期刊名称：Electronic Colloquium on Computational Complexity
印刷版ISSN：1433-8092
出版年度：1999
卷号：1999
出版社：Universität Trier, Lehrstuhl für Theoretische Computer-Forschung
摘要：We show that given oracle access to a subroutine which
returns approximate closest vectors in a lattice, one may find in
polynomial-time approximate shortest vectors in a lattice.
The level of approximation is maintained; that is, for any function
f, the following holds:
Suppose that the subroutine, on input a lattice L and a target
vector w (not necessarily in the lattice), outputs vL
such that v−wf(n)u−w for any uL.
Then, our algorithm, on input a lattice L, outputs a nonzero
vector vL such that vf(n)u for
any nonzero vector uL.
The result holds for any norm, and preserves the dimension of the
lattice, i.e., the closest vector oracle is called on lattices of
exactly the same dimension as the original shortest vector problem.
This result establishes the widely believed conjecture by which
the shortest vector problem is not harder than the closest vector
problem.
The proof can be easily adapted to establish an analogous result
for the corresponding computational problems for linear codes.
关键词：Computational Problems in Integer Lattices, linear error-correcting codes, reducibility among approximation problems
