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.
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
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)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer Berlin Heidelberg
About this paper
Cite this paper
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
Download citation
DOI: https://doi.org/10.1007/978-3-540-69507-3_17
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-69506-6
Online ISBN: 978-3-540-69507-3
eBook Packages: Computer ScienceComputer Science (R0)