Abstract
The largest common point set problem (LCP) is, given two point set P and Q in d-dimensional Euclidean space, to find a subset of P with the maximum cardinality that is congruent to some subset of Q. We consider a special case of LCP in which the size of the largest common point set is at least (|P|+|Q|–k)/2. We develop efficient algorithms for this special case of LCP and a related problem. In particular, we present an O(k 3 n 1.34 + kn 2 log n) time algorithm for LCP in two dimensions, which is much better for small k than an existing O(n 3.2 log n) time algorithm, where n = max {|P|,|Q|}.
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References
Akutsu, T.: Approximate String Matching with Don’t Care Characters. Information Processing Letters 55, 235–239 (1995)
Akutsu, T.: On Determining the Congruence of Point Sets in d Dimensions. Computational Geometry, Theory and Applications 9, 247–256 (1998)
Akutsu, T., Tamaki, H., Tokuyama, T.: Distribution of Distances and Triangles in a Point Set and Algorithms for Computing the Largest Common Point Sets. Discrete and Computational Geometry 20, 307–331 (1998)
Alt, H., Melhorn, K., Wagener, H., Welzl, E.: Congruence, Similarity, and Symmetrics of Geometric Objects. Discrete and Computational Geometry 3, 237–256 (1988)
Amir, A., Farach, M.: Efficient 2-Dimensional Approximate Matching of Half- Rectangular Figures. Information and Computation 118, 1–11 (1995)
Atkinson, M.D.: An Optimal Algorithm for Geometrical Congruence. J. Algorithms 8, 159–172 (1987)
Cardoze, D.E., Schulman, L.J.: Pattern Matching for Spatial Point Sets. In: Proc. 38th Symp. Foundations of Computer Science, pp. 156–165 (1998)
Clarkson, K., Edelsbrunner, H., Guibas, L., Sharir, M., Welzl, E.: Combinatorial Complexity Bounds for Arrangements of Curves and Spheres. Discrete and Computational Geometry 5, 99–160 (1990)
Crochemore, M., Rytter, W.: Jewels of Stringology. World Scientific, Singapore (2002)
Highnam, P.T.: Optimal Algorithms for Finding the Symmetries of a Planar Point Set. Information Processing Letters 18, 219–222 (1986)
Indyk, P., Venketasubramanian, S.: Approximate Congruence in Nearly Linear Time. Computational Geometry, Theory and Applications 24, 115–128 (2003)
Landau, G.M., Vishkin, U.: Fast Parallel and Serial Approximate String Matching. J. Algorithms 10, 157–169 (1989)
Manacher, G.: An Application of Pattern Matching to a Problem in Geometrical Complexity. Information Processing Letters 5, 6–7 (1976)
McCright, E.M.: A Space-Economical Suffix Tree Construction Algorithm. J. ACM 23, 262–272 (1976)
Schieber, B., Vishkin, U.: On Finding Lowest Common Ancestors: Simplification and Parallelization. SIAM J. Computing 17, 1253–1262 (1988)
Székely, L.: Crossing Numbers and Hard Erdös Problems in Discrete Geometry. Combinatorics, Probability and Computing 6, 353–358 (1997)
Szemerédi, E., Trotter, W.T.: Extremal Problems in Discrete Geometry. Combinatorica 3, 381–392 (1983)
Tamayo, P., Slonim, D., Mesirov, J., Zhu, Q., Kitareewan, A., Dmitrovsky, E., Lander, E.S., Golub, T.R.: Interpreting Patterns of Gene Expression with Self- Organizing Maps: Methods and Application to Hematopoietic Differentiation. Proc. Natl. Acad. Sci. USA 96, 2907–2912 (1999)
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© 2004 Springer-Verlag Berlin Heidelberg
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Akutsu, T. (2004). Algorithms for Point Set Matching with k-Differences. In: Chwa, KY., Munro, J.I.J. (eds) Computing and Combinatorics. COCOON 2004. Lecture Notes in Computer Science, vol 3106. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-27798-9_28
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DOI: https://doi.org/10.1007/978-3-540-27798-9_28
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-22856-1
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