Simple, deterministic, constant-round coloring in congested clique and MPC Czumaj, Artur Davies, Peter ; https://orcid.org/0000-0002-5646-9524 Parter, Merav General Mathematics General Computer Science We settle the complexity of the (∆ + 1)-coloring and (∆ + 1)-list coloring problems intheCONGESTED CLIQUEmodel by presenting a simpledeterministicalgorithm for both problemsrunning in a constant number of rounds. This matches the complexity of the recent breakthroughrandomizedconstant-round (∆ + 1)-list coloring algorithm due to Chang et al. [Proceedings of the38th ACM Symposium on Principles of Distributed Computing, 2019] and significantly improvesupon the state-of-the-artO(log ∆)-round deterministic (∆ + 1)-coloring bound of Parter [Proceed-ings of the 45th Annual International Colloquium on Automata, Languages and Programming]. Aremarkable property of our algorithm is its simplicity. Whereas the state-of-the-artrandomizedal-gorithms for this problem are based on the quite involved local coloring algorithm of Chang, Li, andPettie [Proceedings of the 50th Annual ACM SIGACT Symposium on Theory of Computing, 2018],our algorithm can be described in just a few lines. At a high level, it applies a careful derandomiza-tion of a recursive procedure which partitions the nodes and their respective palettes into separatebins. We show that afterO(1) recursion steps, the remaining uncolored subgraph within each bin haslinear size and thus can be solved locally by collecting it to a single node. This algorithm can alsobe implemented in the massively parallel computation (MPC) model provided that each machine haslinear (inn, the number of nodes in the input graph) space. We also show an extension of our algo-rithm to theMPCregime, in which machines havesublinearspace: we present the first deterministic(∆ + 1)-list coloring algorithm designed for sublinear-spaceMPC, which runs inO(log ∆ + log logn)rounds. Society for Industrial and Applied Mathematics 2021 info:eu-repo/semantics/article doc-type:article text http://purl.org/coar/resource_type/c_2df8fbb1 https://research-explorer.ista.ac.at/record/15271 Czumaj A, Davies P, Parter M. Simple, deterministic, constant-round coloring in congested clique and MPC. <i>SIAM Journal on Computing</i>. 2021;50(5):1603-1626. doi:<a href="https://doi.org/10.1137/20m1366502">10.1137/20m1366502</a> eng info:eu-repo/semantics/altIdentifier/doi/10.1137/20m1366502 info:eu-repo/semantics/altIdentifier/issn/0097-5397 info:eu-repo/semantics/altIdentifier/e-issn/1095-7111 info:eu-repo/semantics/altIdentifier/wos/000713008600004 info:eu-repo/semantics/closedAccess