Hardness of approximating the Shortest Vector Problem in high p norms

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Abstract

We present a new hardness of approximation result for the Shortest Vector Problem in p norm (denoted by SVPp). Assuming NP ZPP, we show that for every ε>0, there is a constant p(ε) such that for all integers pp(ε), the problem SVPp has no polynomial time approximation algorithm with approximation ratio p1-ε.

Keywords

Computational complexity
Lattices
Shortest vector problem
Approximation algorithms
Hardness of approximation

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A preliminary version of this paper appeared in Proceedings of the 44th IEEE Symposium on Foundations of Computer Science, 2003. This research was supported in part by Sanjeev Arora's NSF Awards 0205594, CCR 0098180 and the David and Lucile Packard Fellowship.