Optimal Dynamic Sequence Representations

Navarro, Gonzalo; Nekrich, Yakov

doi:10.1137/130908245

Cited by 36 publications

(9 citation statements)

References 46 publications

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“…Tangentially related to the problem of text indexing is the problem of sequence representation [NN14], where we store a string S [1 . . n] under character insertions and deletions and support the access to S, rank(i, c) (returning |{j ∈ [1 .…”

Section: Our Resultsmentioning

confidence: 99%

Dynamic Suffix Array with Polylogarithmic Queries and Updates

Kempa,

Kociumaka

2022

Preprint

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The suffix array SA[1 . . n] of a text T of length n is a permutation of {1, . . . , n} describing the lexicographical ordering of suffixes of T , and it is considered to be among of the most important data structures in string algorithms, with dozens of applications in data compression, bioinformatics, and information retrieval. One of the biggest drawbacks of the suffix array is that it is very difficult to maintain under text updates: even a single character substitution can completely change the contents of the suffix array. Thus, the suffix array of a dynamic text is modelled using suffix array queries, which return the valuePrior to this work, the fastest dynamic suffix array implementations were by Amir and Boneh. At ISAAC 2020, they showed how to answer suffix array queries in O(k) time, where k ∈ [1 . . n] is a trade-off parameter, with O( n k )-time text updates. In a very recent preprint [arXiv, 2021], they also provided a solution with O(log 5 n)-time queries and O(n 2/3 )-time updates.We propose the first data structure that supports both suffix array queries and text updates in O(polylog n) time (achieving O(log 4 n) and O(log 3+o(1) n) time, respectively). Our data structure is deterministic and the running times for all operations are worst-case. In addition to the standard single-character edits (character insertions, deletions, and substitutions), we support (also in O(log 3+o(1) n) time) the "cut-paste" operation that moves any (arbitrarily long) substring of T to any place in T . To achieve our result, we develop a number of new techniques which are of independent interest. This includes a new flavor of dynamic locally consistent parsing, as well as a dynamic construction of string synchronizing sets with an extra local sparsity property; this significantly generalizes the sampling technique introduced at STOC 2019. We complement our structure by a hardness result: unless the Online Matrix-Vector Multiplication (OMv) Conjecture fails, no data structure with O(polylog n)-time suffix array queries can support the "copy-paste" operation in O(n 1−ε ) time for any ε > 0.

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Section: Our Resultsmentioning

confidence: 99%

Dynamic Suffix Array with Polylogarithmic Queries and Updates

Kempa,

Kociumaka

2022

Preprint

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“…Handling updates to the collections is possible in principle, as there are dynamic data structures for sequences, trees, and text collections . However, their practicality has not yet been established nor how they relate to classical schemes that maintain a log of changes and re‐index periodically.…”

Section: Discussionmentioning

confidence: 99%

Fast in‐memory XPath search using compressed indexes

et al. 2013

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Artículo de publicación ISIExtensible Markup Language (XML) documents consist of text data plus structured data (markup). XPath allows to query both text and structure. Evaluating such hybrid queries is challenging. We present a system for in-memory evaluation of XPath search queries, that is, queries with text and structure predicates, yet without advanced features such as backward axes, arithmetics, and joins. We show that for this query fragment, which contains Forward Core XPath, our system, dubbed Succinct XML Self-Index (‘SXSI’), outperforms existing systems by 1–3 orders of magnitude. SXSI is based on state-of-the-art indexes for text and structure data. It combines two novelties. On one hand, it represents the XML data in a compact indexed form, which allows it to handle larger collections in main memory while supporting powerful search and navigation operations over the text and the structure. On the other hand, it features an execution engine that uses tree automata and cleverly chooses evaluation orders that leverage the speeds of the respective indexes. SXSI is modular and allows seamless replacement of its indexes. This is demonstrated through experiments with (1) a text index specialized for search of bio sequences, and (2) a word-based text index specialized for natural language search.Fondecyt, Chile 1-11006

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“…A natural question is how much the latter bound can be improved using extra space. For example, using the dynamic wavelet tree data structure [26] in additional O (n + | | log n) bits of space, we can maintain the BWT through insertion and deletion operations of individual symbols, supporting rank and select operations, with a cost of O (log n/ log log n) time per operation. Using the latter data structure, our algorithms in Sections 2 and 3 would give a bound of O (n log n) time with additional O (n + | | log n) bits of space besides that needed for storing the n characters of the input text T .…”

Section: Practical Trade-off Between Space and Timementioning

confidence: 99%

“…Using the latter data structure, our algorithms in Sections 2 and 3 would give a bound of O (n log n) time with additional O (n + | | log n) bits of space besides that needed for storing the n characters of the input text T . 3 However the resulting solution is not very practical as the data structure in [26] is quite sophisticated. We show next how to smoothly adapt our algorithms in Sections 2 and 3 to a situation where extra memory is allowed, producing some trade-off solutions that are amenable for implementation with a flexible parameter k for the additional space.…”

Section: Practical Trade-off Between Space and Timementioning

confidence: 99%

See 1 more Smart Citation

Computing the Burrows–Wheeler transform in place and in small space

Crochemore

Grossi

Kärkkäinen

et al. 2015

Journal of Discrete Algorithms

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International audienceWe introduce the problem of computing the Burrows–Wheeler Transform (BWT) using small additional space. Our in-place algorithm does not need the explicit storage for the suffix sort array and the output array, as typically required in previous work. It relies on the combinatorial properties of the BWT, and runs in $O(n2)$ time in the comparison model using $O(1)$ extra memory cells, apart from the array of n cells storing the n characters of the input text. We then discuss the time–space trade-off when $O(k⋅σk)$ extra memory cells are allowed with σk distinct characters, providing an $O((n2/k+n)log⁡k)$-time algorithm to obtain (and invert) the BWT. For example in real systems where the alphabet size is a constant, for any arbitrarily small $ϵ>0$, the BWT of a text of n bytes can be computed in $O(nϵ−1log⁡n)$ time using just ϵn extra bytes

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Optimal Dynamic Sequence Representations

Cited by 36 publications

References 46 publications

Dynamic Suffix Array with Polylogarithmic Queries and Updates

Dynamic Suffix Array with Polylogarithmic Queries and Updates

Fast in‐memory XPath search using compressed indexes

Computing the Burrows–Wheeler transform in place and in small space

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