We consider two content-based music retrieval problems where the music is modeled as sets of points in the Euclidean plane, formed by the (on-set time, pitch) pairs. We introduce fast filtering methods based on indexing the underlying database. The filters run in a sublinear time in the length of the database, and they are lossless if a quadratic space may be used. By taking into account the application, the search space can be narrowed down, obtaining practically lossless filters using linear size index structures. For the checking phase, which dominates the overall running time, we exploit previously designed algorithms suitable for local checking. In our experiments on a music database, our best filter-based methods performed several orders of a magnitude faster than previous solutions.

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, |M|α}) 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, bit-parallelism, sparse dynamic programming 1