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Flexible music retrieval in sublinear time
 IN PROC. 10TH PRAGUE STRINGOLOGY CONFERENCE (PSC'05)
, 2005
"... 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 s ..."
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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 close to optimal and much better than existing approaches in many practical cases.
Speeding up TranspositionInvariant String Matching
"... Finding the longest common subsequence (LCS) of two given sequences A = a0a1... am−1 and B = b0b1... bn−1 is an important and well studied problem. We consider its generalization, transpositioninvariant LCS (LCTS), which has recently arisen in the field of music information retrieval. In LCTS, we l ..."
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Finding the longest common subsequence (LCS) of two given sequences A = a0a1... am−1 and B = b0b1... bn−1 is an important and well studied problem. We consider its generalization, transpositioninvariant LCS (LCTS), which has recently arisen in the field of music information retrieval. In LCTS, we look for the longest common subsequence between the sequences A + t = (a0 + t)(a1 + t)... (am−1 + t), and B where t is some integer. This means that shifting all the symbols in the A sequence by some value is allowed. We present two new algorithms, matching the currently best known complexity O(mn log log σ), where σ is the alphabet size. Then, we show in the experiments that our algorithms outperform the best ones from literature. Key words: longest transposition invariant common subsequence, LCS, music information retrieval, transposition invariance 1
Improved Time and Space Complexities for Transposition Invariant String Matching
, 2004
"... Given strings A = a1a2...am and B = b1b2...bn over a finite alphabet Σ ⊂ Z of size O(σ), and a distance d() defined among strings, the transposition invariant version of d() is d t (A,B) = mint∈Z d(A+t,B), where A+t = (a1+t)(a2+t)...(am+t). Distances d() of most interest are Levenshtein distance an ..."
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Given strings A = a1a2...am and B = b1b2...bn over a finite alphabet Σ ⊂ Z of size O(σ), and a distance d() defined among strings, the transposition invariant version of d() is d t (A,B) = mint∈Z d(A+t,B), where A+t = (a1+t)(a2+t)...(am+t). Distances d() of most interest are Levenshtein distance and indel distance (the dual of the Longest Common Subsequence), which can be computed in O(mn) time. Recent algorithms compute d t (A,B) in O(mn log log min(m,n)) time for those distances. In this paper we show how those complexities can be reduced to O(mn log log σ). Furthermore, we reduce the space requirements from O(mn) to O(σ 2 + min(m,n)).
A.: An O(1) solution to the prefix sum problem on a specialized memory architecture
 In: IFIP TCS
, 2006
"... Abstract. In this paper we study the Prefix Sum problem introduced by Fredman. We show that it is possible to perform both update and retrieval in O(1) time simultaneously under a memory model in which individual bits may be shared by several words. We also show that two variants (generalizations) ..."
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Abstract. In this paper we study the Prefix Sum problem introduced by Fredman. We show that it is possible to perform both update and retrieval in O(1) time simultaneously under a memory model in which individual bits may be shared by several words. We also show that two variants (generalizations) of the problem can be solved optimally in Θ(lg N ) time under the comparison based model of computation.
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.
International Journal of Foundations of Computer Science cfl World Scientific Publishing Company
"... Received (received date) Revised (revised date) Communicated by Editor's name ABSTRACT 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 a ..."
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Received (received date) Revised (revised date) Communicated by Editor's name ABSTRACT 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.
Restricted Transposition Invariant Approximate String Matching Under Edit Distance
"... Abstract. Let A and B be strings with lengths m and n, respectively, over a finite integer alphabet. Two classic string mathing problems are computing the edit distance between A and B, and searching for approximate occurrences of A inside B. We consider the classic Levenshtein distance, but the dis ..."
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Abstract. Let A and B be strings with lengths m and n, respectively, over a finite integer alphabet. Two classic string mathing problems are computing the edit distance between A and B, and searching for approximate occurrences of A inside B. We consider the classic Levenshtein distance, but the discussion is applicable also to indel distance. A relatively new variant [8] of string matching, motivated initially by the nature of string matching in music, is to allow transposition invariance for A. This means allowing A to be “shifted ” by adding some fixed integer t to the values of all its characters: the underlying string matching task must then consider all possible values of t. Mäkinen et al. [12, 13] have recently proposed O(mn log log m) and O(dn log log m) algorithms for transposition invariant edit distance computation, where d is the transposition invariant distance between A and B, and an O(mn log log m) algorithm for transposition invariant approximate string matching. In this paper we first propose a scheme to construct transposition invariant algorithms that depend on d or k. Then we proceed to give an O(n + d 3) algorithm for transposition invariant edit distance, and an O(k 2 n) algorithm for transposition invariant approximate string matching. 1
On Data Structures and Memory Models
, 2006
"... In this thesis we study the limitations of data structures and how they can be overcome through careful consideration of the used memory models. The word RAM model represents the memory as a finite set of registers consisting of a constant number of unique bits. From a hardware point of view it is n ..."
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In this thesis we study the limitations of data structures and how they can be overcome through careful consideration of the used memory models. The word RAM model represents the memory as a finite set of registers consisting of a constant number of unique bits. From a hardware point of view it is not necessary to arrange the memory as in the word RAM memory model. However, it is the arrangement used in computer hardware today. Registers may in fact share bits, or overlap their bytes, as in the RAM with Byte Overlap (RAMBO) model. This actually means that a physical bit can appear in several registers or even in several positions within one register. The RAMBO model of computation gives us a huge variety of memory topologies/models depending on the appearance sets of the bits. We show that it is feasible to implement, in hardware, other memory models than the word RAM memory model. We do this by implementing a RAMBO variant on a memory board for the PC100 memory bus. When alternative
O(mn log σ) Time Transposition Invariant LCS Computation
"... Abstract. Given strings A and B of lengths m and n over a finite alphabet Σ ⊂ Z of size O(σ), the length of the longest common transposition invariant subsequence is LCTS(A, B) = maxt∈Z{LCS(A +t, B)}, where A + t = (a1 + t)(a2 + t)...(am + t) and LCS(A + t, B) is the length of the longest common su ..."
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Abstract. Given strings A and B of lengths m and n over a finite alphabet Σ ⊂ Z of size O(σ), the length of the longest common transposition invariant subsequence is LCTS(A, B) = maxt∈Z{LCS(A +t, B)}, where A + t = (a1 + t)(a2 + t)...(am + t) and LCS(A + t, B) is the length of the longest common subsequence between A + t and B. LCTS(A, B) can be computed naively in O(mn σ) time. We present a simple and easy to implement algorithm obtaining O(mnlog σ) time. We also show that transposition invariant Levenshtein distance can be computed in O(mn √ σ) time. 1