Polynomial dependence on the doubling constant in algorithmic PFR
Establish whether there exist classical or quantum algorithms for the algorithmic PFR task whose query and time complexities scale polynomially in the doubling constant K when K grows with n, thereby improving current bounds that suppress or incur superpolynomial dependence on K.
References
One concrete question that is left open from our work is to improve the dependence on the doubling constant K. As is standard in additive combinatorics, K is assumed to be a constant, but for asymptotically growing K it is an interesting open problem whether there exists an algorithm with query and time complexities that scale polynomially in K.
— Algorithmic Polynomial Freiman-Ruzsa Theorems
(Arunachalam et al., 2 Sep 2025) in Introduction, Technical overview, Future directions