Sublinear time width-bounded separators and their application to the protein side-chain packing problem - Fu, Bin; Chen, Zhixiang (Journal of combinatorial optimization, 2008)
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 sublinear time such that Q has at most points on either side of the hyper-plane, and at most points within 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 ).