Deterministic (1+ε)-approximation algorithm for the volume of the unit hypercube truncated by k sums-of-univariate-convex constraints, running in poly_k(n, 1/ε, L, L_o) time.
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Superlinear approximation of permutons by permutations occurs only when the permuton is supported on the graph of a measure-preserving function, with local regularity controlling the rate; the biased Brownian separable permuton has a positive lower bound on approximation error almost surely.
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Deterministic Volume Estimation of Truncated Hypercubes
Deterministic (1+ε)-approximation algorithm for the volume of the unit hypercube truncated by k sums-of-univariate-convex constraints, running in poly_k(n, 1/ε, L, L_o) time.
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On the approximation of permutons
Superlinear approximation of permutons by permutations occurs only when the permuton is supported on the graph of a measure-preserving function, with local regularity controlling the rate; the biased Brownian separable permuton has a positive lower bound on approximation error almost surely.