Chlebik and Chlebikova prove that the problem “maximum 3-dimensional matching” is NP-hard to approximate within a multiplicative factor of $95/94$.

This means that, unless $P=NP$, there is no polynomial-time algorithm that finds a 3-dimensional matching with at least $(94/95)cdot OPT$ edges, where $OPT$ is the number of edges in a maximum matching.

Suppose we would like an *additive* approximation algorithm, that finds a 3-dimensional matching with at least $OPT-1$ edges. Is such algorithm theoretically possible (if $Pneq NP$)?