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Approximations with axis-aligned rectangles (extended abstract)

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Fundamentals of Computation Theory (FCT 1993)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 710))

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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

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Authors and Affiliations

  1. Lehrstuhl Informatik II, Universität Dortmund, D-4600, Dortmund 50, Germany

    Paul Fischer, Klaus -U. Höffgen & Hanno Lefmann

  2. Mathematical Institute of the Polish Academy of Sciences, Poznań, Poland

    Tomasz Luczak

Authors
  1. Paul Fischer
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  2. Klaus -U. Höffgen
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  3. Hanno Lefmann
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  4. Tomasz Luczak
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Editor information

Zoltán Ésik

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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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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-57163-6

  • Online ISBN: 978-3-540-47923-9

  • eBook Packages: Springer Book Archive

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