Abstract
In this paper we investigate the following problem arising from pattern recognition: given a matrix with real entries we search for a rectangle which covers the maximum sum of entries. We give efficient algorithms for this and the related problem of finding the maximum consistent rectangle. These problems are also discussed for the important class of bitonic connected matrices.
Moreover, we develop algorithms for such problems if we are given random matrices. We also consider the case where a large rectangle is blurred by additional noise. These algorithms have sublinear expected running time.
The author gratefully acknowledges the support of Deutsche Forschungsgemeinschaft grant 1066/6-1.
The author gratefully acknowledges the support of Bundesministerium für Forschung und Technologie grant 01IN102C/2. The author takes the responsibility for the content.
On leave from Department of Discrete Mathematics, Adam Mickiewicz University, Poznaň, Poland.
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References
Alok Aggarwal and Subhash Suri. Fast algorithms for computing the largest empty rectangle. In Proceedings of the 3rd Symposium on Computational Geometry, p. 278–290, 1987.
Helmut Alt, Johannes Blömer, Michael Godau, and Hubert Wagener. Approximation of convex polygons. In Proceedings of the 17th International Colloquium on Automata, Languages and Programming, p. 703–716, 1990.
Jon Bentley. Programming Pearls. Addison Wesley, 1986.
David Eppstein, Mark Overmars, Günter Rote, and Gerhard Woeginger. Finding minimum area k-gons. Discrete and Computational Geometry, 7, p. 45–58, 1992.
Maria M. Klawe and Daniel J. Kleitman. An almost linear time algorithm for generalized matrix searching. SIAM Journal on Discrete Mathematics, 3(1), p. 81–97, 1990.
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© 1993 Springer-Verlag Berlin Heidelberg
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Fischer, P., Höffgen, K.U., Lefmann, H., Luczak, T. (1993). Approximations with axis-aligned rectangles (extended abstract). In: Ésik, Z. (eds) Fundamentals of Computation Theory. FCT 1993. Lecture Notes in Computer Science, vol 710. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57163-9_20
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DOI: https://doi.org/10.1007/3-540-57163-9_20
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