Window Subsequence Problems for Compressed Texts

Cegielski, Patrick; Guessarian, Irène; Lifshits, Yury; Matiyasevich, Yuri

doi:10.1007/11753728_15

Cited by 23 publications

(40 citation statements)

References 15 publications

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“…Finally, after the matrices A and E are recalculated, Baum-Welch updates the model parameters according to (10).…”

Section: Baum-welch Trainingmentioning

confidence: 99%

“…Note that this approach, denoted "acceleration by text-compression", has been recently applied to some classical problems on strings. Various compression schemes, such as LZ77, LZW-LZ78, Huffman coding, Byte Pair Encoding (BPE) and Run Length Encoding (RLE), were employed to accelerate exact string matching [19,24,31,22], subsequence matching [10], approximate pattern matching [1,18,20,28] and sequence alignment [3,4,9,15,23]. In light of the practical importance of HMM-based classification methods in state-of-the-art research, and in view of the fact that such techniques are also based on dynamic programming, we set out to answer the following question: can "acceleration by text compression" be applied to HMM decoding and training algorithms?…”

Section: Introductionmentioning

confidence: 99%

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Speeding Up HMM Decoding and Training by Exploiting Sequence Repetitions

Mozes

Weimann

Ziv-Ukelson

Combinatorial Pattern Matching

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Abstract. We present a method to speed up the dynamic program algorithms used for solving the HMM decoding and training problems for discrete time-independent HMMs. We discuss the application of our method to Viterbi's decoding and training algorithms [33], as well as to the forward-backward and BaumWelch [6] algorithms. Our approach is based on identifying repeated substrings in the observed input sequence. Initially, we show how to exploit repetitions of all sufficiently small substrings (this is similar to the Four Russians method). Then, we describe four algorithms based alternatively on run length encoding (RLE), Lempel-Ziv (LZ78) parsing, grammar-based compression (SLP), and byte pair encoding (BPE). Compared to Viterbi's algorithm, we achieve speedups of Θ(log n) using the Four Russians method, Ω( r log r ) using RLE, Ω( log n k ) using LZ78, Ω( r k ) using SLP, and Ω(r) using BPE, where k is the number of hidden states, n is the length of the observed sequence and r is its compression ratio (under each compression scheme). Our experimental results demonstrate that our new algorithms are indeed faster in practice. Furthermore, unlike Viterbi's algorithm, our algorithms are highly parallelizable.

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“…Finally, after the matrices A and E are recalculated, Baum-Welch updates the model parameters according to (10).…”

Section: Baum-welch Trainingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Speeding Up HMM Decoding and Training by Exploiting Sequence Repetitions

Mozes

Weimann

Ziv-Ukelson

Combinatorial Pattern Matching

View full text Add to dashboard Cite

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“…The minimal-window, fixed-window and bounded minimal-window subsequence recognition problems for a GC-text against a plain pattern have been considered by Cégielski et al [24]. They gave algorithms that run in time O(m 2 log m ·n + output) for the reporting versions, and O(m 2 log m ·n) for the counting versions of the problems.…”

Section: Local Subsequence Recognitionmentioning

confidence: 99%

Semi-local String Comparison: Algorithmic Techniques and Applications

Tiskin

2008

Math.comput.sci.

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The longest common subsequence (LCS) problem is a classical problem in computer science. The semi-local LCS problem is a generalisation of the LCS problem, arising naturally in the context of string comparison. In this work, we present a number of algorithmic techniques related to the semi-local LCS problem, and give a number of algorithmic applications of these techniques. Summarising the presented results, we conclude that semilocal string comparison turns out to be a useful algorithmic plug-in, which unifies, and often improves on, a number of previous approaches to various substring-and subsequence-related problems.

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“…Algorithms for finding an explicitly given pattern in a compressed texts were the first results in the field [1,6]. Next, polynomial algorithms for regular expression matching [19], approximate pattern matching [11] and subsequence matching [5] were constructed for SLP-generated texts. Encouraging experimental results are reported in [20].…”

Section: Introductionmentioning

confidence: 99%

Processing Compressed Texts: A Tractability Border

Lifshits

Combinatorial Pattern Matching

Self Cite

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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Window Subsequence Problems for Compressed Texts

Cited by 23 publications

References 15 publications

Speeding Up HMM Decoding and Training by Exploiting Sequence Repetitions

Speeding Up HMM Decoding and Training by Exploiting Sequence Repetitions

Semi-local String Comparison: Algorithmic Techniques and Applications

Processing Compressed Texts: A Tractability Border

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