Optimal superprimitivity testing for strings

Apostolico, Alberto; Farach, Martin; Iliopoulos, Costas S.

doi:10.1016/0020-0190(91)90056-n

Cited by 89 publications

(66 citation statements)

References 3 publications

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“…The first one, by Apostolico et al [4], is a linear-time procedure finding the shortest cover of a word. Moore and Smyth [5,6] showed that all covers can be determined in the same time complexity.…”

Section: Introductionmentioning

confidence: 99%

Efficient algorithms for shortest partial seeds in words

Kociumaka

Pissis

Radoszewski

et al. 2018

Theoretical Computer Science

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A factor u of a word w is a cover of w if every position in w lies within some occurrence of u in w. A factor u is a seed of w if it is a cover of a superstring of w. Covers and seeds extend the classical notions of periodicity. We introduce a new notion of α-partial seed, that is, a factor covering as a seed at least α positions in a given word. We use the Cover Suffix Tree, recently introduced in the context of α-partial covers (Kociumaka et al., Algorithmica, 2015); an O(n log n)-time algorithm constructing such a tree is known. However, it appears that partial seeds are more complicated than partial covers-our algorithms require algebraic manipulations of special functions related to edges of the modified Cover Suffix Tree and the border array. We present a procedure for computing shortest α-partial seeds that works in O(n) time if the Cover Suffix Tree is already given. This is a full version, which includes all the proofs, of a paper that appeared at CPM 2014 [1].

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Section: Introductionmentioning

confidence: 99%

Efficient algorithms for shortest partial seeds in words

Kociumaka

Pissis

Radoszewski

et al. 2018

Theoretical Computer Science

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“…A period of string T is a string W (and also an integer |W |) such that T is a prefix of W k for some integer k. A cover (notion originated from [3]) of a string T is a string C such that any character in T is covered by some occurrence of C in T . Problem of compressed periods/covers: given a compressed string T , find the length of minimal period/cover and compute a "compressed" representation of all periods/covers.…”

Section: Consequences and Open Problemsmentioning

confidence: 99%

Processing Compressed Texts: A Tractability Border

Lifshits

Combinatorial Pattern Matching

121

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Abstract. What kind of operations can we perform effectively (without full unpacking) with compressed texts? In this paper we consider three fundamental problems: (1) check the equality of two compressed texts, (2) check whether one compressed text is a substring of another compressed text, and (3) compute the number of different symbols (Hamming distance) between two compressed texts of the same length. We present an algorithm that solves the first problem in O(n 3 ) time and the second problem in O(n 2 m) time. Here n is the size of compressed representation (we consider representations by straight-line programs) of the text and m is the size of compressed representation of the pattern. Next, we prove that the third problem is actually #P-complete. Thus, we indicate a pair of similar problems (equivalence checking, Hamming distance computation) that have radically different complexity on compressed texts. Our algorithmic technique used for problems (1) and (2) helps for computing minimal periods and covers of compressed texts.

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“…This minimal cover is of course the cover of x of minimum length. A recent paper by Apostolico et al 3] computes the minimal cover of x in linear time and space, while another by Breslauer 5] determines, also in linear space and time, whether or not a proper cover of x exists. The algorithm described in the next section computes solutions to both of these problems as byproducts of the computation of all the covers of x.…”

Section: A Characterization Of Coversmentioning

confidence: 99%

An optimal algorithm to compute all the covers of a string

Moore

Smyth

1994

Information Processing Letters

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Let x denote a given nonempty string of length n = jxj 1. A string u is a cover of x if and only if every position of x lies within an occurrence of u within x. Thus x is always a cover of itself. In this paper we c haracterize all the covers of x in terms of an easily computed normal form for x. T h e c haracterization theorem then gives rise to a simple recursive algorithm which computes all the covers of x in time (n).

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Optimal superprimitivity testing for strings

Cited by 89 publications

References 3 publications

Efficient algorithms for shortest partial seeds in words

Efficient algorithms for shortest partial seeds in words

Processing Compressed Texts: A Tractability Border

An optimal algorithm to compute all the covers of a string

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