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problems
The discrete-time Kac walk on S^n-1 started from a coordinate vector exhibits total variation cutoff at C_BRW n log n, where C_BRW ≈ 3.8916 is set by the speed of the leftmost particle in a branching random walk. The cutoff is therefore…
Furthest Pair and its relatives admit f(d) n^2-Θ(1/d) algorithms, making them the standard examples of barely subquadratic computation, and whether that is optimal in superconstant dimension was open. Under SETH it is: Furthest Pair…
VibeMathed records no statement for this problem. See erdosproblems.com for the original.
At the conjectured density, must every k-uniform hypergraph contain a short nontrivial even cover - a set of hyperedges covering each vertex an even number of times - with no superfluous polylogarithmic factors? Known up to polylog factors…
Does two-terminal reliability, the probability that s still reaches t when edges fail independently, admit a fully polynomial-time randomised approximation scheme? Asked explicitly in Kannan's 1994 survey and left open while the…
VibeMathed records no statement for this problem. See erdosproblems.com for the original.