A Faster Query Algorithm for the Text Fingerprinting Problem

Chan, Chi-Yuan; Yu, Hung-I; Hon, Wing-Kai; Wang, Biing-Feng

doi:10.1007/978-3-540-75520-3_13

Cited by 2 publications

(5 citation statements)

References 8 publications

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“…We define fos(i, j) as the string formed by concatenating the first occurrences of each distinct character touched when reading s from position i (included) to position j (included). For instance, if s = a1b2a3c4e5a6b7a8c9d10#, fos (3,9) = aceb and fos(5, 10) = eabcd. Definition 3.…”

Section: Naming Techniquementioning

confidence: 99%

“…We now present the fingerprint trie (this is called backtracking tree in [3,4]). The fingerprint trie is a tree representation of the fingerprints.…”

Section: Fingerprint Triementioning

confidence: 99%

“…This is step 2 in our query algorithm. Given two strings s1 and s2 where |s1| = |s2|, we would wish to test whether the two strings are permutations of the same set 3 . That is, we are asking if we can obtain the string s1 by doing a permutation on the characters of the string s2.…”

Section: Deterministic and Probabilistic Set Equality Testingmentioning

confidence: 99%

“…The Θ(n 2 ) bound is obtained using the algorithm of Didier et al [6]. Problem 2 is solved in O(|f | log(σ/|f |)) time and O(|F|) space (O(|F| log n) bits) and Problem 3 in O(|f | log(σ/|f |) + occ) time (where occ is the number of maximal locations that match the given fingerprint) and O(|F| + |L|) space (O((|F| + |L|) log n) bits) in [3,4].…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Various improvements to text fingerprinting

Belazzougui

Kolpakov

Raffinot

2013

Journal of Discrete Algorithms

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Let s = s1..sn be a text (or sequence) on a finite alphabet Σ of size σ. A fingerprint in s is the set of distinct characters appearing in one of its substrings. The problem considered here is to compute the set F of all fingerprints of all substrings of s in order to answer efficiently certain questions on this set. A substring si..sj is a maximal location for a fingerprint f ∈ F (denoted by i, j ) if the alphabet of si..sj is f and si−1, sj+1, if defined, are not in f . The set of maximal locations in s is L (it is easy to see that |L| ≤ nσ). Two maximal locations i, j and k, l such that si..sj = s k ..s l are named copies, and the quotient set of L according to the copy relation is denoted by LC .We first present new exact efficient algorithms and data structures for the following three problems: (1) to compute F;(2) given f as a set of distinct characters in Σ, to answer if f represents a fingerprint in F;(3) given f , to find all maximal locations of f in s. As well as in papers concerning succinct data structures, in the paper all space complexities are counted in bits. Problem 1 is solved either in O(n + |LC | log σ) worst-case time (in this paper all logarithms are intended as base two logarithms) using O((n + |LC | + |F| log σ) log n) bits of space, or in O(n + |L| log σ) randomized expected time using O((n + |F| log σ) log n) bits of space. Problem 2 is solved either in O(|f |) expected time if only O(|f | log n) bits of working space for queries is allowed, or in worst-case O(|f |/ ) time if a working space of O(σ log n) bits is allowed (with a constant satisfying 0 < < 1). These algorithms use a data structure that occupies |F|(2 log σ + log 2 e)(1 + o(1)) bits. Problem 3 is solved with the same time complexity as Problem 2, but with the addition of an occ term to each of the complexities, where occ is the number of maximal locations corresponding to the given fingerprint. Our solution of this last problem requires a data structure that occupies O((n + |LC |) log n) bits of memory.In the second part of our paper we present a novel Monte Carlo approximate construction approach. Problem 1 is thus solved in O(n + |L|) expected time using O(|F| log n) bits of space but the algorithm is incorrect with an extremely small probability that can be bounded in advance.1. In expected O(|s1|) time with high probability using only O(|s1| log σ) bits of space. 2. In worst case O(k|s1|) time using (σ 1/k log σ) bits of space.

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Section: Naming Techniquementioning

confidence: 99%

“…We now present the fingerprint trie (this is called backtracking tree in [3,4]). The fingerprint trie is a tree representation of the fingerprints.…”

Section: Fingerprint Triementioning

confidence: 99%

Section: Deterministic and Probabilistic Set Equality Testingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Various improvements to text fingerprinting

Belazzougui

Kolpakov

Raffinot

2013

Journal of Discrete Algorithms

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show abstract

“…To design our indexing structures and algorithms, we extend the definition of fingerprints (or sets of distinct characters), initially defined on sequences [2,6,7,12], to images. While classical pattern matching approaches on images have already been studied [3,1,4], this paper is the first (to our knowledge) to focus on the character sets.…”

Section: Introductionmentioning

confidence: 99%

Indexing and querying color sets of images

Belazzougui

Kolpakov

Raffinot

2016

Theoretical Computer Science

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We aim to study the set of color sets of continuous regions of an image given as a matrix of $m$ rows over $n\geq m$ columns where each element in the matrix is an integer from $[1,\sigma]$ named a {\em color}. The set of distinct colors in a region is called fingerprint. We aim to compute, index and query the fingerprints of all rectangular regions named rectangles. The set of all such fingerprints is denoted by ${\cal F}$. A rectangle is {\em maximal} if it is not contained in a greater rectangle with the same fingerprint. The set of all locations of maximal rectangles is denoted by $\mathcal{L}.$ We first explain how to determine all the $|\mathcal{L}|$ maximal locations with their fingerprints in expected time $O(nm^2\sigma)$ using a Monte Carlo algorithm (with polynomially small probability of error) or within deterministic $O(nm^2\sigma\log(\frac{|\mathcal{L}|}{nm^2}+2))$ time. We then show how to build a data structure which occupies $O(nm\log n+\mathcal{|L|})$ space such that a query which asks for all the maximal locations with a given fingerprint $f$ can be answered in time $O(|f|+\log\log n+k)$, where $k$ is the number of maximal locations with fingerprint $f$. If the query asks only for the presence of the fingerprint, then the space usage becomes $O(nm\log n+|{\cal F}|)$ while the query time becomes $O(|f|+\log\log n)$. We eventually consider the special case of squared regions (squares).Comment: 20 pages, 5 figure

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A Faster Query Algorithm for the Text Fingerprinting Problem

Cited by 2 publications

References 8 publications

Various improvements to text fingerprinting

Various improvements to text fingerprinting

Indexing and querying color sets of images

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