Deterministic O(n m) algorithm finds L1-norm <= (m+n)/2 vector avoiding m hyperplanes in Z^n (tight), proves NP-hardness for other p-norms, and yields O(ν² n³ Δ³) integer-point counting in polytopes.
arXiv:2110.0173 2 [cs.CC] (2023)
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Hyperplanes Avoiding Problem and Integer Points Counting in Polyhedra
Deterministic O(n m) algorithm finds L1-norm <= (m+n)/2 vector avoiding m hyperplanes in Z^n (tight), proves NP-hardness for other p-norms, and yields O(ν² n³ Δ³) integer-point counting in polytopes.