Streaming max-cut requires Ω(n) space for dense graphs but Ω(n log(ε² n)/ε²) space for graphs with Θ(n/ε²) edges when outputting the cut, with matching upper bounds for dense case and similar separations for densest subgraph.
A subpolynomial approximation algorithm for graph crossing number in low-degree graphs
6 Pith papers cite this work. Polarity classification is still indexing.
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A unified FPT framework reduces many crossing-number variants on surfaces to simplicial-complex embeddability, parameterized by genus and crossing bound, with linear or quadratic dependence.
Minimax sample complexity for uniform L_infty estimation is Theta(n^{d+1}) for degree-d polynomials and Theta(ns^2) for s-sparse Fourier-Walsh polynomials under noise, exceeding noiseless rates by factors of n and s.
Symmetric Boolean CSP predicates of arity at most 5 have their non-redundancy NRD_n(R) classified as O(n^t) for small t, with all arity-4 cases and all but two arity-5 cases resolved via t-balancedness and OR-reductions.
A two-pass sublinear-space streaming algorithm achieves (1/2-ε)-approximation for Max-DICUT on unbounded-degree graphs.
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Near-optimal streaming approximation for Max-DICUT in sublinear space using two passes
A two-pass sublinear-space streaming algorithm achieves (1/2-ε)-approximation for Max-DICUT on unbounded-degree graphs.