Efficient Deterministic Distributed Coloring with Small Bandwidth [article]

Philipp Bamberger, Fabian Kuhn, Yannic Maus
2020 arXiv   pre-print
We show that the (degree+1)-list coloring problem can be solved deterministically in O(D ·log n ·log^2Δ) rounds in the model, where D is the diameter of the graph, n the number of nodes, and Δ the maximum degree. Using the recent polylogarithmic-time deterministic network decomposition algorithm by Rozhoň and Ghaffari [STOC 2020], this implies the first efficient (i.e., log n-time) deterministic algorithm for the (Δ+1)-coloring and the (degree+1)-list coloring problem. Previously the best known
more » ... algorithm required 2^O(√(log n)) rounds and was not based on network decompositions. Our techniques also lead to deterministic (degree+1)-list coloring algorithms for the congested clique and the massively parallel computation (MPC) model. For the congested clique, we obtain an algorithm with time complexity O(logΔ·loglogΔ), for the MPC model, we obtain algorithms with round complexity O(log^2Δ) for the linear-memory regime and O(log^2Δ + log n) for the sublinear memory regime.
arXiv:1912.02814v3 fatcat:gwjhbkamubfuhkk4s5qie4gcvy