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Lovász $\delta$ condition for LLL Algorithm
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?
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Approximate volume computation and lattice point enumeration - hardness
Both volume computation and lattice point enumeration of convex polyhedron are $\#P$ hard. However there is a randomized polytime algorithm for constant factor approximation for volume computation.
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