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Improved Sublinear Time Algorithm for Width-Bounded Separators

  • Liang Ding
  • Bin Fu
  • Yunhui Fu
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6213)

Abstract

A width-bounded separator is a simple structured hyperplane which divides the given set into two balanced subsets, while at the same time maintaining a low density of the set within a given distance to the hyperplane. For a given set Q of n grid points in a d-dimensional Euclidean space, we develop an improved (Monte carlo) algorithm to find a w-wide separator L in \(\tilde{O}(n^{1\over d})\) sublinear time such that Q has at most \(({d\over d+1}+o(1))n\) points on one either side of the hyperplane L, and at most \(c_dwn^{d-1\over d}\) points within \(\frac{w}{2}\) distance to L, where c d is a constant for fixed d. This improves the existing \(\tilde{O}(n^{2\over d})\) algorithm by Fu and Chen. Furthermore, we derive an \(\Omega(n^{1\over d})\) time lower bound for any randomized algorithm that tests if a given hyperplane satisfies the conditions of width-bounded separator. This lower bound almost matches the upper bound.

Keywords

Planar Graph Failure Probability Signed Distance Separator Theorem Balance Partition 
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 2010

Authors and Affiliations

  • Liang Ding
    • 1
  • Bin Fu
    • 1
  • Yunhui Fu
    • 1
  1. 1.Department of Computer ScienceUniversity of Texas-Pan AmericanEdinburgUSA

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