Affiliation:
1. Georgia Institute of Technology, Atlanta, Georgia
Abstract
Let
p
> 1 be any fixed real. We show that assuming NP ⊈ RP, there is no polynomial time algorithm that approximates the Shortest Vector Problem (SVP) in ℓ
p
norm within a constant factor. Under the stronger assumption NP ⊈ RTIME(2
poly
(log
n
)
), we show that there is no polynomial-time algorithm with approximation ratio 2
(log
n
)
1/2−ϵ
where
n
is the dimension of the lattice and ϵ > 0 is an arbitrarily small constant.We first give a new (randomized) reduction from Closest Vector Problem (CVP) to SVP that achieves
some
constant factor hardness. The reduction is based on BCH Codes. Its advantage is that the SVP instances produced by the reduction
behave well
under the
augmented tensor product
, a new variant of tensor product that we introduce. This enables us to boost the hardness factor to 2
(log
n
)
1/2-ϵ
.
Publisher
Association for Computing Machinery (ACM)
Subject
Artificial Intelligence,Hardware and Architecture,Information Systems,Control and Systems Engineering,Software
Cited by
91 articles.
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