Tight complexity for intermediate matrix product variants

Determine whether O(n^{2.5}) is the optimal running time (when the matrix multiplication exponent ω equals 2) for the static variants of matrix multiplication including min-max product, min-witness product, equality (Hamming) product, dominance product, threshold product, plus-max product, and ℓ_{2p+1} product, i.e., establish whether faster-than-O(n^{2.5}) algorithms are impossible or identify matching lower bounds for these problems.

Background

The authors survey numerous matrix multiplication variants whose fastest known algorithms have running times expressed as functions of the matrix multiplication exponent ω, converging to O(n^{2.5}) when ω=2.

They explicitly point out that it remains open whether this convergence reflects the true optimal complexity for all these problems, despite partial evidence from fine-grained reductions.