Year: 2008
Type: preprint
Abstract: We present an efficient reduction from the Bounded integer programming (BIP) to the Subspace avoiding problem (SAP) in lattice theory. The reduction has some special properties with some interesting consequences. The first is the new upper time bound for BIP, $poly(φ)\cdot n^{n+o(n)}$ (where $n$ and $φ$ are the dimension and the input size of the problem, respectively). This is the best bound up to now for BIP. The second consequence is the proof that #SAP, for some norms, is #P-hard under semi-reductions. It follows that the counting version of the Generalized closest vector problem is also #P-hard under semi-reductions. Furthermore, we also show that under some reasonable assumptions, BIP is solvable in probabilistic time $2^{O(n)}$.
Source: arXiv (Cornell University)
Author: Khoát, Thân Quang
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1555679443