Linear-time computation of prefix table for weighted strings &amp; applications

Barton, Carl; Liu, Chang; Pissis, Solon P.

doi:10.1016/j.tcs.2016.04.029

Cited by 8 publications

(4 citation statements)

References 26 publications

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“…We give an algorithm for the WSCS problem with pseudo-polynomial running time that depends polynomially on n and z. Note that such algorithms have already been proposed for several problems on weighted strings: pattern matching [9,12,21,24], indexing [3,8,7,11], and finding regularities [10]. In contrast, we show that no such algorithm is likely to exist for the WLCS problem.…”

Section: Our Resultsmentioning

confidence: 97%

Weighted Shortest Common Supersequence Problem Revisited

Charalampopoulos

Kociumaka

Pissis

et al. 2019

Lecture Notes in Computer Science

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A weighted string, also known as a position weight matrix, is a sequence of probability distributions over some alphabet. We revisit the Weighted Shortest Common Supersequence (WSCS) problem, introduced by Amir et al. [SPIRE 2011], that is, the SCS problem on weighted strings. In the WSCS problem, we are given two weighted strings W 1 and W 2 and a threshold 1 z on probability, and we are asked to compute the shortest (standard) string S such that both W 1 and W 2 match subsequences of S (not necessarily the same) with probability at least 1 z . Amir et al. showed that this problem is NP-complete if the probabilities, including the threshold 1 z , are represented by their logarithms (encoded in binary).We present an algorithm that solves the WSCS problem for two weighted strings of length n over a constant-sized alphabet in O(n 2 √ z log z) time. Notably, our upper bound matches known conditional lower bounds stating that the WSCS problem cannot be solved in O(n 2−ε ) time or in O * (z 0.5−ε ) time 1 unless there is a breakthrough improving upon long-standing upper bounds for fundamental NP-hard problems (CNF-SAT and Subset Sum, respectively).We also discover a fundamental difference between the WSCS problem and the Weighted Longest Common Subsequence (WLCS) problem, introduced by Amir et al. [JDA 2010]. We show that the WLCS problem cannot be solved in O(n f (z) ) time, for any function f (z), unless P = NP.

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Section: Our Resultsmentioning

confidence: 97%

Weighted Shortest Common Supersequence Problem Revisited

Charalampopoulos

Kociumaka

Pissis

et al. 2019

Lecture Notes in Computer Science

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“…X [2] X [3] X [4] MATCHING problem works in O(nm + mσ ) time. A broad spectrum of heuristics improving this algorithm in practice is known; for a survey, see [22].…”

Section: X[1]mentioning

confidence: 99%

Pattern Matching and Consensus Problems on Weighted Sequences and Profiles

2018

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We study pattern matching problems on two major representations of uncertain sequences used in molecular biology: weighted sequences (also known as position weight matrices, PWM) and profiles (scoring matrices). In the simple version, in which only the pattern or only the text is uncertain, we obtain efficient algorithms with theoretically-provable running times using a variation of the lookahead scoring technique. We also consider a general variant of the pattern matching problems in which both the pattern and the text are uncertain. Central to our solution is a special case where the sequences have equal length, called the consensus problem. We propose algorithms for the consensus problem parameterised by the number of strings that match one of the sequences. As our basic approach, a careful adaptation of the classic meet-in-the-middle algorithm for the knapsack problem is used. On the lower bound side, we prove that our dependence on the parameter is optimal up to lower-order terms conditioned on the optimality of the original algorithm for the knapsack problem. Therefore, we make an effort to keep the lower order terms of the complexities of our algorithms as small as possible.

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“…The symmetric variant of the Weighted Pattern Matching problem, when only the pattern is weighted, is closely related to the problem of profile matching [21] and admits O(n log n)-time and O(n log z)-time solutions as well. Finally, the variant when both the text and the pattern are weighted was introduced in [4], where an O(nz 2 log z)-time solution was presented. Later a more efficient O(n √ z log log z)-time solution was devised in [20].…”

Section: Introductionmentioning

confidence: 99%

Streaming k-mismatch with error correcting and applications

Radoszewski

Starikovskaya

2020

Information and Computation

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We present a new streaming algorithm for the k-Mismatch problem, one of the most basic problems in pattern matching. Given a pattern and a text, the task is to find all substrings of the text that are at the Hamming distance at most k from the pattern. Our algorithm is enhanced with an important new feature called Error Correcting, and its complexities for k = 1 and for a general k are comparable to those of the solutions for the k-Mismatch problem by Porat and Porat (FOCS 2009) and Clifford et al. (SODA 2016). In parallel to our research, a yet more efficient algorithm for the k-Mismatch problem with the Error Correcting feature was developed by Clifford et al. (SODA 2019). Using the new feature and recent work on streaming Multiple Pattern Matching we develop a series of streaming algorithms for pattern matching on weighted strings, which are a commonly used representation of uncertain sequences in molecular biology. We also show that these algorithms are space-optimal up to polylog factors.A preliminary version of this work was published at DCC 2017 conference [24].

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Linear-time computation of prefix table for weighted strings & applications

Cited by 8 publications

References 26 publications

Weighted Shortest Common Supersequence Problem Revisited

Weighted Shortest Common Supersequence Problem Revisited

Pattern Matching and Consensus Problems on Weighted Sequences and Profiles

Streaming k-mismatch with error correcting and applications

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