# Towards a Complexity Classification of LCL Problems in Massively Parallel Computation

@inproceedings{Brandt2021TowardsAC, title={Towards a Complexity Classification of LCL Problems in Massively Parallel Computation}, author={Sebastian Brandt and Rustam Latypov and Jara Uitto}, year={2021} }

In this work, we develop the low-space Massively Parallel Computation (MPC) complexity landscape for a family of fundamental graph problems on trees. We present a general method that solves most locally checkable labeling (LCL) problems exponentially faster in the low-space MPC model than in the LOCAL message passing model. In particular, we show that all solvable LCL problems on trees can be solved in O(log n) time (high-complexity regime) and that all LCL problems on trees with deterministic…

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