# Coloring Trees in Massively Parallel Computation

@inproceedings{Latypov2021ColoringTI, title={Coloring Trees in Massively Parallel Computation}, author={Rustam Latypov and Jara Uitto}, year={2021} }

We present O(log log n) time 3-coloring, maximal independent set and maximal matching algorithms for trees in the Massively Parallel Computation (MPC) model. Our algorithms are deterministic, apply to arbitrary-degree trees and work in the low-space MPC model, where local memory is O(nδ) for δ ∈ (0, 1) and global memory is O(m). Our main result is the 3-coloring algorithm, which contrasts the randomized, state-of-the-art 4-coloring algorithm of Ghaffari, Grunau and Jin [DISC’20]. The maximal…

## One Citation

### Brief Announcement: Memory Efficient Massively Parallel Algorithms for LCL Problems on Trees

- Computer ScienceDISC
- 2021

This work presents 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 and shows that all solvable LCL problems on trees can be solved in O(log n) time.

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