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.
An algorithm extracts large localized clusters in metric measure spaces to denoise distances with near-linear time for fixed error r, plus sharp info-theoretic scales for vanishing r suggesting statistical-computational gaps beyond Riemannian cases.
citing papers explorer
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Streaming Complexity Separations for Dense and Sparse Graphs
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.
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Tight $L_\infty$ Sample Complexity for Low-Degree and Sparse Boolean Polynomials
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.
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Denoising Distances in Metric Measure Spaces
An algorithm extracts large localized clusters in metric measure spaces to denoise distances with near-linear time for fixed error r, plus sharp info-theoretic scales for vanishing r suggesting statistical-computational gaps beyond Riemannian cases.