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Efficient algorithms for pattern matching with general gaps
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SOLVING THE (δ, α)APPROXIMATE MATCHING PROBLEM UNDER TRANSPOSITION INVARIANCE IN MUSICAL SEQUENCES
"... The δapproximate matching problem arises in many questions concerning musical information retrieval and musical analysis. In the case in which gaps are not allowed between consecutive pitches of the melody, transposition invariance is automatically taken care of, provided that the musical melodies ..."
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The δapproximate matching problem arises in many questions concerning musical information retrieval and musical analysis. In the case in which gaps are not allowed between consecutive pitches of the melody, transposition invariance is automatically taken care of, provided that the musical melodies are encoded using the pitch interval encoding. However, in the case in which nonnull gaps are allowed between consecutive pitches of the melodies, transposition invariance is not dealt with properly by the algorithms present in literature. In this paper, we propose two slightly different variants of the approximate matching problem under transposition invariance and for each of them provide an algorithm, obtained by adapting an efficient algorithm for the δapproximate matching problem with αbounded gaps.
Efficient algorithms for (δ, γ, α)matching
"... Abstract. We propose new algorithms for (δ, γ, α)matching. In this string matching problem we are given a pattern P = p0p1... pm−1 and a text T = t0t1... tn−1 over some integer alphabet Σ = {0... σ − 1}. The pattern symbol pi matches the text symbol tj iff pi − tj  ≤ δ. The pattern P (δ, γ)match ..."
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Abstract. We propose new algorithms for (δ, γ, α)matching. In this string matching problem we are given a pattern P = p0p1... pm−1 and a text T = t0t1... tn−1 over some integer alphabet Σ = {0... σ − 1}. The pattern symbol pi matches the text symbol tj iff pi − tj  ≤ δ. The pattern P (δ, γ)matches some text substring tj... tj+m−1 iff for all i it holds that pi − tj+i  ≤ δ and�pi − tj+i  ≤ γ. Finally, in (δ, γ, α)matching we also permit at most α length gaps (text substrings) between each matching text symbol. The only known previous algorithm runs in O(mn) time. We give several algorithms that improve the average case up to O(n) for small α, and the worst case to O(min{mn, Mα}) or O(mn log γ/w), where M = {(i, j)  pi − tj  ≤ δ} and w is the number of bits in a machine word. We conclude with experimental results showing that the algorithms are very efficient in practice. Key words: approximate string matching, music information retrieval, bitparallelism, sparse dynamic programming 1
V.: A survey of querybyhumming similarity methods
 In: Conf. on Pervasive Technologies Related to Assistive Environments (PETRA
, 2012
"... Performing similarity search in large databases is a problem of particular interest in many communities, such as music, database, and data mining. Although several solutions have been proposed in the literature that perform well in many application domains, there is no best method to solve this kind ..."
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Performing similarity search in large databases is a problem of particular interest in many communities, such as music, database, and data mining. Although several solutions have been proposed in the literature that perform well in many application domains, there is no best method to solve this kind of problem in a QueryByHumming (QBH) application. In QBH the goal is to find the song(s) most similar to a hummed query in an efficient manner. In this paper, we focus on providing a brief overview of the representations to encode music pieces, and also on the methods that have been proposed for QBH or other similarly defined problems.
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"... global manuscript No. (will be inserted by the editor) Efficient algorithms for pattern matching with general gaps, ..."
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global manuscript No. (will be inserted by the editor) Efficient algorithms for pattern matching with general gaps,
ICNAAM header will be provided by the publisher Simple Algorithm for PatternMatching with Bounded Gaps in Genomic Sequences
, 2005
"... Key words Approximate pattern matching, matching with gaps, information retrieval. ..."
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Key words Approximate pattern matching, matching with gaps, information retrieval.
Transposition invariant string matching ✩
"... Given strings A = a1a2...am and B = b1b2...bn over an alphabet Σ ⊆ U, whereU is some numerical universe closed under addition and subtraction, and a distance function d(A,B) that gives the score of the best (partial) matching of A and B, thetransposition invariant distance is ..."
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Given strings A = a1a2...am and B = b1b2...bn over an alphabet Σ ⊆ U, whereU is some numerical universe closed under addition and subtraction, and a distance function d(A,B) that gives the score of the best (partial) matching of A and B, thetransposition invariant distance is
On Tuning The (, )SequentialSampling Algorithm For
 In Proceedings of ISMIR’05
, 2005
"... We present a very efficient variant of the (#, #) SEQUENTIALSAMPLING algorithm, recently introduced by the authors, for the #approximate string matching problem with #bounded gaps, which often arises in many questions on musical information retrieval and musical analysis. ..."
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We present a very efficient variant of the (#, #) SEQUENTIALSAMPLING algorithm, recently introduced by the authors, for the #approximate string matching problem with #bounded gaps, which often arises in many questions on musical information retrieval and musical analysis.
International Journal of Foundations of Computer Science c ○ World Scientific Publishing Company FLEXIBLE MUSIC RETRIEVAL IN SUBLINEAR TIME
"... Communicated by Editor’s name Music sequences can be treated as texts in order to perform music retrieval tasks on them. However, the text search problems that result from this modeling are unique to music retrieval. Up to date, several approaches derived from classical string matching have been pro ..."
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Communicated by Editor’s name Music sequences can be treated as texts in order to perform music retrieval tasks on them. However, the text search problems that result from this modeling are unique to music retrieval. Up to date, several approaches derived from classical string matching have been proposed to cope with the new search problems, yet each problem had its own algorithms. In this paper we show that a technique recently developed for multipattern approximate string matching is flexible enough to be successfully extended to solve many different music retrieval problems, as well as combinations thereof not addressed before. We show that the resulting algorithms are averageoptimal in many cases and close to averageoptimal otherwise. Empirically, they are much better than existing approaches in many practical cases.
New Upper Bounds on Various String Manipulation Problems
"... In this chapter we deal with various string manipulation problems which originate from the field of computational biology and musicology. ..."
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In this chapter we deal with various string manipulation problems which originate from the field of computational biology and musicology.