New NP-Complete Problems Associated with Lattices
S. HAYASHI, M. TADA · IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences · 2007
In this paper, we introduce a new decision problem associated with lattices, named the Exact Length Vector Problem (ELVP), and prove the NP-completeness of ELVP in the l∞ norm. Moreover, we define two variants of ELVP. The one is a binary variant of ELVP, named the Binary Exact Length Vector Problem (BELVP), and is shown to be NP-complete in any lp norm (1 ≤ p ≤ ∞). The other is a nonnegative variant of ELVP, named the Nonnegative Exact Length Vector Problem (NELVP). NELVP is defined in the l1 norm, and is also shown to be NP-complete.