Summary: The Hardness of Approximate Optima in Lattices,
Codes,
and Systems of Linear Equations
Sanjeev Arora \Lambda
Computer Science
Princeton University
L'aszl'o Babai y
University of Chicago and
E¨otv¨os University, Hungary
Jacques Stern
Laboratoire d'Informatique
Ecole Normale Sup'erieure
Z Sweedyk z
CS Division
U. C. Berkeley
Abstract
We prove the following about the Nearest Lattice Vector Problem (in any
` p norm), the Nearest Codeword Problem for binary codes, the problem of
learning a halfspace in the presence of errors, and some other problems.
1. Approximating the optimum within any constant factor is NP­hard.

Source: Arora, Sanjeev - Department of Computer Science, Princeton University

Collections: Computer Technologies and Information Sciences