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Polynomial Time Algorithms for Bichromatic Problems

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Algorithms and Discrete Applied Mathematics (CALDAM 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10156))

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Abstract

In this article, we consider a collection of geometric problems involving points colored by two colors (red and blue), referred to as bichromatic problems. The motivation behind studying these problems is two fold; (i) these problems appear naturally and frequently in the fields like Machine learning, Data mining, and so on, and (ii) we are interested in extending the algorithms and techniques for single point set (monochromatic) problems to bichromatic case. For all the problems considered in this paper, we design low polynomial time exact algorithms. These algorithms are based on novel techniques which might be of independent interest.

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Notes

  1. 1.

    The red rectangle may contain blue points on its boundary.

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Acknowledgements

We would like to thank an anonymous reviewer of an earlier version of this paper for suggestions that has helped us improve the running time of the algorithm for MaxCol.

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Authors and Affiliations

  1. Computer Science, University of Iowa, Iowa City, USA

    Sayan Bandyapadhyay

  2. Department of Computer Science and Engineering, Indian Institute of Technology, Jodhpur, India

    Aritra Banik

Authors
  1. Sayan Bandyapadhyay
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  2. Aritra Banik
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Correspondence to Aritra Banik .

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Editors and Affiliations

  1. University of Lethbridge, Lethbridge, Alberta, Canada

    Daya Gaur

  2. Indian Institute of Technology Madras, Chennai, India

    N.S. Narayanaswamy

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Bandyapadhyay, S., Banik, A. (2017). Polynomial Time Algorithms for Bichromatic Problems. In: Gaur, D., Narayanaswamy, N. (eds) Algorithms and Discrete Applied Mathematics. CALDAM 2017. Lecture Notes in Computer Science(), vol 10156. Springer, Cham. https://doi.org/10.1007/978-3-319-53007-9_2

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  • DOI: https://doi.org/10.1007/978-3-319-53007-9_2

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