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A PTAS for the k-Consensus Structures Problem Under Euclidean Squared Distance

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Frontiers in Algorithmics (FAW 2008)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5059))

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Abstract

In this paper we consider a basic clustering problem that has uses in bioinformatics. A structural fragment is a sequence of ℓ points in a 3D space, where ℓ is a fixed natural number. Two structural fragments f 1 and f 2 are equivalent iff under some rotation and translation . We consider the distance between two structural fragments to be the sum of the Euclidean squared distance between all corresponding points of the structural fragments. Given a set of n structural fragments, we consider the problem of finding k (or fewer) structural fragments g 1, g 2,..., g k , so as to minimize the sum of the distances between each of f 1, f 2, ..., f n to its nearest structural fragment in g 1, ..., g k . In this paper we show a PTAS for the problem through a simple sampling strategy.

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Authors and Affiliations

  1. David R. Cheriton School of Computer Science, University of Waterloo, Waterloo, ON N2L 3G1, Canada

    Shuai Cheng Li

  2. Department of Computer Science and Communication Engineering, Kyushu University, Fukuoka, 819-0395, Japan

    Yen Kaow Ng

  3. Department of Mathematics, National University of Singapore, Singapore, 117543

    Louxin Zhang

Authors
  1. Shuai Cheng Li
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  2. Yen Kaow Ng
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  3. Louxin Zhang
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Franco P. Preparata Xiaodong Wu Jianping Yin

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© 2008 Springer-Verlag Berlin Heidelberg

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Li, S.C., Ng, Y.K., Zhang, L. (2008). A PTAS for the k-Consensus Structures Problem Under Euclidean Squared Distance. In: Preparata, F.P., Wu, X., Yin, J. (eds) Frontiers in Algorithmics. FAW 2008. Lecture Notes in Computer Science, vol 5059. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-69311-6_7

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  • DOI: https://doi.org/10.1007/978-3-540-69311-6_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-69310-9

  • Online ISBN: 978-3-540-69311-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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