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

  • Authors:

  • Bin Fu;Zhixiang Chen

  • Affiliations:

  • Dept. of Computer Science, University of New Orleans, LA;Dept. of Computer Science, University of Texas – Pan American, TX

  • Venue:
  • AAIM'06 Proceedings of the Second international conference on Algorithmic Aspects in Information and Management
  • Year:
  • 2006

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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 cd is a constant for fixed d. In particular, c3 = 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].