Abstract
We investigate randomised algorithms for subset matching with spatial point sets—given two sets of d-dimensional points: a data set T consisting of n points and a pattern P consisting of m points, find the largest match for a subset of the pattern in the data set. This problem is known to be 3-SUM hard and so unlikely to be solvable exactly in subquadratic time. We present an efficient bit-parallel O(nm) time algorithm and an O(nlogm) time solution based on correlation calculations using fast Fourier transforms. Both methods are shown experimentally to give answers within a few percent of the exact solution and provide a considerable practical speedup over existing deterministic algorithms.
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References
Cardoze, D.E., Schulman, L.J.: Pattern Matching for Spatial Point Sets. In: IEEE Symposium on Foundations of Computer Science, pp. 156–165 (1998)
Clifford, R., Christodoulakis, M., Crawford, T., Meredith, D., Wiggins, G.: A Fast, Randomised, Maximal Subset Matching Algorithm for Document-Level Music Retrieval. In: Proceedings of the 7th International Conference on Music Information Retrieval (ISMIR ’06), to appear (2006)
Cole, R., Hariharan, R.: Verifying Candidate Matches in Sparse and Wildcard Matching. In: Proceedings of the Annual ACM Symposium on Theory of Computing, pp. 592–601 (2002)
Cormen, T.H., Leiserson, C.E., Rivest, R.L.: Introduction to Algorithms. MIT Press, Cambridge (1990)
Frigo, M., Johnson, S.G.: The Design and Implementation of FFTW3. Proceedings of the IEEE (Special issue on Program Generation, Optimization, and Platform Adaptation) 93, 216–231 (2005)
Meredith, D., Lemström, K., Wiggins, G.A.: Algorithms for Discovering Repeated Patterns in Multidimensional Representations of Polyphonic Music. Journal of New Music Research 31(4), 321–345 (2002)
Ukkonen, E., Lemström, K., Mäkinen, V.: Geometric Algorithms for Transposition Invariant Content–Based Music Retrieval. In: Proceedings of the 4th International Conference on Music Information Retrieval (ISMIR ’03), pp. 193–199. Johns Hopkins University (2003)
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Clifford, R., Sach, B. (2007). Fast Approximate Point Set Matching for Information Retrieval. In: van Leeuwen, J., Italiano, G.F., van der Hoek, W., Meinel, C., Sack, H., Plášil, F. (eds) SOFSEM 2007: Theory and Practice of Computer Science. SOFSEM 2007. Lecture Notes in Computer Science, vol 4362. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-69507-3_17
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DOI: https://doi.org/10.1007/978-3-540-69507-3_17
Publisher Name: Springer, Berlin, Heidelberg
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