Sublinear Time Width-Bounded Separators and Their Application to the Protein Side-Chain Packing Problem
نویسندگان
چکیده
Given d > 2 and a set of n grid points Q in <, we design a randomized algorithm that finds a w-wide separator, which is determined by a hyper-plane, in O(n 2 d log n) sublinear time such that Q has at most ( d d+1 + o(1))n points one either side of the hyper-plane, and at most cdwn d−1 d points within 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
منابع مشابه
Response to Reviewer Comments
Given d > 2 and a set of n grid points Q in R, we design a randomized algorithm that finds a w-wide separator, which is determined by a hyper-plane, in O(n 2 d log n) sublinear time such that Q has at most ( d d+1 + o(1))n points one either side of the hyper-plane, and at most cdwn d−1 d points within w 2 distance to the hyper-plane, where cd is a constant for fixed d. In particular, c3 = 1.209...
متن کاملOn Separators, Segregators and Time versus Space
We give the first extension of the result due to Paul, Pippenger, Szemeredi and Trotter [24] that deterministic linear time is distinct from nondeterministic linear time. We show that NTIME(n √ log∗(n)) 6= DTIME(n √ log∗(n)). We show that if the class of multi-pushdown graphs has (o(n), o(n/log(n))) segregators, then NTIME(nlog(n)) 6= DTIME(nlog(n)). We also show that atleast one of the followi...
متن کاملTheory and application of width bounded geometric separators
We introduce the notion of the width bounded geometric separator and develop the techniques for the existence of the width bounded separator in any fixed ddimensional Euclidean space. The separator is applied in obtaining 2O( √ n) time exact algorithms for a class of NP-complete geometric problems, whose previous algorithms take nO( √ n) time . One of those problems is the well known disk cover...
متن کاملA PTAS for a Disc Covering Problem Using Width-Bounded Separators
In this paper, we study the following disc covering problem: Given a set of discs of 6 various radii on the plane, find a subset of discs to maximize the area covered by exactly one 7 disc. This problem originates from the application in digital halftoning, with the best known 8 approximation factor being 5.83 (Asano et al., 2004). We show that if the maximum radius 9 is no more than a constant...
متن کاملRapid Protein Side-Chain Packing via Tree Decomposition
This paper proposes a novel tree decomposition based side-chain assignment algorithm, which can obtain the globally optimal solution of the side-chain packing problem very efficiently. Theoretically, the computational complexity of this algorithm isO((N +M)n rot ) whereN is the number of residues in the protein,M the number of interacting residue pairs, nrot the average number of rotamers for e...
متن کامل