2016
DOI: 10.1145/2836166
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Sparse Text Indexing in Small Space

Abstract: In this work we present efficient algorithms for constructing sparse suffix trees, sparse suffix arrays and sparse positions heaps for b arbitrary positions of a text T of length n while using only O(b) words of space during the construction.Attempts at breaking the naive bound of Ω(nb) time for constructing sparse suffix trees in O(b) space can be traced back to the origins of string indexing in 1968. First results were only obtained in 1996, but only for the case where the b suffixes were evenly spaced in T … Show more

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Cited by 13 publications
(44 citation statements)
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“…However, we design a new way to combine Karp-Rabin fingerprints together with approximately min-wise hash functions, in order to use this method using only small amount of space. In previous results for the LCE problem [3,4,19,37], a set of positions of size O( n τ ) was also considered by the data structures. In contrast to these algorithms, where the selected positions were dependent only on the length of the text, we introduce the first algorithm that exploit the actual text using local properties in order to decide which positions to select.…”
Section: Algorithmic Overviewmentioning
confidence: 99%
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“…However, we design a new way to combine Karp-Rabin fingerprints together with approximately min-wise hash functions, in order to use this method using only small amount of space. In previous results for the LCE problem [3,4,19,37], a set of positions of size O( n τ ) was also considered by the data structures. In contrast to these algorithms, where the selected positions were dependent only on the length of the text, we introduce the first algorithm that exploit the actual text using local properties in order to decide which positions to select.…”
Section: Algorithmic Overviewmentioning
confidence: 99%
“…Text indexing is one of the most fundamental problems in the area of string algorithms and information retrieval (e.g. see [40,24,39,30,13,3,15,16,6,17,1,26,23,8,34]). In this paper we consider two closely related problems of text indexing in sub-linear working space.…”
Section: Introductionmentioning
confidence: 99%
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“…The authors of these papers showed that suffix sorting is possible within the same space of the text and the final suffix array, that is, in place. Parallel to the study of techniques to sort all suffixes of a text, several authors started considering the problem of efficiently sorting only a subset of b text's suffixes [2,3,6,11,17,19,20], a fundamental step in the construction of compressed and sparse text indexes [20] and space-efficient compression algorithms. Very recently, Gawrychowski and Kociumaka [11] gave the first optimal time-and-space solution to the problem, showing that O(b) working space and O(n) running time are achievable with a Monte Carlo algorithm (they also consider a Las Vegas algorithm with higher running time).…”
Section: Introductionmentioning
confidence: 99%
“…It is well known (see, e.g. [2]) that the Longest Common Extension problem (LCE) -that is, to find the length of the longest common prefix between any two text suffixes -is closely related to the suffix sorting problem. In this paper, we exploit this relation and give the first in-place solution to the sparse suffix sorting problem.…”
Section: Introductionmentioning
confidence: 99%