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OP-9511Status unassessedAlgorithms and data structures

Single-exponential CVP in general norms

For each p≥1p\geq1, solve exact closest vector in ℓp\ell_p on rank-nn lattices in time 2O(n)2^{O(n)}.

MSC 68W · Algorithms in computer science

Inferred from the community field; finer classification has not been reviewed.

Research-list selection · status unassessedAs of 2022-06-06Source & evidence ↓
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Problem statement

For each p≥1p\geq1, solve exact closest vector in ℓp\ell_p on rank-nn lattices in time 2O(n)2^{O(n)}.

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Background

Editorial selection inspected on 9 September 2026. Current research status has not been independently reassessed; consult the original source and subsequent literature.

Source conventions: CVP is closest vector, SVP is shortest nonzero vector, and SIVP asks for independent vectors minimizing their largest norm. Gap denotes the associated promise decision problem. Approximation factors precede the problem name; Euclidean norm is the default. The source suppresses lower-order terms and input-length factors in exponential running times. Reduction arrows refer to efficient oracle reductions. The source's 2022 best-known bounds are not asserted to be current.

References
  1. [1]Simons Institute — Lattices '22 problems: Single-exponential CVP in general norms (inspected 2026-09-09) link

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