Efficient trisection conjecture for simply-connected complex four-manifolds

Let $X$ be a simply-connected complex four-manifold. An efficient trisection of $X$ is a trisection whose genus equals $b_2(X)$.

Efficient trisection conjecture. Every simply-connected, complex four-manifold admits an efficient trisection.

Many familiar complex surfaces are known to admit efficient trisections, but it remains open whether every simply-connected complex four-manifold does.