Selecting which ℓp norms to precompute for PolyB

Ascertain which ℓp norms of degree sequences should be precomputed for effective use in the Polymatroid Bound (PolyB), beyond the choice of ℓ2, ℓ3, ℓ4, and ℓ∞, balancing accuracy improvements against memory and computation costs.

Background

PolyB uses ℓp norms of degree sequences as input statistics to derive upper bounds via information-theoretic inequalities. While storing ℓ2, ℓ3, ℓ4, and ℓ∞ is suggested as a reasonable configuration, the authors note empirical gains up to ℓ30 with diminishing returns.

The paper explicitly states uncertainty about the optimal stopping point for which ℓp norms to store, framing an unresolved practical question in configuring statistics for PolyB deployments.