conference paper published yes Artur Czumaj author 0000-0002-5646-9524 Peter Davies author 11396234-BB50-11E9-B24C-90FCE56974250000-0002-5646-9524 Merav Parter author DaAl department PODC: Symposium on Principles of Distributed Computing ISTplus - Postdoctoral Fellowships project We settle the complexity of the (Δ+1)-coloring and (Δ+1)-list coloring problems in the CONGESTED CLIQUE model by presenting a simple deterministic algorithm for both problems running in a constant number of rounds. This matches the complexity of the recent breakthrough randomized constant-round (Δ+1)-list coloring algorithm due to Chang et al. (PODC'19), and significantly improves upon the state-of-the-art O(logΔ)-round deterministic (Δ+1)-coloring bound of Parter (ICALP'18). A remarkable property of our algorithm is its simplicity. Whereas the state-of-the-art randomized algorithms for this problem are based on the quite involved local coloring algorithm of Chang et al. (STOC'18), our algorithm can be described in just a few lines. At a high level, it applies a careful derandomization of a recursive procedure which partitions the nodes and their respective palettes into separate bins. We show that after O(1) recursion steps, the remaining uncolored subgraph within each bin has linear size, and thus can be solved locally by collecting it to a single node. This algorithm can also be implemented in the Massively Parallel Computation (MPC) model provided that each machine has linear (in n, the number of nodes in the input graph) space. We also show an extension of our algorithm to the MPC regime in which machines have sublinear space: we present the first deterministic (Δ+1)-list coloring algorithm designed for sublinear-space MPC, which runs in O(logΔ+loglogn) rounds. https://research-explorer.ista.ac.at/download/7803/8624/ColoringArxiv.pdf application/pdfno Association for Computing Machinery2020Salerno, Italy eng 2009.06043 00143669350004210.1145/3382734.3405751 309-318 Czumaj, Artur, et al. “Simple, Deterministic, Constant-Round Coloring in the Congested Clique.” <i>Proceedings of the 2020 ACM Symposium on Principles of Distributed Computing</i>, Association for Computing Machinery, 2020, pp. 309–18, doi:<a href="https://doi.org/10.1145/3382734.3405751">10.1145/3382734.3405751</a>. Czumaj, Artur, Peter Davies, and Merav Parter. “Simple, Deterministic, Constant-Round Coloring in the Congested Clique.” In <i>Proceedings of the 2020 ACM Symposium on Principles of Distributed Computing</i>, 309–18. Association for Computing Machinery, 2020. <a href="https://doi.org/10.1145/3382734.3405751">https://doi.org/10.1145/3382734.3405751</a>. Czumaj, A., Davies, P., &#38; Parter, M. (2020). Simple, deterministic, constant-round coloring in the congested clique. In <i>Proceedings of the 2020 ACM Symposium on Principles of Distributed Computing</i> (pp. 309–318). Salerno, Italy: Association for Computing Machinery. <a href="https://doi.org/10.1145/3382734.3405751">https://doi.org/10.1145/3382734.3405751</a> A. Czumaj, P. Davies, and M. Parter, “Simple, deterministic, constant-round coloring in the congested clique,” in <i>Proceedings of the 2020 ACM Symposium on Principles of Distributed Computing</i>, Salerno, Italy, 2020, pp. 309–318. Czumaj A, Davies P, Parter M. 2020. Simple, deterministic, constant-round coloring in the congested clique. Proceedings of the 2020 ACM Symposium on Principles of Distributed Computing. PODC: Symposium on Principles of Distributed Computing, 309–318. Czumaj A, Davies P, Parter M. Simple, deterministic, constant-round coloring in the congested clique. In: <i>Proceedings of the 2020 ACM Symposium on Principles of Distributed Computing</i>. Association for Computing Machinery; 2020:309-318. doi:<a href="https://doi.org/10.1145/3382734.3405751">10.1145/3382734.3405751</a> A. Czumaj, P. Davies, M. Parter, in:, Proceedings of the 2020 ACM Symposium on Principles of Distributed Computing, Association for Computing Machinery, 2020, pp. 309–318. 78032020-05-06T09:02:14Z2025-09-10T10:18:18Z