Algorithms for Transposition Invariant String Matching

Restricted Transposition Invariant Approximate String Matching Under Edit Distance

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 in...

Transposition invariant string matching

Given strings A = a1a2 . . . am and B = b1b2 . . . bn over an alphabet Σ ⊆ U, where U 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, the transposition invariant distance is mint∈U{d(A+ t,B)}, where A+ t = (a1 + t)(a2 + t) . . . (am + t). We study the problem of computing the transpo...

Speeding up transposition-invariant 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, transposition-invariant 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) . . ....

Searching Monophonic Patterns within Polyphonic Sources

The string matching problem for strings in which one should find the occurrences of a pattern string within a text, is well-studied in the past literature. The problem can be solved efficiently, e.g., by using so-called bit-parallel algorithms. We adapt the bit-parallel approach to music information retrieval. We consider a situation where the pattern is monophonic and the text (the musical sou...

Algorithms for Transposition Invariant String Mat hing ( Extended