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Sublinear Time Width-Bounded Separators and Their Application to the Protein Side-Chain Packing Problem

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Algorithmic Aspects in Information and Management (AAIM 2006)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 4041))

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Abstract

Given d > 2 and a set of n grid points Q in \(\Re^d\), we design a randomized algorithm that finds a w-wide separator, which is determined by a hyper-plane, in \(O(n^{2\over d}\log n)\) sublinear time such that Q has at most \(({d\over d+1}+o(1))n\) points one either side of the hyper-plane, and at most \(c_dwn^{d-1\over d}\) points within \(\frac{w}{2}\) distance to the hyper-plane, where c d is a constant for fixed d. In particular, c 3 = 1.209. To our best knowledge, this is the first sublinear time algorithm for finding geometric separators. Our 3D separator is applied to derive an algorithm for the protein side-chain packing problem, which improves and simplifies the previous algorithm of Xu [26].

This research is supported by Louisiana Board of Regents fund under contract number LEQSF(2004-07)-RD-A-35, and in part by NSF Grant CNS-0521585.

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Author information

Authors and Affiliations

  1. Dept. of Computer Science, University of New Orleans, LA, 70148, USA

    Bin Fu

  2. Research Institute for Children, 200 Henry Clay Avenue, New Orleans, LA, 70118, USA

    Bin Fu

  3. Dept. of Computer Science, University of Texas – Pan American, TX, 78539, USA

    Zhixiang Chen

Authors
  1. Bin Fu
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  2. Zhixiang Chen
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Editor information

Editors and Affiliations

  1. Department of Computer Science, Clear Water Bay, Hong Kong University of Science and Technology, Hong Kong, China

    Siu-Wing Cheng

  2. Department of Computer Science, City University of Hong Kong,  

    Chung Keung Poon

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Fu, B., Chen, Z. (2006). Sublinear Time Width-Bounded Separators and Their Application to the Protein Side-Chain Packing Problem. In: Cheng, SW., Poon, C.K. (eds) Algorithmic Aspects in Information and Management. AAIM 2006. Lecture Notes in Computer Science, vol 4041. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11775096_15

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  • DOI: https://doi.org/10.1007/11775096_15

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-35157-3

  • Online ISBN: 978-3-540-35158-0

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