MPS admit efficient Δ- and (1+λ_max)-approximations for additive maximization and (2+λ_max) / Δ^{2}(1-1/e-δ)^{-1} approximations for monotone submodular maximization, with Gap-ETH hardness ruling out min{Δ,λ_max}^{o(1)}.
Journal of Combinatorial Theory, Series B , volume=
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Any fixed integer linear program with a finite feasible set can be answered by a precomputed linear decision tree using polynomially many arithmetic operations per cost query; a practical construction works on small instances.
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