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

  • Bin Fu
  • Zhixiang Chen
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4041)


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].


Planar Graph Signed Distance Balance Partition Sublinear Time Geometric Separator 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Bin Fu
    • 1
    • 2
  • Zhixiang Chen
    • 3
  1. 1.Dept. of Computer ScienceUniversity of New OrleansUSA
  2. 2.Research Institute for ChildrenNew OrleansUSA
  3. 3.Dept. of Computer ScienceUniversity of Texas – Pan AmericanUSA

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