#5468. Approximate CVPp in time 20.802n

August 2026publication date
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Journal’s subject area:
Applied Mathematics;
Computational Theory and Mathematics;
Theoretical Computer Science;
Computer Networks and Communications;
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Abstract:
We show that a constant factor approximation of the shortest and closest lattice vector problem in any ?p-norm can be computed in time 2(0.802+?)n. This matches the currently fastest constant factor approximation algorithm for the shortest vector problem in the ?2 norm. To obtain our result, we combine the latter algorithm for ?2 with geometric insights related to coverings.
Keywords:
Algorithmic geometry of numbers; Geometric covering; Lattice and integer programming; Sieving

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