Fine-grained Complexity Meets IP = PSPACE

Understand

In this paper we study the fine-grained complexity of finding exact and approximate solutions to problems in P.

• Our main contribution is showing reductions from exact to approximate solution for a host of such problems.
• As one (notable) example, we show that the Closest-LCS-Pair problem (Given two sets of strings $A$ and $B$, compute exactly the maximum $\textsf{LCS}(a, b)$ with $(a, b) \in A \times B$) is equivalent to its approximation version (under near-linear time reductions, and with a constant approximation factor).
• More generally, we identify a class of problems, which we call BP-Pair-Class, comprising both exact and approximate solutions, and show that they are all equivalent under near-linear time reductions.