Summary: The Hardness of Approximate Optima in Lattices,
and Systems of Linear Equations
Sanjeev Arora \Lambda
L'aszl'o Babai y
University of Chicago and
Ešotvšos University, Hungary
Ecole Normale Sup'erieure
Z Sweedyk z
U. C. Berkeley
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.