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 ...
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...
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. ...
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 pre...
Note on shortest and nearest lattice vectors 来自 Elsevier 喜欢 0 阅读量: 39 作者: M Henk 摘要: We show that with respect to a certain class of norms the so-called shortest lattice vector problem is polynomial-time Turing (Cook) reducible to the nearest lattice vector problem. This ...
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 ...
p norms. We also describe polynomial time reductions for four classical problems from the geometry of numbers, the shortest vector problem , the closest vector problem , the successive minima problem , and the shortest independent vectors problem ( ) to Sap, establishing probabilistic single ...
. , bn ∈ Zn be n-dimensional linearly independent column (integral) vectors. The (full rank) lattice L spanned by a matrix B = (b1, . . . , bn) is defined as the set L = L(B) = {Bx | x ∈ Zn}. Such a B is called a lattice basis of L, and each v ∈ L is ...
Next, the shortest vectors of the root lattice E6 may be taken as a derived spherical design of E7. As the parameters we compute (smallest degree of a non-trivial polynomial in the ideal, smallest possible maximum degree of polynomials in any generating set) are independent of the choice of...