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 


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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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