Fine-grained reduction

In computational complexity theory, a fine-grained reduction is a transformation from one computational problem to another, used to relate the difficulty of improving the time bounds for the two problems. Intuitively, it provides a method for solving one problem efficiently by using the solution to the other problem as a subroutine. If problem ${\displaystyle A}$ can be solved in time ${\displaystyle a(n)}$ and problem ${\displaystyle B}$ can be solved in time ${\displaystyle b(n)}$, then the existence of an ${\displaystyle (a,b)}$-reduction from problem ${\displaystyle A}$ to problem ${\displaystyle B}$ implies that any significant speedup for problem ${\displaystyle B}$ would also lead to a speedup for problem ${\displaystyle A}$.