Abstract
The point set pattern matching problem is, given two sets “pattern” and “text” of points in Euclidean space, to find a linear transformation that maps the pattern to a subset of the text. We introduce an approximate point set pattern matching for axis-sorted point sequences that allows a translation, space insertions and deletions between points. We present an approximate pattern matching algorithm that runs with pattern size n and text size m in O(nm 2) time in general, and in O(nm) time if distances between two contiguous points in texts and patterns are finite. A variant of the four-Russian technique achieving O(nm/log n + n log n) time is also provided. Furthermore, as a natural extension we present an approximate point set pattern matching on the plane, and give a polynomial-time algorithm that solves this problem.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Akutsu, T., Kanaya, K., Ohyama, A., Fujiyama, A.: Matching of spots in 2D electrophoresis images. Point matching under non-uniform distortions. In: Crochemore, M., Paterson, M. (eds.) CPM 1999. LNCS, vol. 1645, pp. 212–222. Springer, Heidelberg (1999)
Arlazarov, V.L., Dinic, E.A., Kronrod, M.A., Faradzev, I.A.: On economic construction of the transitive closure of a directed graph. Dokl. Acad. Nauk SSSR 194, 487–488 (1970)
Gusfield, D.: Algorithms on strings, trees, and sequences computer science and computational biology. Cambridge University Press, Cambridge (1997)
Hoffmann, F., Kriegel, K., Wenk, C.: Matching 2D patterns of protein spots. In: Proc. 14th ACM Symposium on Computational Geometry, pp. 231–239 (1998)
Jokisch, S., Müller, H.: Inter-point-distance-dependent approximate point set matching, Research Report No. 653, Dept. of Computer Science, University of Dortmund (1997)
Kadota, T., Hirao, M., Ishino, A., Takeda, M., Shinohara, A., Matsuo, F.: Musical sequence comparison for melodic and rhythmic similarities. In: Proc. 8th String Processing and Information Retrieval, pp. 111–122 (2001)
Lemström, K., Mäkinen, V.: On minimizing pattern splitting in multi-track string matching. In: Proc. 14th Annual Symposium on Combinatorial Pattern Matching, vol.2672. LNCS, pp. 237–253 (2003)
Mäkinen, V.: Using edit distance in point-pattern matching. In: Proc. 8th String Processing and Information Retrieval, pp. 153–161 (2001)
Mäkinen, V.: Parameterized approximate string matching and local-similaritybased point-pattern-matching, Ph.D. thesis, Report A–2003–6, Dept. of Computer Science, Univ. Helsinki (August 2003)
Mäkinen, V., Navarro, G., Ukkonen, E.: Algorithms for transposition invariant string matching. In: Alt, H., Habib, M. (eds.) STACS 2003. LNCS, vol. 2607, pp. 191–202. Springer, Heidelberg (2003)
Mäkinen, V., Ukkonen, E.: Local similarity based point-pattern matching. In: Apostolico, A., Takeda, M. (eds.) CPM 2002. LNCS, vol. 2373, pp. 115–132. Springer, Heidelberg (2002)
Meredith, D., Wiggins, G., Lemström, K.: Pattern induction and matching in polyphonic music and other multi-dimensional databasets. In: Proc. 5th World Multi-Conference on Systems, Cybernetics and Informatics, vol. X, pp. 61–66 (2001)
Mongeau, M., Sankoff, D.: Comparison of musical sequences. Computers and the Humanities 24(3), 161–175 (1990)
de Rezende, P.J., Lee, D.T.: Point set pattern matching in d-dimensions. Algorithmica 13(4), 387–404 (1995)
Ukkonen, E., Lemström, K., Mäkinen, V.: Geometric algorithms for transposition invariant content-based music retrieval. In: Proc. International Symposium on Music Information Retrieval, pp. 193–199 (2003)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Suga, T., Shimozono, S. (2004). Approximate Point Set Pattern Matching on Sequences and Planes. In: Sahinalp, S.C., Muthukrishnan, S., Dogrusoz, U. (eds) Combinatorial Pattern Matching. CPM 2004. Lecture Notes in Computer Science, vol 3109. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-27801-6_7
Download citation
DOI: https://doi.org/10.1007/978-3-540-27801-6_7
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-22341-2
Online ISBN: 978-3-540-27801-6
eBook Packages: Springer Book Archive