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Expected Computations on Color Spanning Sets

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Frontiers in Algorithmics and Algorithmic Aspects in Information and Management

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7924))

Abstract

Given a set of n points, each is painted by one of the k given colors, we want to choose k points with distinct colors to form a color spanning set. For each color spanning set, we can construct the convex hull and the smallest axis-aligned enclosing rectangle, etc. Assume that each point is chosen independently and identically from the subset of points of the same color, we propose an O(n 2logn) time algorithm to compute the expected area of convex hulls of the color spanning sets and an O(n 2logn) time algorithm to compute the expected perimeter of convex hulls of the color spanning sets. For the expected perimeter (resp. area) of the smallest perimeter (resp. area) axis-aligned enclosing rectangles of the color spanning sets, we present an O(nlogn) (resp. O(n 2)) time algorithm. We also propose an approximation algorithm to compute the expected diameter of the color spanning sets.

This research has been partially funded by the International Science & Technology Cooperation Program of China (2010DFA92720) and NSF of China under poject 11271351.

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Author information

Authors and Affiliations

  1. Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences, Shenzhen, China

    Chenglin Fan & Jun Luo

  2. Zhejiang Normal University, China

    Farong Zhong

  3. Department of Computer Science, Montana State University, Bozeman, MT, 59717, USA

    Binhai Zhu

Authors
  1. Chenglin Fan
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  2. Jun Luo
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  3. Farong Zhong
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  4. Binhai Zhu
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Editor information

Editors and Affiliations

  1. School of Engineering and Information Technology, Charles Darwin University, 0909, Darwin, NT, Australia

    Michael Fellows

  2. School of High-Technology for Human Welfare, Tokai University, 317 Nishimo, 410-0395, Numazu, Japan

    Xuehou Tan

  3. Department of Computer Science, Montana State University, 59717, Bozeman, MT, USA

    Binhai Zhu

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Fan, C., Luo, J., Zhong, F., Zhu, B. (2013). Expected Computations on Color Spanning Sets. In: Fellows, M., Tan, X., Zhu, B. (eds) Frontiers in Algorithmics and Algorithmic Aspects in Information and Management. Lecture Notes in Computer Science, vol 7924. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38756-2_15

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  • DOI: https://doi.org/10.1007/978-3-642-38756-2_15

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-38755-5

  • Online ISBN: 978-3-642-38756-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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