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Covering with Ellipses

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Abstract

We address the problem of how to cover a set of required points by a small number of axis-parallel ellipses that avoid a second set of forbidden points. We study geometric properties of such covers and present an efficient randomized approximation algorithm for the cover construction. This question is motivated by a special pattern recognition task where one has to identify ellipse-shaped protein spots in two-dimensional electrophoresis images.

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Authors and Affiliations

  1. Computer Science Department, Gould-Simpson 721, University of Arizona, 1040 E 4th St., Tucson, AZ 85721-0077, USA

    Alon Efrat & Caola Wenk

  2. Institute of Computer Science, Freie Universität Berlin, Takustraße 9, D-14195 Berlin, Germany

    Frank Hoffmann, Christian Knauer, Klaus Kriegel & Günter Rote

Authors
  1. Alon Efrat
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  2. Frank Hoffmann
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  3. Christian Knauer
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  4. Klaus Kriegel
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  5. Günter Rote
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  6. Caola Wenk
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Corresponding authors

Correspondence to Alon Efrat, Frank Hoffmann, Christian Knauer, Klaus Kriegel, Günter Rote or Caola Wenk.

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Efrat, A., Hoffmann, F., Knauer, C. et al. Covering with Ellipses. Algorithmica 38, 145–160 (2004). https://doi.org/10.1007/s00453-003-1047-0

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  • DOI: https://doi.org/10.1007/s00453-003-1047-0

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