منابع مشابه
Dual vectors and lower bounds for the nearest lattice point problem
We prove that given a point ~z outside a given lattice L then there is a dual vector which gives a fairly good estimate for how far from the lattice the vector is. To be more precise, there is a set of translated hyperplanes Hi such that L S iHi and d(~z; S iHi) 1 6n+1 d(~z; L). Warning: Essentially this paper has been published in Combinatorica and is hence subject to copyright restrictions. I...
متن کاملTowards a Converse for the Nearest Lattice Point Problem
We consider the problem of distributed computation of the nearest lattice point for a two dimensional lattice. An interactive model of communication is considered. The problem is to bound the communication complexity of the search for a nearest lattice point. Upper bounds have been developed in two recent works [3], [16]. Here we prove the optimality of a particular step in the derivation of th...
متن کاملImproved upper and lower bounds for the point placement problem
The point placement problem is to determine the positions of a set of n distinct points, P = {p1, p2, p3, . . . , pn}, on a line uniquely, up to translation and reflection, from the fewest possible distance queries between pairs of points. Each distance query corresponds to an edge in a graph, called point placement graph (ppg), whose vertex set is P . The uniqueness requirement of the placemen...
متن کاملCircuit Lower Bounds, Help Functions, and the Remote Point Problem
We investigate the power of Algebraic Branching Programs (ABPs) augmented with help polynomials, and constant-depth Boolean circuits augmented with help functions. We relate the problem of proving explicit lower bounds in both these models to the Remote Point Problem (introduced in [3]). More precisely, proving lower bounds for ABPs with help polynomials is related to the Remote Point Problem w...
متن کاملNote on Shortest and Nearest Lattice Vectors
K is a centrally symmetric convex body with nonempty interior and fK(·) is also called the distance function of K because fK(x) = min{ρ ∈ R≥0 : x ∈ ρK}. The Euclidean norm is denoted by fB(·), where B is the n-dimensional unit ball, and the associated inner product is denoted by 〈·, ·〉. Finally, we denote by C the cube with edge length 2 and center 0, and thus fC(·) denotes the maximum norm. As...
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ژورنال
عنوان ژورنال: Combinatorica
سال: 1988
ISSN: 0209-9683,1439-6912
DOI: 10.1007/bf02122554