Weizmann Logo
ECCC
Electronic Colloquium on Computational Complexity

Under the auspices of the Computational Complexity Foundation (CCF)

Login | Register | Classic Style



REPORTS > DETAIL:

Revision(s):

Revision #1 to TR97-047 | 11th November 1997 00:00

The Shortest Vector Problem in L_2 is NP-hard for Randomized Reductions.

RSS-Feed




Revision #1
Authors: Miklos Ajtai
Accepted on: 11th November 1997 00:00
Downloads: 1267
Keywords: 


Abstract:

We show that the shortest vector problem in lattices
with L_2 norm is NP-hard for randomized reductions. Moreover we
also show that there is a positive absolute constant c, so that to
find a vector which is longer than the shortest non-zero vector by no
more than a factor of 1+2^{-n^c} (with respect to the L_{2} norm) is
also NP-hard for randomized reductions. The corresponding decision
problem is NP-complete for randomized reductions.

Revision of: TR97-047


Paper:

TR97-047 | 20th October 1997 00:00

The Shortest Vector Problem in L_2 is NP-hard for Randomized Reductions.





TR97-047
Authors: Miklos Ajtai
Publication: 21st October 1997 09:51
Downloads: 1036
Keywords: 


Abstract:

We show that the shortest vector problem in lattices
with L_2 norm is NP-hard for randomized reductions. Moreover we
also show that there is a positive absolute constant c, so that to
find a vector which is longer than the shortest non-zero vector by no
more than a factor of 1+2^{-n^c} (with respect to the L_{2} norm) is
also NP-hard for randomized reductions. The corresponding decision
problem is NP-complete for randomized reductions.



ISSN 1433-8092 | Imprint