, Volume 14, Issue 2, pp 97-100

Some simple distributed algorithms for sparse networks

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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.