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http://en.wikipedia.org/wiki/Lenstra%E2%80%93Lenstra%E2%80%93Lov%C3%A1sz_lattice_basis_reduction_algorithm

What is the importance of the $\delta$ parameter for LLL bases called Lovász condition?

Wiki seems to mention that the higher the $\delta$ the better.

What does it mean when $\delta = 1$? Can we finding find shortest vector and closest vector easily if $\delta =1$? What are typical error in approximations when $\delta = 1$?

In the SVP and CVP algorithm presented below, is there any connection to $\delta$ on the approximation error(wiki seems to mention that the higher the $\delta$ the better).

http://www.cs.tau.ac.il/~odedr/teaching/lattices_fall_2004/ln/cvp.pdf

Can $\delta \ge 1$ be satisfied and is there a consequence on the bases and estimate of minimum distance between lattice points and CVP distance estimates if this is so?

Finally is there a reference that talks about connections to CVP and minimum distance?

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http://en.wikipedia.org/wiki/Lenstra%E2%80%93Lenstra%E2%80%93Lov%C3%A1sz_lattice_basis_reduction_algorithm

What is the importance of the $\delta$ parameter for LLL bases called Lovász condition?

What does it mean when $\delta = 1$? Can we finding shortest vector and closest vector easily if $\delta =1$?

In the CVP algorithm presented below, is there any connection to $\delta$ on the approximation error (wiki seems to mention that the higher the $\delta$ the better).

http://www.cs.tau.ac.il/~odedr/teaching/lattices_fall_2004/ln/cvp.pdf

Can $\delta \ge 1$ be satisfied and is there a consequence on the bases and estimate of minimum distance between lattice points and CVP distance estimates if this is so?

Finally is there a reference that talks about connections to CVP and minimum distance?

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