Some simple distributed algorithms for sparse networks

Summary.

We give simple, deterministic, distributed algorithms for computing maximal matchings, maximal independent sets and colourings. We show that edge colourings with at most $2\Delta-1$ colours, and maximal matchings can be computed within ${\cal O}(\log^* n + \Delta)$ deterministic rounds, where $\Delta$ is the maximum degree of the network. We also show how to find maximal independent sets and $(\Delta+1)$-vertex colourings within ${\cal O}(\log^* n + \Delta^2)$ deterministic rounds. All hidden constants are very small and the algorithms are very simple.