closest vector problemshortest independent vectors problemreductionGiven an n-dimensional lattice L and some target vector, this paper studies the algorithms for approximate closest vector problem (CVPγ) by using an approximate shortest independent vectors problem oracle (SIVPγ). More precisely, if ...
, theclosest vector problem , thesuccessive minima problem , and theshortest independent vectors problem ( )toSap, establishing probabilistic single exponential time algorithms for them. The result generalize and extend previous results of Ajtai, Kumar and Sivakumar. The results on and are new for a...
We study four problems from the geometry of numbers, the shortest vector problem (SVP), the closest vector problem (CVP), the successive minima problem (SMP), and the shortest independent vectors problem (SIVP). Extending and generalizing results of Ajtai, Kumar, and Sivakumar we present probabi...
Algorithm for SVP Our Three-Level Sieve Algorithm Analysis of Complexity 4 / 57 Lattice The lattice spanned by linearly independent vectors b1 , b2 , ··· , bn ∈ Rm is b1 b2 Lattice n L={ i =1 xi bi |xi ∈ Z} 5 / 57 Lattice Let B = [b1 , b2 , ··· , bn ]m×n...
研究点推荐 approximate shortest independent vectors oracle closest vector instances 站内活动 0关于我们 百度学术集成海量学术资源,融合人工智能、深度学习、大数据分析等技术,为科研工作者提供全面快捷的学术服务。在这里我们保持学习的态度,不忘初心,砥砺前行。了解更多>>...
We prove the several inequalities on the determinants of sublattices in LLL-reduced bases, namely: Theorem 1. Let b1,..., bn ∈ R m be an LLL-reduced basis of the lattice L, and d1,..., dk arbitrary linearly independent vectors in L. Then (a) ‖b1 ‖≤ 2 (n−k)/2+(k−...
Then the problem of minimizing cumulative RV index is formulated and the corresponding solution techniques based on Benders decomposition are developed. The travel times/uncertain demands in Jaillet et al. (2016) are assumed to be either independent or inherently dependent via a linear regression ...
only according to the number of edges connected to the node and independent of the edge costs. This seems like a reasonable choice for moving in a street network, if we consider that the decision of direction of the random walker in an intersection is not affected by the lengths of the ...
Any finite set of linearly independent vectors b1, b2, ⋯, bm∈RN generates a lattice: L={∑i=1mzibi|zi∈Z}. Denote by B the matrix whose column vectors are the bi’s. We say B is a basis (in matrix form) for L; m and N are the rank and dimension of L, respectively. ...
In most vehicle routing and crew scheduling applications solved by column generation, the subproblem corresponds to a shortest path problem with resource constraints (SPPRC) or one of its variants. This chapter proposes a classification and a generic formulation for the SPPRCs, briefly discusses compl...