Characterize P-complete problems efficiently parallelizable in MPC

Characterize which P-complete problems exhibit a sufficiently local structure that permits efficient parallelization in the Massively Parallel Computation (MPC) model with strongly sublinear local memory.

Background

The paper distinguishes classical parallel models, where P-complete problems are generally viewed as resistant to polylogarithmic-time parallelization, from the Massively Parallel Computation model, which permits sequential local computation combined with restricted global communication. The authors explain that P-completeness reductions neither rule out efficient MPC algorithms nor necessarily preserve MPC complexity.

The paper resolves this issue for one natural problem—exact edge ranking of trees—by showing that it is P-complete while also admitting an efficient MPC algorithm. However, it does not determine which other P-complete problems possess similarly local combinatorial structure, leaving open a broader classification problem concerning efficient MPC parallelization of P-complete problems.

References

It is still poorly understood which $P$-complete problems exhibit a sufficiently local structure to admit efficient MPC parallelization.

— Parallel Edge Ranking of Trees  (2610.12438 - Giliberti et al., 8 Oct 2026) in Section 1, Introduction, paragraph beginning “However, the reverse direction”