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Sublinear time width-bounded separators and their application to the protein side-chain packing problem

Author

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  • Bin Fu

    (University of Texas)

  • Zhixiang Chen

    (University of Texas)

Abstract

Given d>2 and a set of n grid points Q in ℜ 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 on either side of the hyper-plane, and at most $c_{d}wn^{d-1\over d}$ 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 (Research in computational molecular biology, 9th annual international conference, pp. 408–422, 2005).

Suggested Citation

  • Bin Fu & Zhixiang Chen, 2008. "Sublinear time width-bounded separators and their application to the protein side-chain packing problem," Journal of Combinatorial Optimization, Springer, vol. 15(4), pages 387-407, May.
    • Handle: RePEc:spr:jcomop:v:15:y:2008:i:4:d:10.1007_s10878-007-9092-2
    DOI: 10.1007/s10878-007-9092-2
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    References listed on IDEAS

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    1. Zhixiang Chen & Bin Fu & Yong Tang & Binhai Zhu, 2006. "A PTAS for a disc covering problem using width-bounded separators," Journal of Combinatorial Optimization, Springer, vol. 11(2), pages 203-217, March.
    2. Bernard Chazelle & Carl Kingsford & Mona Singh, 2004. "A Semidefinite Programming Approach to Side Chain Positioning with New Rounding Strategies," INFORMS Journal on Computing, INFORMS, vol. 16(4), pages 380-392, November.
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    Cited by:

    1. Bin Fu & Zhiyu Zhao, 2009. "Separating sublinear time computations by approximate diameter," Journal of Combinatorial Optimization, Springer, vol. 18(4), pages 393-416, November.

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