (DBF k [i]) as identifiers for queries (1) and (2), where for each level k, the permutation π k is drawn uniformly at random from S m k . Proof.…”

Section: Compactdbfmentioning

confidence: 99%

Internal Pattern Matching Queries in a Text and Applications

Kociumaka¹,

Radoszewski²,

Rytter³

et al. 2014

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

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We consider several types of internal queries: questions about subwords of a text. As the main tool we develop an optimal data structure for the problem called here internal pattern matching. This data structure provides constanttime answers to queries about occurrences of one subword x in another subword y of a given text, assuming that |y| = O(|x|), which allows for a constant-space representation of all occurrences. This problem can be viewed as a natural extension of the well-studied pattern matching problem. The data structure has linear size and admits a linear-time construction algorithm.Using the solution to the internal pattern matching problem, we obtain very efficient data structures answering queries about: primitivity of subwords, periods of subwords, general substring compression, and cyclic equivalence of two subwords. All these results improve upon the best previously known counterparts. The linear construction time of our data structure also allows to improve the algorithm for finding δ-subrepetitions in a text (a more general version of maximal repetitions, also called runs). For any fixed δ we obtain the first linear-time algorithm, which matches the linear time complexity of the algorithm computing runs. Our data structure has already been used as a part of the efficient solutions for subword suffix rank & selection, as well as substring compression using Burrows-Wheeler transform composed with run-length encoding.The model of internal queries in texts is connected to the well-studied problem of text indexing. Both models have their origins in the introduction of suffix trees. However, there is an important difference: in our model the size of the representation of a query is constant and therefore enables faster query time. Our results can be viewed as efficient solutions to "internal" equivalents of several basic problems of regular pattern matching and make an improvement in a majority of already published results related to internal queries.

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Section: Compactdbfmentioning

confidence: 99%

Internal Pattern Matching Queries in a Text and Applications

Kociumaka¹,

Radoszewski²,

Rytter³

et al. 2014

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

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“…Range query data structures have also been considered specifically for strings [1,3,4,12]. For instance, in bioinformatics applications we are often interested in finding regularities in certain regions of a DNA sequence [5,17].…”

Section: Introductionmentioning

confidence: 99%

Range Shortest Unique Substring Queries

Abedin

Ganguly

Pissis

et al. 2019

String Processing and Information Retrieval

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Let T[1, n] be a string of length n and T[i, j] be the substring of T starting at position i and ending at position j. A substring T[i, j] of T is a repeat if it occurs more than once in T; otherwise, it is a unique substring of T. Repeats and unique substrings are of great interest in computational biology and in information retrieval. Given string T as input, the Shortest Unique Substring problem is to find a shortest substring of T that does not occur elsewhere in T. In this paper, we introduce the range variant of this problem, which we call the Range Shortest Unique Substring problem. The task is to construct a data structure over T answering the following type of online queries efficiently. Given a range [α, β], return a shortest substring T[i, j] of T with exactly one occurrence in [α, β]. We present an O(n log n)-word data structure with O(log w n) query time, where w = Ω(log n) is the word size. Our construction is based on a non-trivial reduction allowing us to apply a recently introduced optimal geometric data structure [Chan et al. ICALP 2018].

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“…A finite ordered sequence of characters (possibly empty) is called a string. characters in a string are enumerated starting from 1, that is, a string w of length n consists of characters w [1], w [2], . .…”

Section: Introductionmentioning

confidence: 99%

“…equality testing and longest common extension computation) in constant time and linear space. Lately a number of studies emerged addressing compressibility [14,28], range longest common prefixes (range LCP) [1,35], periodicity [29,16], minimal/maximal suffixes [4,3], substring hashing [18,21], and fragmented pattern matching [2,21]. Our work focuses on rank/select problems for suffixes of a given substring.…”

Section: Introductionmentioning

confidence: 99%

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Wavelet Trees Meet Suffix Trees

Babenko¹,

Gawrychowski²,

Kociumaka³

et al. 2014

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

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We present an improved wavelet tree construction algorithm and discuss its applications to a number of rank/select problems for integer keys and strings.Given a string of length n over an alphabet of size σ ≤ n, our method builds the wavelet tree in O(n log σ/ √ log n) time, improving upon the state-of-the-art algorithm by a factor of √ log n. As a consequence, given an array of n integers we can construct in O(n √ log n) time a data structure consisting of O(n) machine words and capable of answering rank/select queries for the subranges of the array in O(log n/ log log n) time. This is a log log n-factor improvement in query time compared to Chan and Pȃtraşcu (SODA 2010) and a √ log n-factor improvement in construction time compared to Brodal et al. (Theor. Comput. Sci. 2011).Next, we switch to stringological context and propose a novel notion of wavelet suffix trees. For a string w of length n, this data structure occupies O(n) words, takes O(n √ log n) time to construct, and simultaneously captures the combinatorial structure of substrings of w while enabling efficient top-down traversal and binary search. In particular, with a wavelet suffix tree we are able to answer in O(log |x|) time the following two natural analogues of rank/select queries for suffixes of substrings: 1) For substrings x and y of w (given by their endpoints) count the number of suffixes of x that are lexicographically smaller than y; 2) For a substring x of w (given by its endpoints) and an integer k, find the k-th lexicographically smallest suffix of x. We further show that wavelet suffix trees allow to compute a run-length-encoded Burrows-Wheeler transform of a substring x of w (again, given by its endpoints) in O(s log |x|) time, where s denotes the length of the resulting runlength encoding. This answers a question by Cormode and Muthukrishnan (SODA 2005), who considered an analogous problem for Lempel-Ziv compression.All our algorithms, except for the construction of wavelet suffix trees, which additionally requires O(n) time in expectation, are deterministic and operate in the word RAM model.

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Range LCP

Cited by 16 publications

References 6 publications

Internal Pattern Matching Queries in a Text and Applications

Internal Pattern Matching Queries in a Text and Applications

Range Shortest Unique Substring Queries

Wavelet Trees Meet Suffix Trees

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