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

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...

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Bibliographic Details
Published in:Journal of combinatorial optimization Vol. 15; no. 4; pp. 387 - 407
Main Authors: Fu, Bin, Chen, Zhixiang
Format: Journal Article
Language:English
Published: Boston Springer US 01.05.2008
Springer
Subjects:
Applied sciences
Combinatorics
Convex and Discrete Geometry
Exact sciences and technology
Flows in networks. Combinatorial problems
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
Operational research and scientific management
Operational research. Management science
Operations Research/Decision Theory
Optimization
Probability and statistics
Sampling theory, sample surveys
Sciences and techniques of general use
Statistics
Theory of Computation
Sublinear time algorithm
Random sampling
Width-bounded separator
Randomized design
Grid
Bin packing problem
Molecular biology
Combinatorial optimization
Bioinformatics
Separator
ISSN:1382-6905, 1573-2886
Online Access:Get full text
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Summary: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 ).
ISSN:1382-6905
1573-2886
DOI:10.1007/s10878-007-9092-2