Order-preserving indexing

Crochemore, Maxime; Iliopoulos, S; Kociumaka, Tomasz; Kubica, Marcin; Langiu, Alessio; Pissis, Solon P.; Radoszewski, Jakub; Rytter, Wojciech; Waleń, Tomasz

doi:10.1016/j.tcs.2015.06.050

Cited by 21 publications

(30 citation statements)

References 39 publications

(55 reference statements)

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“…For the offline problem, Crochemore et al showed how, given a sequence T [1, n ], in

scriptO false(n \log false(n false) false/ \log \log n false)

time, we can build an

scriptO false(n \log n false)

‐bit index such that, later, given a pattern P [1, p ], we can return the starting positions of all the occ order‐preserving matches of P in T in optimal

scriptO false(m + sans-serifocc false)

Time. A more space‐economical solution is proposed by Gagie et al consisting of an index taking

scriptO false(n \log \log n false)

extra bits in addition to the text.…”

Section: Problem Formulation and Previous Resultsmentioning

confidence: 99%

A compact index for order‐preserving pattern matching

2019

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Summary Order‐preserving pattern matching has been introduced recently, but it has already attracted much attention. Given a reference sequence and a pattern, we want to locate all substrings of the reference sequence whose elements have the same relative order as the pattern elements. For this problem, we consider the offline version in which we build an index for the reference sequence so that subsequent searches can be completed very efficiently. We propose a space‐efficient index that works well in practice despite its lack of good worst‐case time bounds. Our solution is based on the new approach of decomposing the indexed sequence into an order component, containing ordering information, and a δ component, containing information on the absolute values. Experiments show that this approach is viable, is faster than the available alternatives, and is the first one offering simultaneously small space usage and fast retrieval.

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“…For the offline problem, Crochemore et al showed how, given a sequence T [1, n ], in

scriptO false(n \log false(n false) false/ \log \log n false)

time, we can build an

scriptO false(n \log n false)

‐bit index such that, later, given a pattern P [1, p ], we can return the starting positions of all the occ order‐preserving matches of P in T in optimal

scriptO false(m + sans-serifocc false)

Time. A more space‐economical solution is proposed by Gagie et al consisting of an index taking

scriptO false(n \log \log n false)

extra bits in addition to the text.…”

Section: Problem Formulation and Previous Resultsmentioning

confidence: 99%

A compact index for order‐preserving pattern matching

2019

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“…Let us start by recalling the encoding for op-pattern matching (op-encoding) from [19,37]. For a string S of length n and i ∈ 1..n we define:…”

Section: Algorithmic Toolbox For Op-modelmentioning

confidence: 99%

“….n] such that op-PREF[i] is the length of the longest prefix of S[i..n] that is equivalent to a prefix of S. It is a direct analogue of the PREF array used in standard string matching (see [21]) and can be computed similarly in O(n) time using one of the standard encodings for the op-model that were used in [15,19,37]; see lemma below.…”

Section: Op-pref Tablementioning

confidence: 99%

“…Proof. The order-preserving suffix tree (op-suffix tree) that is constructed in [19] is a compacted trie of op-encodings of all the suffixes of the text. In O(n log log n) expected time or O(n log 2 log n/ log log log n) worst-case time one can construct a so-called incomplete version of the op-suffix tree in which each explicit node may have at most one edge whose first character label is not known.…”

Section: Longest Common Extension Queriesmentioning

confidence: 99%

“…An index for op-pattern matching based on the suffix tree was developed in [19]. For a text of length n it uses O(n) space and answers op-pattern matching queries for a pattern of length m in optimal, O(m) time (or O(m + Occ) time if we are to report all Occ occurrences).…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

String periods in the order-preserving model

Gourdel

Kociumaka

Radoszewski

et al. 2020

Information and Computation

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The order-preserving model (op-model, in short) was introduced quite recently but has already attracted significant attention because of its applications in data analysis. We introduce several types of periods in this setting (op-periods). Then we give algorithms to compute these periods in time O(n), O(n log log n), O(n log 2 log n/ log log log n), O(n log n) depending on the type of periodicity. In the most general variant the number of different periods can be as big as Ω(n 2 ), and a compact representation is needed. Our algorithms require novel combinatorial insight into the properties of such periods.

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