The hardness of approximate optima in lattices, codes, and systems of linear equations

@article{Arora1993TheHO,
  title={The hardness of approximate optima in lattices, codes, and systems of linear equations},
  author={Sanjeev Arora and L. Babai and J. Stern and E. Sweedyk},
  journal={Proceedings of 1993 IEEE 34th Annual Foundations of Computer Science},
  year={1993},
  pages={724-733}
}
  • Sanjeev Arora, L. Babai, +1 author E. Sweedyk
  • Published 1993
  • Mathematics, Computer Science
  • Proceedings of 1993 IEEE 34th Annual Foundations of Computer Science
We prove the following about the Nearest Lattice Vector Problem (in any l/sub p/ norm), the Nearest Code-word 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 NP-hard. 2. If for some /spl epsiv/>0 there exists a polynomial time algorithm that approximates the optimum within a factor of 2/sup log(0.5-/spl epsiv/)/ /sup n/ then NP is in quasi-polynomial deterministic time… Expand
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