Fully compressed pattern matching algorithm for balanced straight-line programs

Hirao, Masahiro; Shinohara, Ayumi; Takeda, Masayuki; Arikawa, Setsuo

doi:10.1109/spire.2000.878188

Cited by 5 publications

(6 citation statements)

References 8 publications

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“…Finally, in 1997 Miyazaki, Shinohara and Takeda [18] constructed new O(n 2 m 2 ) algorithm for FCPM, where m and n are the sizes of SLPs that generate P and T , correspondingly. In 2000 for one quite special class of SLP the FCPM problem was solved in time O(mn) [10]. Nevertheless, nothing was known about complexity of compressed Hamming distance problem.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Introductionmentioning

confidence: 99%

“…As before, m and n are sizes of SLPs generating P and T , correspondingly. This algorithm is not just an improvement over previous ones [8,10,12,18,22] but is also simpler than they are. Next, we prove #P-completeness of computing Hamming distance between compressed texts in Section 4.…”

Section: Introductionmentioning

confidence: 99%

Processing Compressed Texts: A Tractability Border

Lifshits

Combinatorial Pattern Matching

121

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“…are known for various practically used compression methods (LZ, LZW, their variants, etc.) [4,5,6,7,8,9,10,11,24].…”

Section: Introductionmentioning

confidence: 99%

“…In 1997 Miyazaki et al [22] constructed O(n 2 m 2 ) algorithm for FCPM. A faster O(mn) algorithm for a special sub-case (restricting the form of SLPs) was given in 2000 by Hirao et al [11]. Finally, in 2007, a state of the art O(mn 2 ) algorithm was given by Lifshits [19].…”

Section: Introductionmentioning

confidence: 99%

Faster Fully Compressed Pattern Matching by Recompression

Jeż

2015

ACM Trans. Algorithms

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Abstract. In this paper, a fully compressed pattern matching problem is studied. The compression is represented by straight-line programs (SLPs), i.e. a context-free grammars generating exactly one string; the term fully means that both the pattern and the text are given in the compressed form. The problem is approached using a recently developed technique of local recompression: the SLPs are refactored, so that substrings of the pattern and text are encoded in both SLPs in the same way. To this end, the SLPs are locally decompressed and then recompressed in a uniform way.This technique yields an O((n + m) log M ) algorithm for compressed pattern matching, assuming that M fits in O(1) machine words, where n (m) is the size of the compressed representation of the text (pattern, respectively), while M is the size of the decompressed pattern. If only m + n fits in O(1) machine words, the running time increases to O((n + m) log M log(n + m)). The previous best algorithm due to Lifshits had O(n 2 m) running time.

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“…composition systems, which are extensions of SLPs where a non-terminal can derive the concatenation of a suffix and prefix, respectively, of two other non-terminals. Recently, Matsubara, Inenaga, and Shinohara [11] solved the problem for balanced straight-line programs (BSLPs) [5]. BSLPs are essentially SLPs but with a strict condition: the derivation tree rooted at each non-terminal must be a perfect binary tree (except for the non-terminal deriving the whole string, which has a special form so that the length of the string need not be a power of 2).…”

Section: Introductionmentioning

confidence: 99%