Simple Graph Coloring Algorithms for Congested Clique and Massively Parallel Computation
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We present a very simple randomized partitioning procedure for graph coloring, which leads to simplification or improvements of some recent distributed and parallel coloring algorithms. In particular, we get a simple (Δ+1) coloring algorithm with round complexity O(^* Δ) in the CONGESTED CLIQUE model of distributed computing. This matches the bound of Parter and Su [DISC'18], which improved on the O(Δ^* Δ)-round algorithm of Parter [ICALP'18]. Moreover, the same random partitioning leads to a (Δ+1) coloring algorithm with round complexity O(^* Δ+ √( n)) in the Massively Parallel Computation (MPC) model with strongly sublinear memory, which is the first sublogarithmic-time algorithm in this regime. This algorithm uses a memory of O(n^α) per machine and a total memory of O(m+ n^1+ε), for any desirable constants α,ε>0, where m is the size of the graph.
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