Efficient kernelization to non-redundancy for all CSPs

Develop a polynomial-time kernelization procedure that, for every finite domain D, arity r, predicate R ⊆ D^r, and n-variable instance Ψ of CSP(R), outputs an ε-sparsifier (equivalently, a kernelization) whose size is within polylogarithmic factors of the non-redundancy NRD( R̄, n), thereby making the sparsification bound in Theorem 1.2 algorithmically efficient.

Background

The paper proves that for every predicate R, unweighted CSP(R) instances admit ε-sparsifiers of size within polylogarithmic factors of the non-redundancy of the complement predicate R̄. However, the construction is non-algorithmic in general. Making it efficient would yield broadly applicable kernelization routines.

The authors note a barrier: any efficient sparsifier would also be a kernelization algorithm achieving size near the non-redundancy, and achieving such kernelizations for all CSPs is currently unknown in the kernelization literature.