The computational complexity of simultaneous diophantine approximation problems
SIAM Journal on Computing
Approximating integer lattices by lattices with cyclic factor groups
14th International Colloquium on Automata, languages and programming
A hierarchy of polynomial time lattice basis reduction algorithms
Theoretical Computer Science
Asymptotically fast computation of Hermite normal forms of integer matrices
ISSAC '96 Proceedings of the 1996 international symposium on Symbolic and algebraic computation
Generating hard instances of lattice problems (extended abstract)
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
The shortest vector problem in L2 is NP-hard for randomized reductions (extended abstract)
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
On the limits of nonapproximability of lattice problems
Journal of Computer and System Sciences - 30th annual ACM symposium on theory of computing
An Improved Worst-Case to Average-Case Connection for Lattice Problems
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
The Shortest Vector in a Lattice is Hard to Approximate to within Some Constant
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
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In this paper we investigate how the complexity of the shortest vector problem in a lattice Λ depends on the cycle structure of the additive group Zn/Λ. We give a proof that the shortest vector problem is NP-complete in the max-norm for n-dimensional lattices Λ where Zn/Λ has n-1 cycles. We also give experimental data that show that the LLL algorithm does not perform significantly better on lattices with a high number of cycles.